Preprint Number 15–30 THE SIGNIFICANCE OF LIE THEORY IN THE GEOMETRY OF ROLLING MOTIONS

Abstract: The main goal of this paper is to present a unifying theory to describe the pure rolling motions of Riemannian symmetric spaces. We make a clear con-nection between the structure of the kinematic equations of rolling and the natural decomposition of the Lie algebra associated to the symmetric space. This empha-sizes the relevance of Lie theory in the geometry of rolling manifolds. It becomes clear why many particular examples scattered through the existing literature always show a common pattern. 1