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

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

Loading...

Similar Threads - Question geometers describe | Date |
---|---|

A Question About Elementary Fiber Bundle Example | Mar 1, 2018 |

I Some Question on Differential Forms and Their Meaningfulness | Feb 19, 2018 |

A Simple metric tensor question | Aug 14, 2017 |

I Question about Haar measures on lie groups | Jul 12, 2017 |

I Torsion on cylinder described differentially | Oct 31, 2016 |

**Physics Forums - The Fusion of Science and Community**