Consider a pendulum clock with a pendulum whose length is made of aluminum. If the average temperature around the clock is
ΔT=5 C° (=5 K) warmer in the summer than in the winter, then how much faster or slower does the clock run in the summer than in the winter?


For small oscillations, the pendulum can be approximated as a harmonic oscillator, giving the formula for the period t (usually uppercase, but here lowercase to avoid confusion with temperature):
,
where l is the length of the pendulum. More specifically, it is the length from the pivot to the pendulum’s center of mass; since most pendula are constructed with a weight on the end much more massive than the length of the arm, this is roughly just the length of the pendulum arm.

The period depends only on the length of the pendulum and the acceleration of gravity; the latter is a constant for this problem. Thus, taking the derivative
,
we see that for a small change of length Δl, we have change in period
,
and dividing by our period, we see our fractional change in period is
,
or half the fractional change of the length.

Now, solid materials undergo thermal expansion, with the fractional change in length proportional to the change in temperature:
,
where α is the coefficient of linear thermal expansion. α is positive, as materials expand when they get warmer. Substituting this into our finding for the fractional change in period

So in the summer, the pendulum will be slightly longer, meaning the period will be slightly longer, and the clock will run slower in the summer than in the winter. Note that the original length l of the pendulum doesn’t affect the result; the proportional expansion is the same.

According to WebElements, the coefficient of linear thermal expansion for aluminum is α=2.31×10^-5 (C°)^-1.
Thus, for ΔT=5 C°, we have
=5.78×10^-5
This is a difference of 1 second per about every 4.81 hours.

[A short discussion of some methods used in real pendulum clocks to prevent this effect can be found here.]

Last Friday Annie Mac, who is a legend, played this tune on her show. I’d heard the original on a blog about a week earlier, and was surprised by that. It has been a while since I’ve heard anything new by Pendulum and I am pleased with the results.

Stay Too Long (Pendulum Remix) – Plan B

Now here’s a band which I think are very similar in style to Pendulum, but not in set up, Sub Focus.

Dirtee Cash (Sub Focus Remix) – Dizzee Rascal γ song

And finally, I bought this album when it was released and heard this on the radio recently.

Could This Be Real – Sub Focus

Pendulum put some added oompph! behind Plan B’s – Stay Too Long. Not sure i’m liking the new stuff as much as some of the stuff on ‘Who needs actions, when you got words’ but this will still tear up any rave. What you reckon?

Been wanting to put these two song in particular up for a while now. The are not by any means new but what they lack in new-ness (yes i just made up a word) the make up for in the rhythm and vibe they create. Dreamscape by 009 Sound System especially is a song that you can put on repeat and listen to for hours and feel as if you are lost in space. With a simple 1-2 bass line the song relies on simplicity and subtle changes to create an un-real feel.

Dreamscape – 009 Soundsystem 10/10

Yet Pendulum’s track ‘Sounds of Life’ sets a faster pace though achieves a similar vibe to Dreamscape. Both songs are great to relax to while at home if you enjoy your electronic tracks and some time to give. Just like Dreamscape Sounds of Life is not a new song by any means though still holds a modern feel and taste to it which pendulum has achieved in so many of his tracks before him, and definitely due for a new album.

Sound of Life – Pendulum 10/10

So if your up for a relaxed chill session definitely check out these tracks as they will not disappoint.

Leave your comments above

Spread the Beatz!

___________________________________________________________________________________

This was Pendulum’s Scottish debut and it was our 4th birthday – Skynet was also guesting and there’s a recording of his mix around somewhere.

Click flyer to download MP3 of Pendulum’s set

Drawing a large circle on a blank piece of paper, she quartered it and wrote “Lori” in one section, “Jacoby” in another, and “known” and “unknown” in the third and fourth. If it turned out to be neither Lori, nor Jacoby, which was completely possible considering her checkered past, then she supposed she’d have to make a more thorough list of people she might recently have ticked off.

The next part was tricky. Making a loop at the end of a piece of twine, she attempted to slip it around the bullet.

“Hey, what’re you doing?” Robert asked from the doorway as she growled in frustration on her third failed attempt. “Is that a bullet? Are you doing magic?” he queried, crouching down on the other side of the table so he could watch. “Can I help?” he breathed softly, ready to be awed.

“Uh, yeah, actually,” Glory replied in disgust, her shoulders sagging in defeat. Having someone living with her was going to take some getting used to, especially if Robert was always this chatty. But he could actually be useful in this one instance. “Don’t–!” she shouted quickly as he reached for the slug with his bare hands. “Here, use these.”

She handed him the tweezers and he made a face as he concentrated. “I feel like I’m playing Operation,” he muttered ironically, his tongue sticking out of the corner of his mouth.

As he held the bullet up, she slipped the looped twine around it and pulled it tight. “Good, thank you,” she sighed in relief as she held the makeshift pendulum over her chart. “Now please be quiet so I can concentrate.”

Holding the pendulum at the center of her chart, she concentrated on the shooter. Who was he or she? Who’d sent them? She emptied her mind of all but the question of his or her identity.

“Is it supposed to do something?” Robert whispered, already disappointed after only a few seconds had passed.

“Robert?”

“Yeah?”

“If you can’t be quiet, I’ll have to ask you to leave.”

“Well sorry!” he sulked, slouching down so only his eyes sat above the edge of the table.

Starting over, Glory cleared her mind of all but her question. After a few seconds, the slug began to twist on the string and then swing in a widening circle. She slowly moved the pendulum over the different sections of the circle. There was no change as she moved the pendulum over the “unknown” quarter, which was a relief. She didn’t want to have to worry about other enemies when she already had so many.

And as easy as it would have been to pin yet another assassination attempt on Lori, her instincts and the pendulum said otherwise. Just because she hadn’t heard from Lori in several months didn’t mean her sister still wouldn’t like her dead. Hating Glory was practically the only way Lori could show her any affection. The best Glory could hope for was that Lori had called up something particularly nasty with her book and had been torn limb from limb for her troubles, but Glory tended to doubt she’d get off so lucky. Wherever Lori was, she was biding her time while Glory apprehensively waited for her next move .

However the pendulum finally changed its pattern over Jacoby’s quarter, its gyrations becoming smaller and smaller until the slug merely spun clockwise over his name. Glory breathed a sigh of relief, her intuition confirmed. There was no need to continue on to the last quarter of the chart.

“Is that all it’s going to do?” Robert asked in disappointment. His eyes peered up from the edge of the table like a small child who’s been told there is no Santa Clause.

“Most magic is not flashy,” Glory replied gently. “It’s as mundane as turning a dial on a radio.”

Robert harrumphed sourly as she set the pendulum down and used the tweezers and a pair of scissors to remove the twine loop. Unrolling a map of Sybar City and the surrounding areas, she lay it out on the table and then set a clear plastic tray over top of it. Since she’d had to track Mike and Gozala, she’d improved upon the design of her spell, though she had not had any means of testing it out until now.

“Will you go downstairs and get a pitcher of water for me, please?”

Robert shrugged and left since magic was apparently not as exciting as he’d hoped. Taking a piece of cork, she gouged out a space in the middle until it was large enough for her to wedge the bullet inside. Taking a black sharpie, she drew the compass rune with the bullet at its center.

“Thank you,” Glory said as Robert returned with the water. She poured it into the tray slowly until it was full enough that the cork would not drag along the bottom and skew the results, then waited for the small waves to diminish. Gently setting the cork over the map roughly around where her house was, they waited to see what would happen.

The corked bobbed for a moment or two in the still water before slowly turning and drifting in a southwesterly direction. “It’s a trick, right?” Robert asked. “There’s a slope in the floor or something?”

“No, look, it’s following the streets. He’s in the Lincoln tunnel. Jacoby is leaving Sybar City.”

“Jacoby? That’s the guy that was shooting at us?” Robert asked uncertainly, peering at the cork as if it might jump out of the water and bite him.

“Yeah… I wonder if he’s going back to Miskatonic…” she mused.

“So that solves our problem, if he’s leaving.”

“Not really. It doesn’t mean he won’t be back. He was probably just scared off by the police. Skittish is a good word for him. Paranoid schizophrenic is better. Now he’ll be thinking the police are some kind of undercover alien hybrid ninjas planning to turn his brain into guacamole dip to poison the president or some nonsense,” she adlibbed. “No, whether or not he’s going to MU, that’s where I have to go too, if I’m going to get them to put a leash on him.”

to Chapter 7, page 6

Kevin R D Shepherd Defends Psychic Medium Conny Larsson

Kevin R.D. Shepherd is a staunch Anti-New Age, Anti-Psychic, Anti-Superstition, Anti-Guru activist who believes that self-professed psychic channelers, spirit mediums, gurus and/or New Age practitioners are misled, brainwashed, fraudulent and deficient. Nevertheless, when it comes to agendas that Kevin R.D. Shepherd supports, he will cite an entire slew of New Age practitioners, self-professed psychics and/or Guru promoters to support his agendas.

This article will document Kevin R.D. Shepherd’s shameless attempt to defend and cover-up for Psychic Medium Conny Larsson. Although Kevin R.D. Shepherd gave a few tongue-in-cheek criticisms about Conny Larsson’s self-professed psychic abilities, Shepherd actually defended Larsson and claimed that since Larsson gave a talk at FECRIS, Larsson is thereby a credible and reliable reference against Sathya Sai Baba.

What Kevin Shepherd forgot to mention, however, is that Psychotherapist Conny Larsson purposely suppressed his psychic medium claims from FECRIS because FECRIS would never allow a self-professed Psychic Medium to talk at their conferences. FECRIS is extremely critical of alleged “psychic” psychotherapists (like Conny Larsson) who use their training and skills to manipulate, mislead and brainwash others. See: FECRIS: Psychotherapeutic Deviation: The Use Of Psychotherapy In The Case Of Cult Influence. Obviously, Conny Larsson’s training as a psychotherapist has enabled him to con many people, including Kevin R.D. Shepherd.

Kevin R.D. Shepherd cited the following email quote in defense of Conny Larsson:

Conny Larsson: “I could keep on interpreting the texts for hours, and in that sense people sometimes make their own opinion that I’m channelling, but in fact it is only me speaking out what is in my own intuitional knowledge.”
(Kevin R.D. Shepherd: This quote appeared in an email to myself from ex-devotee Robert Priddy dated December 2008.)

It has long been Moreno’s personal opinion that Conny Larsson is a bold-faced and pathological liar. Conny Larsson’s explicit and documented denial of being a Trance Channel & Psychic Medium is more proof of his repeated attempts to mislead through prevarication and deceit.

This article will provide verifiable information that proves that Conny Larsson solicited himself as a Trance Channel & Psychic Medium, which was even documented in a national Swedish newspaper!

