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Standard inelastic shocks and the dynamics of unilateral constraints

Abstract : This paper is devoted to mechanical systems with a finite number of degrees of freedom let $q^1, \ldots, q^n$ denote (possibly local) coordinates inthe 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 $f-\alpha(q) \leq 0$ 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 $f_α$ are supposed $C^1$, with nonzero gradients, at least in some neighborhood of the respective surfaces $f_α = 0$; for the sake of simplicity, we assume them independent of time.
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Jean Jacques Moreau. Standard inelastic shocks and the dynamics of unilateral constraints. Unilateral Problems in Structural Analysis, 1983, 9783211818596. ⟨10.1007/978-3-7091-2632-5_9⟩. ⟨hal-01544442⟩



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