A General Method for Writing the Dynamical Equations of Nonholonomic Systems with Ideal Constraints

The basic notions of the dynamics of nonholonomic systems are revisited in order to give a general and simple method for writing the dynamical equations for linear as well as nonlinear kinematical constraints. The method is based on the representation of the constraints by parametric equations, which are interpreted as dynamical equations, and leads to firstorder differential equations in normal form, involving the Lagrangian coordinates and auxiliary variables (the use of Lagrangian multipliers is avoided). Various examples are illustrated.