“Spherical pendulum”的意思、由来-开放百科全书

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Spherical pendulum

释义

Lagrangian mechanics
Hamiltonian mechanics
See also
References

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. In what follows l is the constant length of the pendulum, so r = l.

Lagrangian mechanics

The Lagrangian is ^[1]

The Euler–Lagrange equations give :

and

showing that angular momentum is conserved.

Hamiltonian mechanics

The Hamiltonian is

where

and

References

1. ^{{cite book | last = Landau | first = Lev Davidovich | authorlink = |author2=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}}

1 : Pendulums

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Lagrangian mechanics

Hamiltonian mechanics

See also

References