Nonholonomic Systems

Nonholonomic constraints only limit the velocity, but not the position of a mechanical system. The positional degree of freedom of nonholonomic systems therefore exceeds the velocity degree of freedom. Based on the formulations used for holonomic multibody systems, the kinematics and dynamics of nonholonomic systems are considered using the introductory example of a cart with two wheels corresponding to a knife sliding on a plane. The equations of motion in dependent absolute motion quantities as well as in minimal coordinates and minimal velocities are compared. Corresponding formulations are derived for a ball rolling without slippage on a rotating plane. In addition, conditions for the integrability of systems of kinematic constraints are formulated and illustrated with examples.