I'm trying to find the path of least time for a hollow sphere (a ping-pong ball) to roll from one point to another through an curve of interpolated points. The main problem here is that the ball isn't allowed to slide, only roll, which limits our steepest angle to about 40°. Although it isn't hard to look up and understand a solution for a sliding object with no height restriction, I found the problem to be significantly more difficult when the slope is limited, and there's a table in the way of dipping under point B.

Also, how does rotation/intertia affect the problem?

Here's a figure to help understand what I mean. The idea is for point A to be all the way up, and point B to be at ground-height. Thanks in advance.

I'm trying to find the path of least time for a hollow sphere (a ping-pong ball) to roll from one point to another through an curve of interpolated points. The main problem here is that the ball isn't allowed to slide, only roll, which limits our steepest angle to about 40°. Although it isn't hard to look up and understand a solution for a sliding object with no height restriction, I found the problem to be significantly more difficult when the slope is limited, and there's a table in the way of dipping under point B.

Also, how does rotation/inertia affect the problem?

Here's a figure to help understand what I mean. The idea is for point A to be all the way up, and point B to be at ground-height. Thanks in advance.