Theoretical analysis on nonholonomic dynamic systems with affine constraints

This paper deals with affine constraints and nonholonomic systems. We first derive nonholonomic dynamic systems with affine constraints under assumption of complete nonintegrability. We next show that the system is strongly locally accessible at any zero-velocity point and small-time locally controllable at any equilibrium under Sussmann´s condition. Moreover a necessary condition of locally asymptotic stabilizability at any equilibrium is derived. Finally, we show a physical example for verification of our theory.