Quadratic Programming in Mechanics: Dynamics of One-Sided Constraints

International audienceLet $S$ be a frictionless mechanical system with $n$ degrees of freedom; we denote by $q_1,q_2,\ldots,q_n$ the generalized coordinates, representing the point $q$ of a configuration space. A finite family of one-sided constraints is imposed on the system; the kinematic effect of these constraints is expressed by the conditions (assumed compatible) $f_{\alpha}(q, t) \geq 0$, $\alpha \in I$, finite set of indexes. For instance, some solid parts of the system may be in contact or become detached but they can never overlap. These constraints are frictionless, i.e., as long as the equalities hold in the expression above, the motion of the system is governed by Lagrange's equations with multipliers $\lambda_{\alpha}$, $\alpha\in I$