# 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 Élie 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.

##### MSC:
 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: