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Spherical pendulum : ウィキペディア英語版
Spherical pendulum

In physics, a spherical pendulum is a higher dimensional analogue of the pendulum. It consists of a mass ''m'' moving without friction on the surface of a sphere. The only forces acting on the mass are the reaction from the sphere and gravity.
Owing to the spherical geometry of the problem, spherical coordinates are used to describe the position of the mass in terms of (''r'', ''θ'', ''φ''), where ''r'' is fixed.
==Lagrangian mechanics==

(詳細はEuler–Lagrange equations give :
:
\frac
\left(mr^2\dot
\right)
-mr^2\sin\theta\cos\theta\dot^2+
mgr\sin\theta =0

and
:
\frac
\left(
mr^2\sin^2\theta
\,
\dot
\right)
=0

showing that angular momentum is conserved.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Spherical pendulum」の詳細全文を読む



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