Penalty method for impact in generalized coordinates

The dynamical impact problem in generalized coordinates is approximated by the penalty method, which is often used for numerical approximation. The correct penalty terms are devised to include loss of energy at impact, i.e. an arbitrary restitution coefficient eε [0, 1]. There is a certain freedom in the choice of the penalty term, which permits more convenient practical choices. The convergence of this approximation is proved. The result presented here is much more general than the results already known: beyond generalized coordinates, it includes a smooth time-dependent set of constraints and the possibility of zero restitution coefficients.