zbMATH — the first resource for mathematics

\(G_2\) and the rolling distribution. (English) Zbl 1251.70008
Two balls of different radii, \(r\) and \(R\), rolling along each other, without slipping or spinning, are considered. The configuration space for this system is a 5-dimensional manifold on which the no-slip/no-spin condition defines a rank 2 distribution, the rolling distribution which is related with the exceptional Lie group \(G_2\). A theorem concerning properties if this distribution was proved by √Člie Cartan in 1898 which is valid only for the radii ratio \(3:1\) or \(1:3\). The authors propose another proof of this theorem avoiding the Cartan’s sophisticated approach.

70E18 Motion of a rigid body in contact with a solid surface
37J60 Nonholonomic dynamical systems
70F25 Nonholonomic systems related to the dynamics of a system of particles
Lie groups
Full Text: DOI Link