Standard Inelastic Shocks and the Dynamics of Unilateral Constraints

This paper is devoted to mechanical systems with a finite number of degrees of freedom; let q1,...,qn denote (possibly local) coordinates in the configuration manifold Q. In addition to the constraints, bilateral and frictionless, which have permitted such a finite-dimensional parametrization of Q, we assume the system submitted to a finite family of unilateral constraints whose geometrical effect is expressed by v inequalities $${f_\alpha }\left( q \right) \leq 0$$ (1.1) defining a closed region L of Q. As every greek index in the sequel, α takes its values in the set {1,2,...,v}. The v functions fα are supposed C1, with nonzero gradients, at least in some neighborhood of the respective surfaces fα = 0; for the sake of simplicity, we assume them independent of time.