Reduction of nonholonomic systems

Abstract

The positional degrees of freedom of a mechanical system are by nonholonomic constraints further reduced to a smaller number of motional degrees of freedom. It is shown how the corresponding equations of motion can be reduced to a minimal number using generalized coordinates and generalized velocities. The theoretical results are applied to an actively controlled vehicle with stiff tires. One scalar control variable provides full contollability of the position of the vehicle moving on a plane surface. The control strategy is found for stationary and instationary motions.