# Spherical Pendulum

1. Jan 3, 2013

### praeclarum

I thought of this question the other day, and I was unable to solve it. A Google search has not helped, so I thought I might post it here.

A point mass hangs from a rod of length "l" from the center of a pendulum. The only forces acting upon the point mass are the force of gravity and the force of constraint (keeping it distance "l" from the center). Is there a function that describes the motion of the point mass?

2. Jan 3, 2013

### tiny-tim

hi praeclarum!
do you mean two pendulums hinged together?

show us what you've tried, and where you're stuck, and then we'll know how to help!

3. Jan 3, 2013

### praeclarum

OK. It's not as complicated as a double pendulum. It's just a single pendulum where the mass is constrained to a sphere (rather than the 2-dimensional case where you have a circle).

Well, one thought I had was to solve for the potential energy of the system, since that's just

mgh+1/2mv^2 = C

The mass is just a constant, and we can get rid of it.

From this point, I am stuck, however, and I don't know where to go from here. I was thinking the initial velocity must be perpendicular to the force of constraint and was wondering if you could split up the motion into just x and y components to solve it, but that seemed fruitless upon inspection.

I am looking for a general function that describes the motion of the point around the sphere. Your help is appreciated greatly.

4. Jan 3, 2013

### tiny-tim

so it's basically a mass moving on the inside of a sphere?

hmm … in linear problems we usually use conservation of energy and conservation of momentum, sooo …

have you tried conservation of angular momentum ?