It is an irrefutable fact that Conny Larsson was solicited twice on his official website at vedicmasterclass.org as being a psychic “trance channel” for the immortal sage, rishi & chiranjeevin Vyasa. After Joe Moreno (a Pro-Sai Activist) exposed Conny Larsson’s psychic claims on SaiSathyaSai.com, Conny Larsson rushed to do damage control by changing his profile and by changing the written testimony of Judith Bourque (essentially falsifying her first-hand testimony as originally published on the vedicmasterclass.org domain since mid to late 2006 – February 2009). See the ‘before’ and ‘after’ screencaps:

——————————————————————————————————————

BEFORE (relevant text is highlighted) →

[CLICK HERE For ScreenCap Reference]
“Conny Larsson, Sweden/Cyprus – Founder of Vedic Mantra Meditation school in Europe. – Author and psychotherapist. Transchannel for ‘Vyaasa, the first Rishi’ During the Master Class Conny guided participants in the knowledge of the Vedic Mantra systems with regard to the 7 chakras of the nervous system. As Vyaasa he channeled 4000 year old knowledge for the group as a whole and at times for us as individuals. He also took us through processes to expand our levels of consciousness. conny@email.com”

AFTER (note that the relevant text was removed) →

[CLICK HERE For ScreenCap Reference]
“Conny Larsson, Sweden/Cyprus Founder of Vedic Mantra Meditation school in Europe. – Author and psychotherapist. During the Master Class Conny guided participants in the knowledge of the Vedic Mantra systems with regard to the 7 chakras of the nervous system. He took us through processes to expand our levels of consciousness. conny@email.com”

——————————————————————————————————————

BEFORE (relevant text is highlighted) →

[CLICK HERE For ScreenCap Reference]
“Meeting for the Masters’ Class in Cypress was truly inspiring and an excellent example of how to spend a meaningful holiday. We were a group of teachers from several different countries, each bringing to the class an area of acquired knowledge and experience…Conny spoke about the seven different states of consciousness and also did some trance channeling of Vyaasa, ‘the first Rishi, or Seer’. That, for sure was an extra bonus at the seminar…I really look forward to the next event of this kind that Conny organises! Judith Bourque, Holistic Therapist and Independent Filmmaker”

AFTER (note that the relevant text was changed) →

[CLICK HERE For ScreenCap Reference]
“Meeting for the Masters’ Class in Cypress was truly inspiring and an excellent example of how to spend a meaningful holiday. We were a group of teachers from several different countries, each bringing to the class an area of acquired knowledge and experience…Conny spoke about the seven different states of consciousness and also did some interpretations from Vyaasa, ‘the first Rishi, or Seer’. That, for sure was an extra bonus at the seminar…I really look forward to the next event of this kind that Conny organises! Judith Bourque, Holistic Therapist and Independent Filmmaker”

——————————————————————————————————————

[CLICK HERE For ScreenCap Reference]
Click Here to view the archive.org results for Judith Bourque’s original testimony as published on the vedicmasterclass.org domain (archive.org results are still available as of September 8th 2009). Archive.org has four results (from July 4th 2007 to February 13th 2008) for the webpage that contained Judith Bourque’s original testimony. It is important to note that archive.org only indexes webpages after a period of 6 – 12 months. Therefore, Judith Bourque’s testimony was published on the vedicmasterclass.org domain sometime in mid to late 2006 and remained there until February 2009 when it was altered. The screencap shows the archive.org results for the webpage containing Judith Bourque’s first-hand testimony about Conny Larsson’s “trance channeling” of Vyasa.

——————————————————————————————————————

[CLICK HERE For ScreenCap Reference]
Further strengthening the fact that Conny Larsson posed as a psychic healer are pictures of him giving “trance healings” that were originally released on the joga harmonia website (which were subsequently deleted at Conny Larsson’s request). If Conny gets this intimate and physical with women while in public, one can only wonder how intimate and physical he gets with women during his “private” psychic consultations. As they say, “seeing is believing” & “a picture is worth a thousand words”.

——————————————————————————————————————

[CLICK HERE For ScreenCap Reference]
The screencap above specifically states the following about Conny Larsson:

1. Conny Larsson will give private consultations for psychic trance healings.
2. Conny Larsson will give a demonstration of his trance healing to the audience.
3. Conny Larsson is a trance healer.
4. Conny Larsson diagnoses the aura.
5. Conny Larsson promotes and endorses the power of Vedic mantras.
6. Conny Larsson will perform a séance.
7. Conny Larsson will sell and autograph his new book that speaks against Sathya Sai Baba.
8. Conny Larsson charged members 80 kroner (US $12) and non-members 120 kroner (US $17) for a talk on trance healing and aura diagnosis.

——————————————————————————————————————

[CLICK HERE For ScreenCap Reference]
The screencap above specifically states the following about Conny Larsson (Original Reference):

1. Conny Larsson will solicit his book “Behind The Clown’s Mask”.
2. Conny Larsson will channel his spirit guide to help diagnose people’s medical problems
3. Conny Larsson will talk about trance healing and will demonstrate his trance healings on various members of the audience.
4. Conny Larsson offers private trance healing consultations
5. Conny Larsson is a life philosopher.
6. Conny Larsson is a psychotherapist.
7. Conny Larsson will teach the healing benefits of meditation and how it can increase life-force and well-being.
8. Conny Larsson is on the Swedish board for Neal Donald Walsh’s “Humanity Team”.
9. Conny Larsson teaches the TM method of meditation.
10. Conny Larsson will channel a banshee (ghost / spirit) that transfers healing energies.
11. In private consultations, Conny Larsson will perform aura cleansing and trance healing.
12. Conny Larsson will demonstrate trance channeling in front of the audience and on a few volunteers.
13. In private consultations and with the guidance of his spirit guides, Conny Larsson will diagnose the real causes of problems in a person’s life.
14. Conny Larsson will use a crystal pendulum to analyze the aura and chakras.
15. Apparently fearing a public exposure from critics, not everyone can book a private trance healing session with Conny Larsson. Private trance healing consultations are made exclusively at Conny Larsson’s sole discretion and he filters and chooses who he will perform his healings on in private.
16. Conny Larsson charged members 60 kroner (US $9) and non-members 100 kroner (US $14) for a trance healing demonstration. Charges 500 (US $72) kroner for a meditation workshop and charges 600 (US $87) kroner for a private psychic medium consultation.

——————————————————————————————————————

[CLICK HERE For ScreenCap Reference]
The screencap above was taken from a national Swedish newspaper (Norrland Social Democrat aka Norrlandska Socialdemokraten) entitled “Medium Draws Full House”, which specifically stated the following about Conny Larsson (Original Reference):

1. Conny Larsson personally claimed he is a psychic trance medium.
2. Conny Larsson gives spirit seances.
3. Conny Larsson personally talked about “protective spirits” on the Astral Realms and claimed he was protected by them.
4. Conny Larsson went into a trance and channeled the dead dog of a woman in the audience, claiming the dog still barks and stands at her house.
5. Conny Larsson channeled an astral message for Gun Isaxon (a Communist party leader in Sweden) from her deceased father, warning of health problems and not to take any office.
6. Conny Larsson gave a demonstration of aura cleansing on an elderly woman in the audience by using a crystal pendulum.
7. Conny Larsson claimed that body piercings affect acupuncture and meridian points and are harmful on the “cellular level”.
8. Conny Larsson claimed he has 10,000 devotees / students in Sweden and around the world.
9. Conny Larsson attracted “large numbers” of women (judging from the picture in the article, 100% were women).
10. Many people remember Conny Larsson as the clown “Beppo”.
11. Conny Larsson claimed that “Words have power. Together we can bring peace and love.”
12. Conny Larsson warned his audience about “charlatans” who charge money for their services. Nevertheless, participants paid 100 kronor (US $14) as an entry fee (the article claimed over a hundred women were present, meaning that Conny Larsson grossed US $1,400+ just on admission fees). The weekend meditation fee is 400 kronor (US $58) and individual psychic healing sessions are 500 kronor (US $72). The article also claimed that over 400 people were learning meditation from Conny Larsson (meaning that he grossed US $23,200+ on his meditation classes alone).
13. Conny Larsson also sold books and CDs about himself at the lecture (notice the money-making trend?).

——————————————————————————————————————

[CLICK HERE For ScreenCap Reference]
The screencap above proves that Conny Larsson is devoted to the Indian Guru Shankaracharya Swami Brahmananda Saraswati (the guru of Maharishi Mahesh Yogi) and posed in front of his pictures between 1998 (while still a Sai Devotee) to 2005 (five years after leaving Sai Baba and several years after accusing Maharishi of having sex with women).

——————————————————————————————————————

[CLICK HERE For ScreenCap Reference]
The screencap above specifically states the following about Conny Larsson (Original Reference):

1. Conny Larsson conducts trance healing “séances”.
2. Conny Larsson can contact the dead.
3. Conny Larsson teaches others how to use crystal pendulums.
4. Conny Larsson teaches others how to “diagnose” blockages in auras.
5. Conny Larsson will demonstrate his trance healings on “selected individuals” in the audience and at his discretion.
6. Conny Larsson claims we all possess a “cosmic reality”.
7. Conny Larsson teaches a nine-step meditation program in which students must pass lower steps in order to advance to higher steps using the TM (Transcendental Meditation) technique.
8. Conny Larsson is on the Swedish board for Neal Donald Walsh’s “Humanity Team”.
9. Conny Larsson conducts private trance healing sessions in which Spirit Guides helps him diagnose the real problems in a person’s life.
10. Conny Larsson analyzes chakras for blockages.
11. Conny Larsson is an internationally renowned psychic trance medium.
12. Conny Larsson claims crystal pendulums help amplify the real causes to problems in a person’s life.
13. Conny Larsson charged 500 kroner (US $72) for the meditation, aura cleansing and crystal pendulum workshop.
14. Conny Larsson charged 600 kroner (US $87) for a private trance healing in which he channels spirit guides.
15. Conny Larsson charged members 60 kroner (US $9) and non-members 100 kroner (US $14) for a public demonstration of a trance medium séance.

——————————————————————————————————————

[CLICK HERE For ScreenCap Reference]
The screencap above specifically states the following about Conny Larsson (Original Reference):

1. Conny Larsson is teaching a meditation class on February 6th 2009
2. Conny Larsson is a life philosopher.
3. Conny Larsson is a psychotherapist.
4. Conny Larsson spent a year in silence meditating in a cave.
5. Conny Larsson teaches meditation from the beginning phase to the most advanced techniques.
6. Conny Larsson is on the Swedish board for Neal Donald Walsh’s “Humanity Team”.
7. Conny Larsson is also known as “God’s Little Clown” (from his devotee phase).
8. Conny Larsson will teach the healing benefits of meditation and how it can increase life-force and well-being.
9. Conny Larsson teaches a nine-step meditation program in which students must pass lower steps in order to advance to higher steps using the TM (Transcendental Meditation) technique.
10. Conny Larsson charged 600 kroner (US $87) for the meditation classes.

——————————————————————————————————————

[CLICK HERE For ScreenCap Reference]
The screencap above specifically states the following about Conny Larsson (Original References: 01 – 02 – 03):

1. Conny Larsson is one of two International Coordinators for the Heart And Soul Exposition (the other International Coordinator is Judith Bourque).
2. The “Heart And Soul Exposition” is a website for: “Many, Local and International workshop leaders and Inspirational speakers plus: Acupressure, Angel therapy, Aura photography, Breath Work, Clairvoyance, Crystal Healing, Crystal Bowl Therapy, Diana Cooper School of Angel Healing, Energy Biofeedback Therapy, Environmental issues, Esoteric teachings, Feldenkreis therapy, Indian Head Massage Practitioner, Life Counsellor, Meditation, Oriental Dance Teachers, Pranic Healing, Psychic Medium, Reflexology, Reiki Practitioners/Masters, Shamanism, Tai Chi, Vedic Meditation Master, Yoga Teachers.”
3. Conny Larsson was a former actor educated at the Royal Sate School of acting in Malmo, Sweden.
4. Conny Larsson became a meditation teacher under the “auspicious guidance of Maharshi Mahesh Yogi” (notice how the wording is positive although Conny Larsson is Anti-Mahesh-Yogi).
5. Conny Larsson teaches his own meditation class free of charge (although the February 2009 program stated he charged 600 kroner for his meditation classes).
6. Conny Larsson is a Vedic Mantra meditation teacher.
7. Conny Larsson founded the Vedic Mantra school of meditation.
8. Conny Larsson founded The Master Class in North Cyprus.
9. For many years Conny Larsson acted as Chairman for the Karnan Institute for criminal and drug abusers in Sweden.
10. Conny Larsson will lecture on the “Sixth Sense”.
11. Eileen August (an aura photographer and reader) will be present.

——————————————————————————————————————

Kevin R.D. Shepherd & Psychic Medium Conny Larsson – In Conclusion

Despite Kevin R.D. Shepherd’s desperate and shameless justifications and cover-ups for Psychic Medium Conny Larsson, the numerous references provided in this article irrefutably prove that Conny Larsson widely solicited himself as a psychic, trance medium, spirit guide channeler, Vyasa channeler, aura reader, aura cleanser, crystal pendulum reader, chakra reader, chakra aligner, Vedic Mantra acharya, séance conductor, meditation master and spiritual healer. Conny Larsson also promotes himself in direct association with other New Age practitioners, psychics, mediums, channelers and healers on his vedicmasterclass.org and heartandsoulexpo.com domains.

When Conny Larsson purposely and knowingly lied about his well-documented Trance Channel & Psychic Medium claims, how can anyone believe anything he has to say, especially in relation to Sathya Sai Baba?

Apparently, Kevin R.D. Shepherd thinks that Conny Larsson (a person who hears voices in his head and who claims to see and converse with dead people) is a credible voice against Sathya Sai Baba! Even more disturbing is the fact that Conny Larsson self-disclosed his psychiatric diagnosis (made by a psychiatrist) of him being “psychoinfantile”, which is also known as Histrionic Personality Disorder.

If you hear voices in your head, channel Vyasa, perform trance healings, converse with dead people, channel the spirits of dead animals, hold negative views about Sathya Sai Baba and have been officially diagnosed with a psychiatric personality disorder, give Kevin R.D. Shepherd a call because you might be his next credible reference against Sai Baba.

Så tror man att man ska vakna och vara på bra humör but no, man vaknar och vill fortfarande skjuta folk i huvudet. Problemet är att jag inte har tid att spela Fallout, vilket annars brukar vara en superbra terapimetod. Inte helt säker på hur allmänfarligt det skulle kunna vara dock, hamnar ofta i att gå och dagdrömma om punktsättarn (m82an), men så är det väl med alla spel. Därför undviker jag GTA.

Planen idag:

- Lyssna bort aggressioner med Pendulum
- Käka frukost
- Packa färdigt en kartong
- Släpa fram saker som ska till Robins farsa & mina bröder
- Montera isär bokhyllorna
- Diska och packa ner köksgrejor
- Henna håret om det hinns

Förutom det så får jag besök här i bloggen senare idag igen! Gissa vem!

Dagens låt – Pendulum – Tarantula.

Ps. Elliott var är du?

• Я не знаю, австралийцы они или англичане
• Я не знаю, инструментал это или электроника
• Я не знаю, драм это или что-то другое

Но я знаю то, что это нереальный драйв!

wiki

I’ve been practicing an interesting technique during my lunchtime dowsing sessions that I’ve not seen mentioned anywhere else.  I talked about it previously in this post.

I will occasionally go on what I would call “Dowsing walks.”  With a map of the area I’m thinking of walking I will begin by asking the following questions.

• Should I go on a dowsing walk today?
• Is there a special pot somewhere in the park I should walk to today?
• May I dowse for that spot?
• Can I dowse for the spot?

Finally, if these are all positive answers, I dowse for the spot using a quadrant search. (And, yes, I’ve gotten negative answers before which resulted in me still going to the park but not with an intent to find a dowsed spot.)

This is a bit different from other dowsing techniques I’ve read about since there’s not really any “target” I am attempting to find.  There is but, really, there isn’t.  The target is the “spot.”  However, whatever might be at the spot is a complete mystery to me.   In effect, I’m letting the Universe take over and point the way for me.  I started it as a simple experiment but the results have been pretty startling.

Once at the site, I take the map with me and begin walking towards the pinpoint.  As I walk I really focus on opening up to my environment.  I do this for relaxation and as a fun excuse to have a target to walk towards.   I allow that energy, that sense of adventure and mystery carry with me.  I keep myself open and I relax.  As I get close, I will let the pendulum direct me in the direction the spot is located.  Once I feel I am within 20 feet or so I will move off at an angle and get a second line in which to triangulate the location.

Here are two stories as examples  of what I’ve encountered going on dowsing walks.

The first began as I walked through the small woods to the spot I’d dowsed and found a moderate clearing.  Once there, I triangulated two other times which gave me three lines total.   At their intersection would be the point I was to find.  I didn’t  see anything at first but as I moved closer, and much to my surprise, the intersection happened to be where a large garter snake was sunning itself on a fallen log.  I’d dowsed a snake.  I was, again, stunned.

I’d be willing to shake this off as some sort of lucky hit but to add to the mix let me mention it was late October.  We had been having a warm snap but it was still jacket weather.  Most snakes, by this point in the year, are well balled up and beginning their hibernation.

And the final bit of weirdness?  Let me reference you back to a previous post where I had drawn some cards concerning my new dowsing hobby.  Remember what cards came up?  Click here to go to that post.

Yeah.

The second story occurred in the same park.  I was led to an area near the same clearing as before.  This time the pendulum directed me to a normal, medium aged tree and nothing else.  It just kept swinging towards the tree no matter where I stood.  I was asking all sorts of questions concerning why I had been led there and getting nothing but negatives.  The only answer I received a positive to was the question, “Is this tree the target?”

So, with time to spare, I sat down on a nearby fallen tree trunk a few feet away.  I was thinking about what questions to ask next when a Pileated Woodpecker buzzed by and began working some nearby trees and vines.

I love these birds a great deal and I always enjoy watching people’s eyes when they see one for the first time in the woods.  It was treat to sit and watch him hang upside down, eating berries from the thick wood vines we have in the area.  The shock came when he suddenly left his perch and landed on the trunk of the tree I had just dowsed.  Suddenly, in a split second, there was my answer!  I was mere feet away from a huge bird I’d loved all my life since he had landed on the lower section of the trunk.  He was there for around five minutes looking for insects, moving up the tree, and then he flew off to another part of the woods.

Dowsing walks for me have helped me get back in touch with the magical.  There was no way I could have known a snake was sunning itself on that log from a few miles away and how could I have known, in advance, that the Pileated would have landed on the exact tree I dowsed?  Something magical happens when you open yourself up to Mother Nature, to the Universe.  In a way, it’s a form of a Medicine Walk and every time I have done a Dowsing walk with that mindset I have not been dissapointed.

A lot of the sites I’ve read on dowsing say you have to have a specific target in mind before you begin.  However, with these and other experiences I am having more and more of, I’m beginning to wonder if by having a specific target in mind you’re not blocking other information from the Universe/God/Higher Self?  Is it possible that it works both ways?

I’ll be continuing to post results here as I experience them.  If you’re curious maybe you can give it a try yourself?  Let me know how it goes if you do.

The blade swinging back and forth struck fear into my soul, and sent chills down to my very core. The metal horror hissed as it sliced through the air sending a rush of wind to my torso. The constant gushes of air caused a tormenting pain in my chest.
Hundreds of rats were shuttling across the cold floor of my cell. They were probably awaiting my death so they could feast on the bloody mess left by the pendulum. I saw them swarming a small area next to my hands. A warm liquid dripped across my palm and before too long I had realized they were nibbling on my fingers. I could not feel the pain in my hand, so I came to the hasty conclusion that my captors had drugged me while I was unconscious.
I struggled to get lose from the bonds holding me so tightly on the wooden structure. The blood on my palms got on to the ropes and the rats began to gnaw on them. Before too long the ropes were weak enough for me to break free. I gave out an extreme sigh of relief and began to push the rats away from me.
I rolled onto the ground and now I could clearly see that the structure I had been lying on was a very poorly made wooden bed. The entire unit was held together by rusty nails. If I had been even a little more careless I could have been stabbed by one and gotten infected.
Soon after I had scared all the rats away I returned my attention to the pendulum, which was now only hanging about two meters above the wooden bed. I saw that there was a large silver wire holding the pendulum from the ceiling. The wire was coming from a square shaped hole that looked like it was big enough for me to fit myself though. I needed to escape from the monstrous dungeon, for if I did not try who knows what fate would have come upon me.
I backed away from the blade and went towards the corner of the room waiting for the blade to hit the ground and lose its momentum. I was beginning to get sleepy watching the blade swing back and forth and back and forth. A thundering crash made me jump up back on to my feet. Chunks of wood flew across the room and hit the cell wall. The entire bed was sliced in half.
A few seconds later the blade hit the ground and sparks flew everywhere. I could hear the rats scurry into little holes in the wall. I paused for a minute or so and moved towards the pendulum and examined it. There was a large reddish brown stain, almost like the mud around a car’s tire after a rainy day, at the bottom by the blade. The top of the pendulum was silver with gold symbols or markings etched into it.
I began to climb the wire that was holding the pendulum up while thinking of what I would come upon next. My fingers spewed out blood from the holes in my skin that the rats had made, but soon it was soon alright because my fingers went numb.
When I went into the passageway I saw many chains like the one I was climbing. I assumed that there were many cells just like the one I had a moment ago been in. The smell in the tunnel was that of dead rats. I continued to climb ignoring all the insects.
As I reached the top I saw an opening. A bright light shone on to my face and as my eyes adjusted I saw a tall figure in golden armur and a red cape. His helmet had a red Mohawk. Before I had any time to react the man yelled out “THIS IS SPARTA” and kicked me in the face. I let go of the chain holding me up and fell back down into the pit.

[Click here for a PDF of this post with nicer formatting]

Motivation

Attempting the multiple spherical pendulum problem with a bivector parameterized Lagrangian has just been attempted ([1]), but did not turn out to be an effective approach. Here a variation is used, employing regular plain old scalar spherical angle parameterized Kinetic energy, but still employing Geometric Algebra to express the Hermitian quadratic form associated with this energy term.

The same set of simplifying assumptions will be made. These are point masses, zero friction at the pivots and rigid nonspringy massless connecting rods between the masses.

The Lagrangian.

A two particle spherical pendulum is depicted in figure (\ref{fig:sPolarMultiPendulum:pendulumDouble})

\begin{figure}[htp]
\centering
\includegraphics[totalheight=0.4\textheight]{pendulumDouble}
\caption{Double spherical pendulum.}
\end{figure}

The position vector for each particle can be expressed relative to the mass it is connected to (or the origin for the first particle), as in

To express the Kinetic energy for any of the masses , we need the derivative of the incremental difference in position

Introducing a Hermitian conjugation , reversing and transposing the matrix, and writing

We can now write the relative velocity differential as

Observe that the inner product is Hermitian under this definition since . \footnote{Realized later, and being too lazy to adjust everything in these notes, the use of reversion here is not neccessary. Since the generalized coordinates are scalars we could use transposition instead of Hermitian conjugation. All the matrix elements are vectors so reversal doesn’t change anything.}

The total (squared) velocity of the th particle is then

(where the zero matrix in is a by one zero). Summing over all masses and adding in the potential energy we have for the Lagrangian of the system

There’s a few layers of equations involved and we still have an unholy mess of matrix and geometric algebra in the kernel of the kinetic energy quadratic form, but at least this time all the generalized coordinates of the system are scalars.

Some tidy up.

