Re: [math-fun] spherical pendulums?

Here's a related problem:

A point particle of mass M (i.e., zero moment of inertia) is sliding frictionlessly around inside a vertical cylinder; gravity is downwards of strength G. What are the paths?

Imagine drawing a parabolic arc on a sheet of transparent paper, and wrapping it around the inside of the cylinder. This is parametrised by: x = r cos(wt) y = r sin(wt) z = -½gt² (w, r and g are constants, namely the angular speed, radius and gravitational field strength, respectively.) Sincerely, Adam P. Goucher