Rolling with Random Slipping and Twisting: A Large Deviation Point of View

Abstract

We revisit the rolling model from the perspective of probability. More precisely, we consider a Riemannian manifold rolling against the Euclidean space, where the rolling is combined with random slipping and twisting. The system is modelled as a stochastic differential equation of Stratonovich-type driven by semimartingales, on the orthonormal frame bundle. We prove the large deviation principles for the projection curves on the base manifold and their horizontal lifts respectively, provided the large deviations hold for the random Euclidean curves as semimartingales. A general large deviation result for the compact manifold and two special results for the noncompact manifold are established.