Before continuing with evaluation of the Euler-Lagrange equations it is helpful to make a couple of observations about the structure of the matrix products that make up our velocity quadratic forms

Specifically, consider the products that make up the elements of the matrices . Without knowing anything about the grades that make up the elements of , since it is Hermitian (by this definition of Hermitian) there can be no elements of grade order two or three in the final matrix. This is because reversion of such grades inverts the sign, and the matrix elements in all equal their reverse. Additionally, the elements of the multivector column matrices are vectors, so in the product we can only have scalar and bivector (grade two) elements. The resulting one by one scalar matrix is a sum over all the mixed angular velocities , , and , so once this summation is complete any bivector grades of must cancel out. This is consistent with the expectation that we have a one by one scalar matrix result out of this in the end (i.e. a number). The end result is a freedom to exploit the convienence of explicitly using a scalar selection operator that filters out any vector, bivector, and trivector grades in the products . We will get the same result if we write

Pulling in the summation over we have

It appears justifiable to lable the factors of the angular velocity matrices as moments of inertia in a generalized sense. Using this block matrix form, and scalar selection, we can now write the Lagrangian in a slightly tidier form

After some expansion, writing , and so forth, one can find that the scalar parts of the block matrixes contained in are

The diagonal blocks are particularily simple and have no dependence

Observe also that , so the scalar matrix

is a real symmetric matrix. We have the option of using this explicit scalar expansion if desired for further computations associated with this problem. That completely eliminates the Geometric algebra from the problem, and is probably a logical way to formulate things for numerical work since one can then exploit any pre existing matrix algebra system without having to create one that understands non-commuting variables and vector products.

Evaluating the Euler-Lagrange equations.

For the acceleration terms of the Euler-Lagrange equations our computation reduces nicely to a function of only

and

The last groupings above made use of , and in particular . We can now form a column matrix putting all the angular velocity gradient in a tidy block matrix representation

A small aside on Hamiltonian form. This velocity gradient is also the conjugate momentum of the Hamiltonian, so if we wish to express the Hamiltonian in terms of conjugate momenta, we require invertability of at the point in time that we evaluate things. Writing

and noting that , we get for the kinetic energy portion of the Hamiltonian

Now, the invertability of cannot be taken for granted. Even in the single particle case we do not have invertability. For the single particle case we have

so at this quadratic form is singlular, and the planar angular momentum becomes a constant of motion.

Returning to the evaluation of the Euler-Lagrange equations, the problem is now reduced to calculating the right hand side of the following system

With back substituition of 22, and 24 we have a complete non-multivector expansion of the left hand side. For the right hand side taking the and derivatives respectively we get

So to procede we must consider the partials. A bit of thought shows that the matrices of partials above are mostly zeros. Illustrating by example, consider , which in block matrix form is

Observe that the diagonal term has a scalar plus its reverse, so we can drop the one half factor and one of the summands for a total contribution to of just

Now consider one of the pairs of off diagonal terms. Adding these we contributions to of

This has exactly the same form as the diagonal term, so summing over all terms we get for the position gradient components of the Euler-Lagrange equation just

The only thing that remains to do is evaluate the matrixes.

It should be possible but it is tedious to calculate the block matrix derivative terms from the partials using

However multiplying this out and reducing is a bit tedious and would be a better job for a symbolic algebra package. With 22 available to use, one gets easily

The right hand side of the Euler-Lagrange equations now becomes

Can the matrices be factored out, perhaps allowing for expression as a function of ? How to do that if it is possible is not obvious. The driving reason to do so would be to put things into a tidy form where things are a function of the system angular velocity vector , but this is not possible anyways since the gradient is non-linear.

Hamiltonian form and linearization.

Having calculated the Hamiltonian equations for the multiple mass planar pendulum in [2], doing so for the spherical pendulum can now be done by inspection. With the introduction of a phase space vector for the system using the conjugate momenta (for angles where these conjugate momenta are non-singlular)

we can write the Hamiltonian equations

The position gradient is given explicitly in 39, and that can be substituted here. That gradient is expressed in terms of and not the conjugate momenta, but the mapping required to express the whole system in terms of the conjugate momenta is simple enough

It is apparent that for any sort of numerical treatment use of a angular momentum and angular position phase space vector is not prudent. If the aim is nothing more than working with a first order system instead of second order, then we are probably better off with an angular velocity plus angular position phase space system.

This eliminates the requirement for inverting the sometimes singular matrix , but one is still left with something that is perhaps tricky to work with since we have the possibility of zeros on the left hand side. The resulting equation is of the form

where is a possibly singular matrix, and is a non-linear function of the components of , and . This is concievably linearizable in the neighbourhood of a particular phase space point . If that is done, resulting in an equation of the form

where and is an appropriate matrix of partials (the specifics of which don’t really have to be spelled out here). Because of the possible singularities of the exponentiation techniques applied to the linearized planar pendulum may not be possible with such a linearization. Study of this less well formed system of LDEs probably has interesting aspects, but is also likely best tackled independently of the specifics of the spherical pendulum problem.

Thoughts about the Hamiltonian singularity.

The fact that the Hamiltonian goes singular on the horizontal in this spherical polar representation is actually what I think is the most interesting bit in the problem (the rest being a lot mechanical details). On the horizontal or radians/sec makes no difference to the dynamics. All you can say is that the horizontal plane angular momentum is a constant of the system. It seems very much like the increasing uncertaintly that you get in the corresponding radial QM equation. Once you start pinning down the angle, you loose the ability to say much about .

It is also kind of curious how the energy of the system is never ill defined but a choice of a particular orientation to use as a reference for observations of the momenta introduces the singularity as the system approaches the horizontal in that reference frame.

Perhaps there are some deeper connections relating these classical and QM similarity. Would learning about symplectic flows and phase space volume invariance shed some light on this?

A summary.

A fair amount of notation was introduced along the way in the process of formulating the spherical pendulum equations. It is worthwhile to do a final consise summary of notation and results before moving on for future reference.

The positions of the masses are given by

With the introduction of a column vector of vectors (where we multiply matrices using the Geometric vector product),

and a matrix of velocity components (with matrix multiplication of the vector elements using the Geometric vector product), we can form the Lagrangian

An explicit scalar matrix evaluation of the (symmetric) block matrix components of was evaluated and found to be

These can be used if explicit evaluation of the Kinetic energy is desired, avoiding redundant summation over the pairs of skew entries in the quadratic form matrix

We utilize angular position and velocity gradients

and use these to form the Euler-Lagrange equations for the system in column vector form

For the canonical momenta we found the simple result

For the position gradient portion of the Euler-Lagrange equations 63 we found in block matrix form

A set of Hamiltonian equations for the system could also be formed. However, this requires that one somehow restrict attention to the subset of phase space where the canonical momenta matrix is non-singular, something not generally possible.

References

[1] Peeter Joot. {Spherical polar pendulum for one and multiple masses, and multivector Euler-Lagrange formulation.} [online]. http://sites.google.com/site/peeterjoot/math2009/sPolarMultiPendulum.pdf.

[2] Peeter Joot. Hamiltonian notes. [online]. http://sites.google.com/site/peeterjoot/math2009/hamiltonian.pdf.

It’s after 1am and I want to go to bed but my mum is emailing me continuously with some corrupted word file that her friend can’t open and that I must fix. The passage of time doesn’t mean very much to her, she stays up all hours and sleeps when she wants – the joys of not working, or rather not wanting to and not needing to. She’s at a stage where she’s stopped thinking about what she has left to do in life and more about how much she has already done. She’s not that old, but she thinks she is, I guess that is the decider in such things.

My mood has been very unstable today, swaying between euphoria and numbness. I think it’s becoming worse as time passes. Like a pendulum picking up speed. Each sway is slightly more extreme than the last. I’ve never considered, until today, that I could be getting worse. But I could be. That fact has had me thinking very seriously about getting outside help.

So I’m thinking about seeing a psychologist. I don’t really have the money to go privately but I can’t wait 9 months for an NHS appointment to come up – I don’t want to let myself sink even deeper into whatever it is we sink. Private help must win out for now, will do some digging to see what I can find in my area.

I won’t let money be the reason that I didn’t fix myself. That would be my biggest regret. I’ve already started having some of those. I’ve never been a regretful person but this last year that has changed. I hate having regrets. Some part of me vehemently believes there should be nothing I do in life that leaves me shamed. A tall order perhaps but until now it’s been as such.

And now… now either I am lapsing or my attitude towards my actions in life has changed. It’s not unimaginable that self-perception is slightly skewed in the brain of a depressed person – I’ve done no more bad things now than a year ago, not really. But… I regret so much and criticize so much of myself, that there must be something to it right? I really really hope not. I hope I’ve just gone a bit crazy. I hope that all the hate and the fear is just hate and fear and has nothing to do with the real me, the me that I can’t remember anymore.

Mum has gone – she realised I have a life to lead when the sun comes up. She is a topic for another day…

RAMfest IV, will take place on the weekend of 26- 28 February 2010, at Nekkies Holiday Resort, Worcester.

It’s time once again to journey headlong into the crazy-wonderful world of RAMfest.  After what was certainly one of the most memorable events in Cape Town in 2009, 2010 is set to be the Year of the Spectacular. Audiomatik Events has secured a phenomenal line up, including Pendulum from Australia, Johnny Foreigner from the UK and top SA acts including Fokofpolisiekar, Taxi Violence, Jack Parow and The Dirty Skirts. RAMfest is also proud to present performances by much loved bands that have not performed in SA for a while: Boo!; Lark and The Narrow.

There has been a bit of a spruce up and spring clean and the furniture has been moved around a bit at Nekkies Holiday Resort, creating a smashing new site layout. When you get here, it should feel beautifully brand new and reassuringly familiar all at the same time.

Thanks to all of our dedicated followers, RAMfest is South Africa’s number 1 alternative music festival. RAMfest IV will surpass its predecessors, both in scale and in skandes.

Join our RAMFEST IV, 2010, event page here http://www.facebook.com/home.php?ref=home#/event.php?eid=80072657682

Line up:

MAIN STAGE

Pendulum DJ set & Verse (UK/AUS),  Johnny Foreigner (UK), Boo!, The Narrow, Lark, Fokofpolisiekar, Taxi Violence, Isochronous, Desmond & the Tutu’s, Kidofdoom, 7th Son , The Rudimentals, Tidal Waves, Red Five Point Star, Half Price, The Monroes, 3rd World Spectator, Cutout Collective, The Ragdolls, Stereo Zen, The Sleepers, Heldervue, The Realist, Jack Parow, The Dirty Skirts, Checked Zebra …..more to be announced soon!

METAL 4 AFRICA STAGE

We at www.metal4africa.com are very pleased to announce our formal involvement at the upcoming RAMfest IV with our own festival area.

You can expect a complete stage and festival area dedicated solely to your metal/alternative needs, benefitting from the infrastructure of a well-established premier music festival, and all the elements which you have come to enjoy and expect from Metal4Africa events crammed into one package, and at a competitive price – still lower than the national average for festivals of this caliber.

A B Turbo, Betray The Emissary, Cold Hand Chemistry, Day Turns Night, Enmity, Facing The Gallows, Guns Go Bang, Mind Assault, Moment Of Clarity, New Altum, Pestroy, Reverse The Sands, SacriFist, Strident, Symphonic Schitzophrenia, The Warinsane

Also featuring:
The Untamed DJ’s (Zepplins, The Doors), DJ Zuul (Mordor, Eye Of Horus)

ELECTRONIC STAGE

“Dynamo Robo Disco”, Pretoria’s most advanced audio-visual dance-floor-destroying experience is charging it’s batteries and powering up to bring the fun to Cape Town. GRIET presents ‘ROBO-RAM!’ RAMfest’s first official dress up after party!
The brainchild of Sassquatch (co-creator of the Sovereign Academy) every Dynamo is powered by a dedicated team of musicians, DJs, designers, animators, illustrators and stuff-makers and brought to life by the small army of robots that flood the dancefloor. With a heavy emphasis on elaborate decor, live lighting and video performance and fun dresscodes based around variations on the robot theme, Dynamo sets its sights on pushing the envelope on event design further than any other series of South African parties has done before.
Now Dynamo is taking the robot apocalypse on the road for a single night of mechanical mayhem at this year’s RAMfest. With the Redbull Van as a platform for constructing “ROBO-RAM!” RAMfest’s first dress up, get down and tear it apart robot after-party!
When the bands are over go back to your tent and transform into the cyborgs we all know you are and come rock out to Yesterday’s Pupil, Sassquatch and Richard The Third who will power you up with their disco-punk-electro-rock sets.

Don’t forget to pack that Hawaiian shirt we all know you have lurking in your closet because on Saturday morning we’re throwing a beach theme party down by the river starting at 11:00am. There will be cocktails, deck chairs, umbrellas, beach fun-stuff and DJ’s all day long! Moe Joe (Kidofdoom), Richard The Third, Mr. Sakitumi (Lark) and Sassquatch, more DJ’s to be announced!

The last dress up afterparty at RAMfest is ‘Strike of the Ninja Thunderkick!’ featuring Cape Town’s grand master of the electro dance floors, HAEZER and the king pin of Drum’n'Bass, Niskerone! Bring your glow sticks, dust off your Karate Kid headbands and head over to the Redbull truck for the final showdown!

Yesterday’s Pupil, Haezer, DJ Sassquatch, Richard The Third, Niskerone, Moe Joe, Mr. Sakitumi … more to be announced soon!

AIR GUITAR CHAMPIONSHIPS

The fourth installment of AIR GUITAR SOUTH AFRICA will once again take place on Saturday afternoon.
IF YOU THINK YOU GOT THE MAD STYLE …ENTER!!!!
contact info@ramfest.co.za and we’ll send you all the detail!

WHAT`S NEW AT RAMfest IV?

SNOW CAFE – MULTIMEDIA CITY
Snow Café is a multimedia tented area offering various forms of entertainment. Drop in, relax and blow off some steam. Our friendly staff will make you feel right at home and will ensure you are energized for that next round!
What is on offer:

* Big Screen Cinema by DVD Nouveau
* Internet Cafe
* Gaming consoles
* Cellphone charging
* Cocktail & Snack Bar

LAYOUT
We will change the layout of the festival this year to make space for more and better camping. Nekkies will undergo a make over with never before seen structures to create a getaway to FANTASIA. Come blow your mind!

ENTERTAINMENT AREA
Both stages, bars and stalls will be inside a fenced off entertainment area. NO GLASS or CANS will be allowed inside. please decant into plastic containers if you want to bring your own drinks in. Booze will be cheap and cold at the bar.

BEER GARDENS
2 x LARGE TENTED bar areas, with tables, benches and parasols = BEER GARDENS.

PARKING
first come first served,you may camp at your cars untill the venue is full, after which you will be directed to a new parking area where you’ll have to leave your car and walk in with your tents and goodies.Don’t worry it’s not far… if you’d like to camp with your car make sure to come early. gates will open on the Thursday allready.

STAGES
We have a new, Bigger and Sexier stage design for the Main Stage, The METAL4AFRICA stage will be hosted in a Marquee and wait till you see the electro stage!

ATM’s
..will be placed around the entertainment area. We promise not to run empty.

MARKET
We strive to bring you the best in festival foods, affordable yet healthy and delicious. Catering for everybody’s needs.Clothing and other festival paraphernalia also…
The Greek merchant’s merchandise stand with credit/debit card facilities.
for bookings please contact info@ramfest.co.za or 021 8833607 during office hours

CAMPING, SWIMMING and BRAAIing
RAM is a full weekend camping excursion, bring your tents caravan’s and camping gear.It is HOT that time of the year bring extra shade i.e Gazebo’s stretch tents, sun hats, umbrellas. There is a large Swimming pool and a river, don’t forget your inflatable’s. There are many designated braai areas around the camp site and braai wood will be for sale.

MEDICS
As always there will be professional medics on site, with all necessary emergency equipment, bring your own headache tablets and please PARTY SAFE!

GREEN
Environmentally Friendly: If It’s Green …Smoke It! haha
Please help to keep us as environmentally friendly as possible. Bring rubbish bags to keep your area clean.Rubbish bags will also be handed to each car on arrival. All rubbish bags will be collected by our cleaners and sorted into the relevant recycling bins. PLEASE LEAVE GLASS AT HOME!!

CARPOOL / LOOKING for a LIFT/ OFFER a LIFT
http://www.liftsplit.com/
the GREENER way of getting to and from the festival

KREEF HOTEL is happy to announce that they will be setting up their point five star festival tent hotel at the RAMfest 2010 at Nekkies in Worcester. Pre-pitched bow tents with mattresses & locks. Secure parking, lighting & 24-hour security – all inside the VIP area on the lawns around the swimming pool. Luggage porters (to help you rest your case), daily breakfast, coffee on tap, cell-phone (cameras, laptops) charging facilities and even a private little bar just for you. Clean toilets (a ply within) & our famous hot showers, exclusively for Kreef guests. All this and more super service crawling distance from the RAMfest stages, at a price to fit your pocket. Rock Hard, Sleep Soft.. KREEF HOTEL …the calm thing is to remain important.. BOOK NOW at www.kreefhotel.co.za

TICKETS
Tickets available form Computicket from 01 November 2009 (country wide)
Earlybird special (01 November – 04 January) R320
3 day wk/end pass: R350 outlets. R400 door
2 day Sat/Sun pass: R350 outlets. R350 door
1 day Sunday pass: R100 door only (entry from 08:00)

STRICTLY NO:Under18’s. Children must be accompanied by a responsible adult, Glass bottles (please decant your drinks into plastic bottles), Littering (Leave No Trace, remove your camping litter!), Fireworks, Domestic animals, Graffiti, Bad attitudes, Weapons, Independent sound systems, illegal substances, Don’t drink & drive; P:L:U:R.

RIGHT OF ADMISSION RESERVED. Entry is entirely at your own risk. The promoters accept no responsibility whatsoever for injury, death, loss or damage of any nature to persons, vehicles & belongings. This applies even to negligence of any kind by the promoters, venue and contractors. All rights reserved.
……………………………………………………………..
We would like to thank:
Audiomatik Events cc, Bundi Productions, Distell, Fender, Hunters, Klein Libertas Theatre,Marshall Music (CT), Oppikoppi Productions, SAB, Snowball Effect, Red Bull, liftsplit.com

… So that statement probably doesn’t hold water for most guys, but I know for me Drum and Bass (D&B) is definitely more pleasurable than T&A. If you don’t know much about the Drum and Bass movement, its okay: neither do I. Apparently we have UK ravers to thank for the fast breakbeats (160-190 bpm) and heavy sub-bass that emerged from overseas circa mid-90s. While us naive Americans were rocking flannel, long hair, and self-loathing, England was getting their mad dance party on to D&B in posh nightclubs. The genre has alternatively been referred to as oldschool jungle, for its syncopated yet “broken” beats, and its tribalistic reggae roots. I still can’t say I quite understand how the fuck this genre evolved from overprivileged kids rolling on E, but I’m too busy busting a move to care.

You will too.

Pendulum ft. DJ Fresh, $Pyda & Tenor Fly – Tarantula

From the 2006 album, Hold Your Colour, which has been hailed by many modern drum and bass critics as the best dNb/deebee album of all time.

28. When Did This Storm Begin (feat. Binary Finary) – Shiny Toy Guns
It was controversy a go-go last year over at Shiny Toy Guns HQ. After the first album failed to do anything in the UK (and indeed anywhere), the band chose to ditch lead singer Carah Faye in a stunt which was perplexing at best and downright stupid at worst. A number of STG fans were up in arms, and the creation of literally tens of groups on Facebook/MySpace etc pledging allegiance to Carah must have been worrying for STG, especially as they replaced Princess Carah with a reject from the Pussycat Dolls search programme – Sisley Treasure, if you followed it. Anyway, back on record, this song is the opening track from an otherwise shit album. And I’m only a little bit biased. It’s the only track which really shows much resemblance to the STG I used to know and love.

27. Epic Last Song – Does It Offend You, Yeah?
I do like DIOY,Y?, but their ridiculous name really irritates me. Their album – which I was really excited about – turned out to be a bit awful really, aside from We Are Rockstars and this little gem. It’s not really typical of DIOY,Y? but it’s a nice enough song. I like the drumming on it, it reminds me of Muse a little bit in places. It is a nice way to round off the album, but it doesn’t work so well on its own in my humble opinion, which is probably why you can buy the CD single for 60p on Amazon (2009 NOTE: pricing correct at time of writing. It’s probably even cheaper now), and that Wikipedia denies it was ever released.

26. See You Again – Miley Cyrus
Anyone who says this isn’t as catchy as crabs is either a. deaf or, b. really stupid. The lyrics sometimes veer on being a bit immature (sorry Lesley, it’s true), but as the song is being targeted at 14 year old girls who fuck up a bit in the company of someone they fancy, I can let it drop. Although it is worth noting that this is hardly a situation which is exclusive to 14 year old girls, let’s be honest here. I also liked Seven Things, but not as much, and the third single was pretty boring, which probably serves as proof enough that I don’t need to listen to the whole album to find the best of it – it is here.

25. Ready For The Floor – Hot Chip
This song is brilliant. It’s up there with Over & Over – you can’t help but start wiggling around a bit when you hear it, which is not such a fantastic side effect when you are on the tube on your own in the rush hour. I was a bit disappointed the whole album wasn’t up to this standard, but with a few more plays, perhaps it will click and everything will be okay (2009 NOTE: this did not happen). I can’t recall any of the follow up songs really doing much either, but Hot Chip seem to have a pretty strong fanbase, I wouldn’t say they have done a Sugababes (2009 NOTE: this was a reference to the Sugas becoming really tired and repetitive, and therefore alienating their fanbase, not to their roundabout of disposable members).

24. What A Catch, Donnie – Fall Out Boy
This song is my favourite from Folie á Deux so far. Not that anyone will know yet as the track-by-track review I have been promising to write has still not materialised (2009 NOTE: it never did). This features Gabe from Cobra Staship, Brendon from Panic At The Disco, and of course Wentz. It is like a Decaydance fangirl wet dream. I do find Stump’s vocals really hard to listen to sometimes, and this song is quite bad for nasal and annoying, which is a shame but that is life. That aside, it has a nice melody, and there’s also an applaudable uuse of tambourines and piano. Viva La FOB!

23. Everyone Nose – N*E*R*D
I don’t think this did well for reasons which I find odd. I have always had a bit of a soft spot of Pharrell though; I heart N*E*R*D even though it probably isn’t cool any more. My only niggles with this song are that I think the middle 8 sucks – there is no excuse for slowing the pace down and putting stupid winebar jazz piano in anything, ever. I also think the outro could be chopped significantly to make it a bit snappier, but I daresay others would disagree. Watch your back Mark Ronson, Max Martin, Rich Costey etc etc.

22. Courtship Dating – Crystal Castles
Some of the cool kids have been going on about Crystal Castles for ages, but until they shoved a song infront of my face that I wanted to dance to, I just didn’t care. It took me a couple of listens to really get in to this, but when I ‘got it’, it was a staple of every playlist I made for about five months. I think that the song is about taxidermy which is a bit bizarre, but I ignore that, and happily strut around with lots of glitter around the world and this on full blast.

21. Rise – Flobots
I don’t think this is one many people liked, but there we go. Flobots are like a watered down Rage Against The Machine for this generation. They’re upbeat and in your face and they also have some pretty good lyrics (take note, Cyrus). The simple but inspiring chorus is great, definitely one of the highlights on the album for me. I wouldn’t be surprised if these guys won a couple of awards over he next few years for the album (2009 NOTE: they did not).

20. Body Crash – Buy Now

The non-event of this release is one of the most bizarre events of 2008, or indeed the entire millenium if you ask me. This should have been absolutely massive; I don’t know what happened to it. It is absolutely fucking awesome, and would have/should have been appreciated by two massive social groups I am friends with.
Group A – The boring Eurovision fans who just love everything that comes out of Sweden, even if it is dire. I have been reliably informed that the artist (or 50% of, I’m not sure on this) is Swedish, therefore they should have loved it.
Group B – The boring dance music fans. Apparently this is house music. I don’t know what house music is; the dance lot confuse the hell out of me, and I have probably commited the biggest musical faux-pas since Kelly Clarkson released My December, but there we go. Anyway it is fucking amazing and that is all you need to know.

19. Stop And Stare – OneRepublic
Yes, I am well aware of how embarassing this admission is. I’m not sure if it is still as socially unacceptable to dislike Ryan Tedder post Bleeding Love and Halo, but whatever. This song is proper Radio 2 fodder, but for some reason, I really like it. I think it is less about the song, and more the fact that I heard it a lot at a certain period of the year which was good and holds some nice memories for me, but this is not a relevant side-gambit. Incidentally, I listened to the whole OneRepublic album last night, and the singles and one other song aside, what a dreary load of shit. Talk about knowing your audience.

18. I Thought It Was Over – The Feeling
This was another good pop song, my favourite moment being the bit with spazzy synths after the “DOES ANYBODY KNOOOOOOOOW?” bit. I seem to remember this was always on the radio at the start of last year, and I went and bought the album on the back of this song. Big mistake. It was terrible, and I only ever listen to this song. Damn you, The Music Industry reeling me in with your great first singles, then trapping me into buying a shit album. Oh well. (2009 NOTE: I have not listened to anything by the Feeling off my own back for the last 12 months. Forgive me.)

17. Up – The Saturdays
As much as I wanted to hate them for their terrible promo campaign before we had even got any music at all, this is a great song. There’s not much to say, it’s catchy, it’s singable and everyone seems to know it. I might add that I didn’t rate If This Is Love, and I also really don’t like Issues. Their generic b&w artwork with coloured lenses is really irking me too, but this is meant to be a list of positivity, not me complaining about everything I don’t like about them.

16. Sensual Seduction – Snoop Dogg
I don’t know why I like this song. This kind of generic top 40 r’n’b usually is the genre that makes me weep for our generation. I really love the Robyn remix of this too, I think it was a crying shame it was not released properly (2009 NOTE: Apparently it was. Hello journalism degree). I like the video for this too, tongue-in cheek music videos are always an easy way to earn points with me. Though it is a pointscore you will have to scout for yourself as I’m not embedding the video on here.

15. A&E – Goldfrapp
I really loved this song. Really, really loved it. The album was great, but this was one of the best from it. It is one of the saddest songs I have ever heard, and it is definitely one I have to avoid when I am feeling a little bit sad because it’s one of those songs which can push you from mild sadness into full blown depression. But that shouldn’t distract from the main point that it is a wonderful song, and if you haven’t heard it you absolutely must.

14. One Month Off – Bloc Party
This is my favourite choon from Intimacy by far. I also quite enjoyed Mercury, but the 12” remix of that was better, and I am not including that on this list because it was a b side or something, so this long and boring explanation means that One Month Off was always going to win at the end of the day. It is no Flux, that is for certain, but Kele may never better that beast of a song.

13. Behind The Sea – Panic At The Disco
Not many people liked this album, and I can understand why. Ze boys got a slight whiff of fame, took waaaay too many drugs, and found themselves holed up in Abbey Road. What is the next logical step? Make an album that sounds a bit like something the Beatles might do in 2008! Idiots. I’m the first to say that this album doesn’t have the sparkle that the first did, but this song does save it somewhat. I can’t work out what in the name of fuck it is about, but it’s probably something to do with LSD. My love for the Urie knows no limits.

12. Make You Feel My Love – Adele
Incredibly, I had not heard this song or any variation on it prior to hearing Adele doing it in the Live Lounge a few weeks ago, and I fell in love. It is one of the most perfect love songs I have ever heard in my life, if not then the most perfect. I have done some research on the original by Dylan and subsequent covers but nothing really matches up to this at all. I love it, love it, love it. The arrangement is so simple, and it just adds to the atmosphere of the song, and makes it even more wonderful. She might not live up to this kind of beauty with her original stuff, but it doesn’t matter now we’ve got this out of her. Bye Adele!

11. Propane Nightmares – Pendulum
I’m sure many people will know this one, it did pretty well last year. I have still not tired of it. I found the whole album to be a bit samey, but this is just Laura heaven. They are Australian, it’s bass heavy, it has synths, fantastique drumming, and did I mention they were Australian? I will be listening to this for years to come for sure (2009 NOTE: I still am, hurray).

10. Megalomania (Live @ RAH) – Muse
Okay, so this wasn’t released last year, but the gig was in April and it was without a doubt one of the most special nights of my life. Seeing my favourite band in one of the best music venues in the world…I’m never going to forget it. With the massive organ there, fans were speculating for weeks as to whether we’d get Megalomania at all, but as the night went on and it didn’t surface, I lost hope that we were. Then after the encore…BAM! It was one of the high points musically for me last year. It’s never going to happen again, and I am so thankful that I was there. Literally amazing.

09. Please Don’t Leave Me – Pink
Some people have called this Who Knew pt II, but I don’t see the link at all. I think this is by far one of the best songs she has ever done. The whole album documenting her breakup with Cary Hart is so beautifully done – I’m sure some situations were exaggerated for the benefit of the album (I am sure she didn’t literally burn her house down, for example), but it is all so heartfelt and you almost feel like you were given access to the pair throughout the breakup.

08. 42 – Coldplay
I genuinely don’t get why more people don’t hear the genius that I hear in this song. It is one of my favourites on VLVODAAHF. It’s one of those Queen-esque songs that has lots of different little melodies to it, and lots of piano and Chris Martin who I love so much that it hurts a little bit. He is a very talented man, and he is a bit like a friend of mine I think in the respect that a lot of people don’t get his comedy, and just think he is a bit of a prick until they actually sit down and talk to him and realise that everything he says is said with a wry smile. You have to be of a certain finesse to get the pair of them I think. I am giving the impression Chris Martin and I are best friends here – alas, we are not.

07. Homecoming – Kanye West (feat. Chris Martin)
My most favourite Kanye moment ever. Chris Martin always adds a sparkle to anything he touches and this is no exception. I do like Kanye doing collaborations, I know I am on my own on this one but I just don’t love his solo stuff as much. I really liked Flashing Lights with Dwele also, but this pipped it to the post. I blame Chris Martin (I LOVE YOU CHRIS MARTIN). I have become a fan of Kanye’s absolute lunacy over the last year too – his CAPS FILLED BLOG RANTS are one of the best parts of the week. I actually read his blog yesterday where he was calling Lady Gaga ‘act of 2009’ as if no one had ever heard of her and it was his own discovery. He is kind of like the black American Jo Whiley.

06. In My Arms – Kylie Minogue
This song is another one of those which, if it comes on my iPod when I am in a public place, I will skip along to wherever I am going, blissfully ignorant of everyone else in the world. I really start stomping around when it comes on, and it is guaranteed to raise my mood tenfold. I don’t know what hand Kylie had in writing it, but whoever it is is a fucking genius (2009 NOTE: I think it was Calvin Harris). It’s amazing. The lyrics are feisty, almost arrogant, and I just love it to bits. I quite happily listen to it on repeat for hours.

05. Nude – Radiohead
This is one song which had one of the biggest hypes prior to release ever I should imagine. The original version was written in the OK Computer sessions in 1997, but the band never released it up until this point because they couldn’t get the arrangement quite right. I’m not sure what it sounded like to start, but it was definitely worth the 11 year (!) wait. I’d go as far as putting it in my top 5 Radiohead songs ever. It’s gorgeous, and if you haven’t heard it, listen listen listen.

04. Phonography – Britney Spears
WHY is this a bonus track. WHY? I don’t get it. It is one of the best songs on Circus. How did NO ONE at Sony hear this and think “Gosh, you know what, this would be better than that My Baby drivel, let’s put it on there and release it as a single with a video where we put Britney in some kind of scenario where she is stalking someone with a bluetooth phone. But making it sexy and not sinister. This would be the best idea we’ve ever had and would make us all a lot of money and add to the case that Britney Spears is better than Madonna”. Someone needs to be fired for not making that call.

03. Kids – MGMT
This is one of those songs that makes an art form of simple lyrics paired off with a really fucking catchy hook. I’d love to see MGMT live at some point, I imagine they would be great in a stuffy little venue where everyone is really out of it and dancing like twats in a cage on acid. The PSB remix which isn’t being released officially canes the Soulwax remix into the ground. Go and listen. It gets really epic at about the three minute mark if you can’t be arsed to listen to the whole thing.

02. A Dustland Fairytale – The Killers
Another one of those songs which I heard for the first time and I just fell in love. This is potentially one of the best songs they have ever done – it isn’t in the same arena as all of the other songs in their back catalogue. Some of those are fantastic and will be remembered forever but this is totally in a league of its own. I don’t know why but I don’t want to see this released as a single. I guess I am kind of protective of it and if it was released and didn’t do well, I’d have some kind of Britney-esque breakdown which would culminate in me being sectioned after purchasing the single 20,000 times on iTunes (forgetting that 19,998 of these wouldn’t officially count in the charts until after I bought them, then attacking Steve Jobs and the entire line up of the OCC in a murderous rage) (2009 NOTE: It was released, it didn’t do well, and I was very sad, but no one died and I was not sectioned). For the love of all that is holy, Island please do not release it. I don’t think any justice can ever be fully done with this masterpiece.

01. Come On Girl – Taio Cruz feat. Luciana)
HEY! This song is definitely in my all time favourite songs list, I will never ever stop loving it. It’s just so good -  one of the songs that you can put on and I will dance and sing my heart out like there is no one watching. It’s another song which is made by some superamazing synth action in the background, and a pretty sassy cameo from Luciana just finishes it off perfectly. I was well disappointed nothing else on the album was up to this standard, but I guess that makes this even more special or something. I seriously doubt Taio will ever make a song this good again but when he has just made #1 in my chart, I doubt he gives a crap about anything else in the world, he can die happy now.

Every word we speak, every action we do, every whatever will push people closer to God or pull them away from Him.

As fallen people, that’s a big burden. It honestly freaks me out to realize how many people I’ve probably pushed away from God with my words or actions or lack thereof.  It upsets me knowing that I have pulled people away from where the belong. I have displaced people.

I know I have done those things because I have felt the weight of the words/actions/lack thereof of those around me. And they have only either pushed me towards God or further away from Him. And honestly I feel the pull-away-from-God a lot more than the push-towards-God.

I hate the pulling-away feeling. And that’s what I’m feeling right now. Not because people are necessarily actively pulling me away. But because I’m not being pushed. And without contact, I feel a loss of relationship and a loss of God.

But God did call us to be His hands and feet. God did give us power to dishonor his name. God gave us a freedom and responsibility to Him. And hopefully we seek to honor that in all we do.

But even when we fudge up… God’s plan is still greater. We are inevitably going to pull people away through what we do/say. But God is still God and He can work things out. I know in my own life I have been pulled away. But fighting against that has created my faith and solidified it. Being pulled away from God has made my faith into my own.

And God is a God of forgiveness and redemption. Our pulling sins are washed away by His blood. He compensates for our wrongdoings and misleadings. I find it hard to accept that He compensates for the wrongdoings of others when they hurt us so badly. But He does. He heals us. He heals the people we hurt. And shows us that He is enough.

I think all of this has the potential to be like a ride on the swing. It’s very difficult to push a 5-year-old on a swing beginning with a push. It is so much easier to pull the swing back and let go. The child is going to go a lot higher and a lot faster….with the constant push. But even if someone else comes running up in the opposite direction and pushes the child “backwards” the child is just going to end up going forward faster and higher.

