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2012-09-29T18:42:53Z

Scanned 1 urls; found 1 archives (1 in CiteWeb Templates; 1 in References). See User:DASHBot/Dead Links for settings, shutoff, info, questions.

← Older revision		Revision as of 20:42, 29 September 2012
Line 1:		Line 1:
	~~Greetings! I am Dalton~~. ~~Acting has been~~ a ~~thing that I was totally addicted to~~. ~~My apartment~~ is ~~now~~ in ~~Vermont and I don~~'~~t program on changing it~~. ~~I am a cashier~~. ~~I'm not awesome at webdesign but retailers . want to check my website~~: ~~http~~://~~circuspartypanama~~.~~com~~<br><br>~~Also visit my web blog - [http~~://~~circuspartypanama.com clash~~ of ~~clans cheat~~]		A '''spherical pendulum''' is a [[generalization]] of the [[pendulum]].
			It consists of a [[mass]] moving without [[friction]] on a [[sphere]]. The only [[force]]s acting on the mass are the [[reaction (physics)\|reaction]] from the sphere and [[gravity]].

			It is convenient to use [[spherical coordinates]] and describe the position of the mass in terms of <math>(r,\theta,\phi)</math>, where ''r'' is fixed.

			The [[Lagrangian]] is <ref>{{cite book
			\| last = Landau
			\| first = Lev Davidovich
			\| authorlink =
			\| coauthors = Evgenii Mikhailovich Lifshitz
			\| title = Course of Theoretical Physics: Volume 1 Mechanics
			\| publisher = Butterworth-Heinenann
			\| year = 1976
			\| location =
			\| pages = 33–34
			\| url =
			\| doi =
			\| id =
			\| isbn = 0750628960}}</ref>

			:<math>
			L=\frac{1}{2}
			mr^2\left(
			\dot{\theta}^2+\sin^2\theta\ \dot{\phi}^2
			\right)
			+ mgr\cos\theta.
			</math>

			The [[Euler-Lagrange equations]] give :

			:<math>
			\frac{d}{dt}
			\left(mr^2\dot{\theta}
			\right)
			-mr^2\sin\theta\cos\theta\dot{\phi}^2+
			mgr\sin\theta =0
			</math>
			and
			:<math>
			\frac{d}{dt}
			\left(
			mr^2\sin^2\theta
			\,
			\dot{\phi}
			\right)
			=0
			</math>
			showing that [[angular momentum]] is conserved.

			And the Hamiltonian is

			:<math>H=P_\theta\dot \theta + P_\phi\dot \phi-L</math>

			where

			:<math>P_\theta=\frac{\partial L}{\partial \dot \theta}=mr^2\dot \theta</math>

			and

			:<math>P_\phi=\frac{\partial L}{\partial \dot \phi} = mr^2\dot \phi \sin^2 \theta</math>

			==See also==
			*[[Conical pendulum\|Conical Pendulum]]
			*[[Newton's laws of motion#The three laws in detail\|Newton's three laws of motion]]
			*[[Pendulum]]
			*[[Pendulum (mathematics)]]

			==References==
			{{reflist}}

			[[Category:Pendulums]]

en>Mindmatrix: links; cleanup

2012-03-29T22:08:11Z

links; cleanup

New page

Greetings! I am Dalton. Acting has been a thing that I was totally addicted to. My apartment is now in Vermont and I don't program on changing it. I am a cashier. I'm not awesome at webdesign but retailers . want to check my website: http://circuspartypanama.com<br><br>Also visit my web blog - [http://circuspartypanama.com clash of clans cheat]

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en>DASHBot: Scanned 1 urls; found 1 archives (1 in CiteWeb Templates; 1 in References). See User:DASHBot/Dead Links for settings, shutoff, info, questions.

en>Mindmatrix: links; cleanup