Application of constraint stabilization to nonholonomic mechanics

This paper compares some methods of solving problems of nonholonomic systems. Appropriate choice of generalized coordinates allows setting up the Chaplygin equations and separating the motion equations from constraints. Another common method of solving such problems is the method of the Lagrange multipliers. However, using numerical integration in this case leads to error accumulation caused by deviations from the constraints equations and, as a result, to the solution instability in relation to the constraints equations. Constraint stabilization can be applied to remove this instability using numerical integration. In this paper, this method of constraint stabilization is applied to generate a stable solution of motion equations with the Lagrange multipliers. The Euler and Runge-Kutta methods are used for numerical integration. In addition, at solving stabilization problem, an appropriate set of parameters can be selected to minimize the difference between the solution of the Chaplygin equations and that of equations with the Lagrange multipliers.