A unifying approach for rolling symmetric spaces

Abstract

The main goal of this paper is to present a unifying theory to describe the pure rolling motions of Riemannian symmetric spaces, which are submanifolds of Euclidean or pseudo-Euclidean spaces. Rolling motions provide interesting examples of nonholonomic systems and symmetric spaces appear associated to important applications. We make a connection between the structure of the kinematic equations of rolling and the natural decomposition of the Lie algebra associated to the symmetric space. This emphasises the relevance of Lie theory in the geometry of rolling manifolds and explains why many particular examples scattered through the existing literature always show a common pattern.