The contact problem in Lagrangian systems with redundant frictional bilateral and unilateral constraints and singular mass matrix. The all-sticking contacts problem. (English) Zbl 1437.70010
Summary: In this article we analyze the following problem: given a mechanical system subject to (possibly redundant) bilateral and unilateral constraints with set-valued Coulomb’s friction, provide conditions such that the state, which consists of all contacts sticking in both tangential and normal directions, is solvable. The analysis uses complementarity problems, variational inequalities, and linear algebra, hence it provides criteria which are, in principle, numerically tractable. An algorithm and several illustrating examples are proposed.
MSC:
| 70E55 | Dynamics of multibody systems |
| 74M10 | Friction in solid mechanics |
| 74M15 | Contact in solid mechanics |
Keywords:
Lagrangian systems; set-valued friction; complementarity conditions; contact problem; redundant constraints; singular mass matrix; variational inequality; tangent cone; normal cone; force closure; form closureReferences:
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