Consider the (physics) situation of a sphere of radius R rolling without slipping on a plane. The configuration of the sphere is given by the cooordinates of the center of the sphere and two angles for its orientation. When the sphere rolls over some given (closed) path in the plane, then its orientation can be changed relative to the starting orientation.(adsbygoogle = window.adsbygoogle || []).push({});

What would be the way to describe the kinematics of this system or systems like this? I would like for example

- to derive formulas for the final orientation given the starting orientation and a closed path on the plane.

- Answer whether any orientation can be achieved at the origin by some path starting from a given orientation at the origin (i suspect yes).

- understand the general framework for decribing such systems and the major theorems known as this is heavily connected to geometric phases in physics. I think mathematics calls it a holonomy, but physicists call it a nonholonomic system (go figure)

Most of what I googled on holonomy was completely incomprehensible to me and I couldn't find any connection with the described physical situation. If anyone can explain (give short overview of) this math-area to a physicist and point to some introductory material I'd be much grateful

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# Question for geometers: How to describe this problems of this kind?

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