Classical Mechanics - Special Interest Problem

Using spherical coordinates (q and f), find the equations of motion for a small mass m that slides without friction on the inside surface of a sphere of radius R. Assume the mass stays in contact with the sphere at all times.

This simplified problem is an approximation to the problem of the motorcycle rider in a spherical cage that performs at some circuses. Once in motion, the rider must make certain that sufficient speed is maintained to keep the motorcycle in contact with cage at all times. Of course, friction plays an important role in allowing the rider to start from rest and change the plane of rotation at will. Torque and angular momentum also play an important roll in maintaining stability.

Hardcopy entries should be submitted in class by noon on Monday of next week. Answers should be concise but complete.