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

The Lagrangian is

The Euler–Lagrange equations give :

and

showing that angular momentum is conserved.

Hamiltonian mechanics

The Hamiltonian is

where

and

See also

References