On stochastic non-holonomic systems

Abstract

A natural mechanical system is considered with ideal stochastic non-holonomic constraints under the action of potential, dissipative, and perturbing forces that depend on random (in general non-normal) paramters satisfying non-linear Ito stochastic differential equations. The corresponding stochastic equations of motion are constructed in Lagrangian and Hamiltonian variables, as well as the equations for finite-dimensional densities and characteristic functions. Stationary one-dimensional distributions are studied in Chaplygin normal stochastic non-holonomic systems. Systematic and fluctuational drift is analysed. The problems of a rolling ball and a rolling convex rigid body on a translationally vibrating horizontal plane are considered.