A particle is confined to move on the surface of a circular cone with its axis on the vertical z axis, vertex at the origin (pointing down), and half-angle α. Required:
a. Write down the Lagrangian L in terms of the spherical polar coordinates r and φ.
b. Find the two equations of motion. Interpret the φ equation in terms of the angular momentum 4, and use it to eliminate φ from the r equation in favor of the constant e. Does your r equation make sense in the case that e-0?