Maybe we’re just on God’s pendulum. And He’s waiting for us to realize that it’s not the high branch in front of us that we’re trying to reach… but it’s the swing set itself, the bar above us holding our swing, the person of God, that is what we need to realize and feel comforted by.

–as long as we don’t get pushed off of the swing–

I feel like if I run towards God I’ll push people and things out-of-the-way. God should be my first priority. But how do I still love others? How do i not push them out-of-the-way when they are in need? I’m not sure. But God knows.

It’s hard to know anything about this. But it’s easy to feel far away from God. Abandoned by God. Abandoned by others.

I dunno. God is so much bigger than we are.

Others have failed and will fail us. We’ve failed God. But God is eternal. God is true. God doesn’t fail. Us or anyone else.

He is bigger than our failures and our deepest pain. And He knows us inside-out and still loves us?? utter ridiculous-ness!

We push and pull and trip and fall. But God is good and He is a constant in our equation.

In all things, God works for the good of those who love Him. I want him to work for my good. But I also want him to work for the people who have been pushed away from Him and have not yet come to love Him.

unfortunately pro at pulling people away,

coop

PENDULUM
http://www.myspace.com/pendulum

Sambata, 7 Noiembrie 2009
Arenele Romane (Parcul Carol, strada Cutitul de Argint, nr. 26)

Pe 7 Noiembrie, la Arenele Romane din Bucuresti, vom avea parte de cel mai cunoscut, premiat si apreciat nume din drumandbass-ul mondial, PENDULUM.

Pendulum s-au format in 2002 in Australia ca urmare a intalnirii a trei muzicieni cu background comun si cu un plan indraznet in minte, acela de a crea ceva nou, energic, eclectic si foarte proaspat, ceva inexistent pana atunci pe scena muzicii de dans.

De atunci si pana in 2009 au crescut, ajungand in anul acesta mai sus ca niciodata.

Pendulum s-au aflat si in aceasta vara cap de afis in circuitul festivalurilor de pretutindeni. S-au dovedit a fi prea mari pentru corturi la ultimele festivaluri, asa cum a demonstrat multimea mult prea numeroasa venita sa-i prinda in actiune, asa ca anul acesta vor primi Scena principala la Download (unde au prestat inaintea celebrului Marlyn Manson), V, T in the park, Isle of Wight si Oxegen. Cererile publicului de peste tot au fost rasplatite cu comfirmarea prezentei lor ca headlineri la Global Gathering in iulie.

In acelasi timp se pregatesc sa se reintalneasca in studio pentru a pregati cel de-al treila album care va include niste colaborari incitante. La sfarsitul anului probabil vom gusta o mostra din acest album.

Pana atunci insa, vom avea parte la Bucuresti de un djset din partea Pendulum, impreuna cu MC Verse, solistul in prestatiile lor live. Toate astea pe 7 noiembrie la Arenel Romane.

In aceeasi seara vor performa
Snow (http://www.myspace.com/djsnowro) din Cluj
Rancha (http://www.myspace.com/djrancha) din Craiova
JTR (http://www.myspace.com/subdustrialkru) din Sibiu

De visualsuri se vor ocupa
Saru de la Malibu Police (http://malibu-police.blogspot.com)
Spulberg (www.usl.ro).

Intrare:
30 lei in avans
40 lei la poarta.

Biletele in avans pot fi cumparate din magazinele:
Base (http://baseteam.ro/default.php?p=contact)
Boarder’s (http://www.boardersshop.ro)
Frogs (http://frogs.ro/cms/locatie-frogs)
Kickback (http://www.kickback.ro/contact_us.html)
Diverta (http://www.diverta.net/gaseste_un_magazin.php)
Online pot fi achizitionate de pe site-ul Ticket Point (http://www.ticketpoint.ro)

Mai multe detalii pe www.arenadnb.ro

Portile se deschid la: 22:30

Pendulum – Granite LIVE @ Brixton Academy

[Click here for a PDF of this post with nicer formatting]

Motivation

The planar multiple pendulum problem proved somewhat tractable in the Hamiltonian formulation. Generalizing this to allow for three dimensional motion is a logical next step. Here this is attempted, using a Geometric Algebra scalar plus bivector parametrization of the spherical position of each dangling mass relative to the position of what it is attached to, as in

The exponential is essentially a unit quaternion, rotating the vector from the polar axis to its angle dependent position. Two sided rotation operators are avoided here by requiring of the unit bivector , where is a vector in the plane of rotation passing through the great circle from through . Note that we are free to pick , the unit vector in the plane at angle from the x-axis. When that is done since these are perpendicular. Setting up the Lagrangian in terms of the bivector instead of the scalar angle will be attempted, since this is expected to have some elegance and will be a fun way to try the problem. This should also provide a concrete example of a multivector Lagrangian in a context much simpler than electromagnetic fields or quantum mechanics.

Note finally that a number of simplifying assumptions will be made. These include use of point masses, zero friction at the pivots and rigid nonspringy massless connecting rods between the masses.

Kinetic energy for the single pendulum case.

Let’s compute derivatives of the unit vector

This can be done with both the left and right factorization of , and are respectively

These derivatives have been grouped into a matrix factors that allow a natural seeming conjugate operation to be defined. That is for a matrix of multivector elements

define a conjugate matrix, as the transpose of the reversed elements

With this definition, plus two helpers

Our velocity becomes

Explicitly, expanding the inner matrix product we can write

This is a slightly unholy mix of geometric and matrix algebra, but it works to compactly express the velocity dependence. Observe that this inner matrix , so it is Hermitian with this definition of conjugation.

Our Lagrangian for the one particle pendulum, measuring potential energy from the horizontal, is then

We also have a mechanism that should generalize fairly easily to the two or many pendulum cases too.

Before continuing, it should be noted that there were assumptions made in this energy expression derivation that are not reflected in the Lagrangian above. One of these was the unit bivector assumption for , as well as a containment assumption for the plane this represents (). So for completeness we should probably add to the Lagrangian above some Lagrange multiplier enforced constraints

Here has got to be a trivector multiplier for the Lagrangian to be a scalar. Can we get away with omitting these constraints?

Two and multi particle case.

Having constructed a way that can express the velocity of a single spherical pendulum in a tidy way, we can move on to consider the multiple pendulum case as shown in figure (\ref{fig:sPolarMultiPendulum:pendulumDouble})

\begin{figure}[htp]
\centering
\includegraphics[totalheight=0.4\textheight]{pendulumDouble}
\caption{Double spherical pendulum.}
\end{figure}

There are two bivectors depicted, and representing oriented planes passing through great circles from a local polar axis (in direction ). Let the positions of the respective masses be and , where each mass is connected by a rigid massless rod of length and respectively. The masses are rotated by angles and in the planes and from an initial direction of . We can express the position of the second mass as

We can use the same factorization as previously used for the single mass case and write for our collection of angular velocities

Using this the total Kinetic energy is

Notation has been switched slightly from the single mass case, and the factor is now incorporated directly into for convenience.

An expansion of is essentially one of block matrix multiplication (where we already have to be careful with order of operations as we do for the geometric product elements themselves). We have something like

We have for the products

So our quadratic form matrix is

In general for the multiple particle case this is

Expanded explicitly this is

Observe that the order of products in this expansion is specifically ordered, since the and bivectors do not necessarily commute.

The potential in the multiple particle case is also fairly straightforward to compute. Consider the two particle case to illustrate the pattern. Using the lowest point as the potential reference we have

Alternately, dropping all the constant terms (using the horizon as the potential reference) we have for the general case

Lets collect all the bits and pieces now for the multiple pendulum Lagrangian now, repeating for coherency, and introducing a tiny bit more notation (mass sums and block angular velocity matrices) for convenience

Building up to the Multivector Euler-Lagrange equations.

Rather than diving right into any abstract math, lets consider a few specific examples of multivector Lagrangians to develop some comfort with non-scalar Lagrangian functions. The generalized “coordinates” in the Lagrangian for the spherical pendulum problem being considered include include bivectors, and we don’t know how to evaluate the Euler Lagrange equations for anything but scalar generalized coordinates.

The goal is to develop Euler-Lagrange equations that can handle a Lagrangian for these more general functions, but until we figure out how to do that, we can at least tackle the problem using variation of the action around a stationary solution.

A first example to build intuition.

To help understand what we have to do, lets consider the very simplest bivector parametrized Lagrangian, that of a spherical pendulum constrained (perhaps by a track or a surface) of moving only in a ring. This is shown pictorially in figure (\ref{fig:sPolarMultiPendulum:pendulumPolarCircular})

\begin{figure}[htp]
\centering
\includegraphics[totalheight=0.4\textheight]{pendulumPolarCircular}
\caption{Circularly constrained spherical pendulum.}
\end{figure}

The potential energy is fixed on this surface, so our Lagrangian is purely kinetic

We’d like to directly vary the action for the Lagrangian around a stationary solution

Introducing a bivector variation , and writing we have

The first term is just . Setting the variation (neglecting the quadratic term) and integrating by parts we have

With arbitrary it appears that the solutions of the variation problem are given by

Has anything been lost by requiring that this is zero identically when all we had originally was the dot product of this with the variation bivector was zero? If this zero describes the solution set, then we should be able to integrate this, yielding a constant. However, following this to its logical conclusion leads to inconsistency. Integrating 46, producing a bivector constant we have

The original constraint on was the bivector spanning the plane from the polar axis to the azimuthal unit vector in the plane at angle a . The dependence wasn’t specified, and left encoded in the bivector representation. Without words that was

Inserting back into 47 this gives

One more integration is trivially possible yielding

There are two possibilities for the grades of , one is , so that the time dependence is a scalar, and the other is so that we have an plane bivector component. Allowing for both, and separating into real and imaginary parts we have

This isn’t anything close to the solution that is expected if we were to start with the scalar Lagrangian for the same problem. That Lagrangian is

and the Euler Lagrange equations give us, for a scalar constant

So the solution for is just

In the absence of friction this makes sense. Our angle increases monotonically, and we have circular motion with constant angular velocity. Compare this to the messier 51 derived from the bivector “solution” to the variational problem. There is definitely something wrong with the variational approach (or conclusion) when the variable is a bivector.

Does it help to include the constraints explicitly? The bivector parametrized Lagrangian with the unit bivector multiplier constraint for this system is

Doing the variation we get a set of two equations

Once again re-inserting one gets

Setting , , , we have

This is now consistent with the scalar Lagrangian treatment. In both cases we have the angle linearly proportional to time, and have a single parameter to adjust the angular velocity (used in the scalar treatment above and have this time (although it was set to one here for convenience). The conclusion has to be that the requirement to include the multipliers for the constraints is absolutely necessary to get the right physics out of this bivector parametrized Lagrangian. The good news is that we can get the right physics out of a non-scalar treatment. What is a bit disturbing is that it was fairly difficult in the end to get from the results of the variation to a solution, and that this will not likely get any easier with a more complex system.

A second example.

The scalar expansion 82 of the kinetic term in our spherical polar Lagrangian shows a couple of other specific multivector functions we can consider the variation of.

We have considered an specific example of a Lagrangian function without (yet) utilizing or deriving a multivector form of the Euler-Lagrange equations. Let’s consider a few more specific simple examples motivated by the expansion of the kinetic energy in 82. Lets start with

where is a bivector constant, a scalar, and a bivector variable for the system. Expanding this around stationary points , and we have to first order

In this simple system where both scalar variable and bivector variable are cyclic “coordinates”, we have solutions to the variational problem given by the pair of equations

As to what, if anything, this particular Lagrangian (a fragment picked out of a real Kinetic energy function) represents physically that doesn’t matter so much, since the point of this example was to build up to treating the more general case where we are representing something physical.

A third example.

If we throw a small additional wrench into the problem above and allow to be one of the variables our system is dependent on.

It is less obvious how to do a first order Taylor expansion of this Lagrangian required for the variation around the stationary solution. If all the coordinates in the Lagrangian were scalars as in

(dropping dot products now that these are all scalar variables), then the variation requires nothing abnormal. Suppose our stationary point has coordinates , with variations that vanish at the extremes of the integral as usual.

With scalar variables our path is clear, and we just form

Here is it implied that all the partials are evaluated at the stationary points . Doing the integration by parts we have

Setting this produces the Euler-Lagrange equations for the system. For our specific Lagrangian this procedure gives

Each time we do the first order expansion we are varying just one of the coordinates. It seems likely that the correct answer for the multivariable case will be

Thus the variational problem produces solutions (the coupled equations we still have to solve) of

Multivector Euler-Lagrange equations.

Derivation.

Having considered a few specific Lagrangians dependent on multivector generalized “coordinates”, some basic comfort that it is at least possible has been gained. Let’s now move on to the general case. It is sufficient to consider Lagrangian functions that only depend on blades, since we can write any more general multivector as a sum of such blades

Write

where is a blade of grade . We can do a regular old chain rule expansion of this Lagrangian if coordinates are (temporarily) introduced for each of the blades . For example, if is a bivector in , we can write

and then we can do a first order Taylor series expansion of in terms of these coordinates. With , for this specific single variable Lagrangian we have

If we write the coordinate expansion of our blades as

where is some set of indexes like from the bivector example, then our chain rule expansion of the Lagrangian to first order about a stationary point becomes

Trying to write this beastie down with abstract indexing variables is a bit ugly. There’s something to be said for not trying to be general since writing this for the single variable bivector example was much clearer. However, having written down the ugly beastie, it can now be cleaned up nicely by introducing position and velocity gradient operators for each of the grades

Utilizing this (assumed) orthonormal basis pair we have

Setting we have a set of equations for each of the blade variables, and the Euler-Lagrange equations take the form

Work some examples.

For the pendulum problem we are really only interested in applying 73 for scalar and bivector variables. Let’s revisit some of the example Lagrangians, functions of bivectors, already considered and see how we can evaluate the position and velocity gradients. This generalized Euler-Lagrange formulation doesn’t do much good if we can’t work with it.

Let’s take the bivector gradient of a couple bivector functions (all the ones considered previously leading up to the multivector Euler-Lagrange equations).

It is actually sufficient (in a less than 4D space) to consider only the first,

For we then have

This is now enough to evaluate our bivector parameterized Lagrangian from the first example, 56, reproducing the result obtained by direct variation (as in Feynman’s lectures)

By inspection we can see that this works for the remaining two motivational examples too.

Evaluating the pendulum Euler-Lagrange equations (scalar, bivector parameterized KE).

We now have the tools to evaluate the Euler-Lagrange equations for the pendulum problem 37. Since all the and dependence is in the kinetic energy we can start with that. For

We want each of and . Of these the derivative is easier, so lets start with that

Each of these are scalars and thus equal their Hermitian conjuagate. This leaves us with just one term doubled

A final evaluation of the derivatives, in block matrix form over rows , gives us

For the bivector velocity gradients, we can do the same,

Only the parts of contribute to the velocity gradients, so we need to know how to evaluate a bivector gradient (as opposed to the square which was done earlier). Expanding in coordinates

(three here because we are in , and our bivectors have three independent coordinates).

These terms are both one-by-one bivector matrixes, and negate with Hermitian conjugation, so we can again double up and eliminate one of the two terms, producing

Completing the Euler-Lagrange equation evaluation we have for the coordinates

plus one equation for each of the bivectors

Because the bivector does not (nessessarily) commute with bivectors that are part of there doesn’t look like there’s much hope of assembling the left hand gradients into a nice non-coordinate form. Additionally, looking back at this approach, and the troubles with producing meaningful equations of motion even in the constrained single pendulum case, it appears that a bivector parameterization of the kinetic energy is genally not a good approach. This is an unfortunate conclusion after going through all the effort to develop intuition that led to the multivector Euler-Lagrange formulation for this problem.

Oh well.

The Hermitian formulation used here should still provide a nice compact way of expressing the kinetic energy, even if we work with plain old scalar spherical polar angles , and . Will try this another day, since adding that to these notes will only make them that much more intractable.

Appendix calculation. A verification that the Kinetic matrix product is a real scalar.

In the kinetic term of the rather scary looking Lagrangian of 37 we have what should be a real scalar, but it is not obvious that this is the case. As a validation that nothing very bad went wrong, it seems worthwhile to do a check that this is in fact the case, expanding this out explicitly in gory detail.

One way to try this expansion is utilizing a block matrix summing over the diagonal and paired skew terms separately. That is

Examining the diagonal matrix products and expanding one of these (dropping the suffix for tidiness), we have

Since we are working in 3D this symmetric sum is twice the dot product of the bivector with its derivative, which means that it is a scalar. We expect this to be zero though, and can observe that this is the case since was by definition a unit bivector

(thus and its derivative represent orthogonal oriented planes rather like and its derivative are orthogonal on a circle or sphere). The implication is that the diagonal subset of the kinetic energy expansion contains just

If we are going to have any complex interaction terms then they will have to come from the off diagonal products. Expanding the first of these

Adding to this the exchanged product and rearranging yields

Each of these multivector sums within the brackets is of the form , a multivector plus its reverse. There can therefore be no bivector or trivector terms since they negate on reversal, and the resulting sum can have only scalar and vector grades. Of these the second term, so it is unarguably a scalar as expected, but additional arguments are required to show this of the other three terms. Of these remaining three, the last two have the same form. Examining the first of these two

The first term actually expands in a similarly straightforward way. The vector terms all cancel, and one is left with just

Writing and (for compactness to fit things all in since the expanded result is messy), all of this KE terms can be assembled into the following explicit scalar expansion

Noting that all the bivector, bivector dot products are scalars really completes the desired verification. We can however, be more explicit using , which gives after a bit of manipulation

These can then be inserted back into 82 in a straightforward fashion, but it is not any more illuminating to do so.

(This is a continuation of a post begun in  Stumbling Onto The Line, Part One. )

–

Back home that evening, I began plotting the spot as well as the course of the line.  I was very curious where it might lead.  As I was drawing it to the South I realized the line was heading directly towards several prehistoric Indian sites along the border.  Out of curiosity I drew a full path line across the state between the major site to the south and another large ancient site which could be found in the northern area of the state.  As I zoomed out I was floored.

My powerspot seemed to be very close to or directly on that line.

What were the odds?  I found myself l in shock over my findings, just staring at the computer screen and shaking my head.  What were the chances?  Could it get any weirder?    Going a step further, I found it also came close to another ancient site even further down in another state.  I just kept asking myself over and over, “How did this happen?  Did I really find this spot?”  I had a hard time getting to sleep that night and on top of it all I realized I was incredibly irritable.  I took a walk with my dog, tried to calm down in the autumn evening, and then headed for bed.

The next day I went back to the site for lunch to confirm the line and to solidify my visual markers.  Perhaps, I told myself, I had misremembered those locations?  Maybe I had drawn the line incorrectly?  With notebook and pen, I went back, stood in the spot, and reconfirmed my information, recording every detail I could get as the pendulum gave me the same exact track again.

I also had a few more questions for the site.  What exactly WAS it?  Through a yes/no series I was able to determine it was simply a spot where the energy line was very near or bubbling onto  the surface.  In a way, it was like an eruption of energy.  I envisioned it like lava extremely close to the surface and making the area warm.  I randomly gave a rating of 1 to 5 and asked to be told what strength the line might be with 1 being the smallest energy line and 5 being the largest, most powerful on the planet.  Surprisingly, I was told a 4!

While there the second time I noticed a preponderance of crows in the trees around me, perhaps twelve or more.   I considered taking it as some sort of omen but I decided eventually to not do so.   As I worked, they flew away.  I did note that, once again, there appeared to be evidence of wildlife as there was a large area flattened area where several deer had slept for the night directly next to the spot.

Still not very sure about what I had stumbled on, I went back to work and later that evening I did some more looking at Google Earth.  I entered in my new information and the angle of the line did change slightly.  I drew a line to the older sites both in the North and the South.  My spot was not on that line but was VERY close to that line (less than a mile) considering the scale.  In addition, the energy line shared the same exact angle to the line between the North and South sites, running almost parallel to it.

That evening, I became aware I was becoming more and more irritable.  Something similar had happened the night before, the first day I had found the powerspot.   I had come home and shortly after dinner had become very cranky and had gone for a walk to cool down.   During this second evening, I had to control my thoughts and words to my family.  My wife commented on how “raw” I seemed to be about things.  I  felt hyperactive and scatterbrained.

Noting that I was not normally like this, I began to wonder if my contact with a high level energy line and powerspot could have that kind of effect on me?  I had stood in the  node for over twenty minutes each day as well as walked the ley line itself twice in two days.  I began to look on the internet and found that, yes, high power ley lines and “nodes” could cause one to have  a high level of energy as well as worse effects if they were “negative” in their energy.  Duh!

I likened the effect to what I had felt when walking around one of Sedona’s vortexes a year ago.  My experience with the Sedona vortex had been very calming, peaceful, and, well, fun.  I had been told, “From a vortex, you get what you bring into it.”  Later that evening in Phoenix, like I was feeling now, I had felt hyperactive and absolutely full of energy.

Being a bit of an idiot, I had not grounded myself before or after the encounters with the because, to be honest, I had not REALLY believed I had stumbled onto anything.  It was only later in the evening, as I noted how close the line came to linking up to the ancient sites in my state, I began to feel differently.  The emotional energy and irritability that followed capped it for me.

I had to accept that I had managed to not only dowse a powerspot (or Node) but had also dowsed the direction of a rather high energy ley line.   What I have not been able to figure out is why me and why hasn’t someone else found this site?   All I can think of is that it’s in a out of the way corner of an out of the way public park.  Perhaps it was just as simple as no one had really asked the question before?    Even as I write this I wonder if there are ancient remains in the area.  Was there something nearby but now lost to time?  Did the old shamans know this place?  Has anyone before me ever stumbled onto it?  I know that I’ll never truly know the answers to those questions.  All I know is that I know where it is.

Since first finding it weeks ago, I’ve been back numerous times.  Every time I do I make sure to be very conscious of my thoughts and being grounded both entering and leaving the area.  It has helped immensely.    I continue to see lots of wildlife in the area, even as we move into Winter.    I plan to do more historical research in the area as well as burying  a crystal there in the coming days; maybe leave some tobacco offerings as well.   I’ve come to believe that it is a very strong medicine area.  I am not sure it is what you would call a vortex but it most definitely carries power.    Perhaps I’ll build a small clandestine shrine?

I’ve had to accept that the powers that be led me here for some reason and wanted me to find it.  To be honest, I don’t understand it.  Dowsing has become an incredible mystery to me and the surprises keep coming every day.  All I know is that I feel very thankful and honored.  I also know that this spot needs to be deeply respected because of the energy there.  As things develop, I promise I will document what I find.

Budget video getting shit on across the board on the blogs. Not a bad tune though with heavy production from UK’s own Chase & Status. What you sayin’?

Începând cu data de 4 noiembrie, Club Bubbles găzduieste în fiecare miercuri o petrecere săptămânală DNB sub denumirea NEW MEDICINE. Vă vor vindeca de monotonie trackurile preferate de la Chase&Status, Infected Mushroom, Evol Intent, Concord Dawn, Noisia, ShyFX, Andy C, Pendulum, Dj Hype, Dj Fresh, The Quemists, Panacea & more.  Sick of bad Music? We’ve found a cure! New Medicine @ Bubbles Club.

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