Rolling balls over spheres in \newcommand{\m}{\mathfrak m} {R}^n}
Abstract
We study the rolling of the Chaplygin ball in over a fixed -dimensional sphere without slipping and without slipping and twisting. The problems can be naturally considered within a framework of appropriate modifications of the L + R and LR systems—well known systems on Lie groups with an invariant measure. In the case of the rolling without slipping and twisting, we describe the -Chaplygin reduction to S n-1 and prove the Hamiltonization of the reduced system for a special inertia operator.
- Publication:
-
Nonlinearity
- Pub Date:
- September 2018
- DOI:
- 10.1088/1361-6544/aac75c
- arXiv:
- arXiv:1804.03697
- Bibcode:
- 2018Nonli..31.4006J
- Keywords:
-
- Mathematical Physics;
- Mathematics - Differential Geometry;
- 37J60;
- 37J35;
- 70H45
- E-Print:
- 22 pages, figure is added, subsection 3.3 is rewritten, to appear in Nonlinearity