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Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with coulomb friction

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Abstract

In this paper, we study the problem of predicting the acceleration of a set of rigid, 3-dimensional bodies in contact with Coulomb friction. The nonlinearity of Coulomb's law leads to a nonlinear complementarity formulation of the system model. This model is used in conjunction with the theory of quasi-variational inequalities to prove for the first time that multi-rigid-body systems with all contacts rolling always has a solution under a feasibility-type condition. The analysis of the more general problem with sliding and rolling contacts presents difficulties that motivate our consideration of a relaxed friction law. The corresponding complementarity formulations of the multi-rigid-body contact problem are derived and existence of solutions of these models is established.

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Authors and Affiliations

  1. Department of Mathematical Sciences, The Johns Hopkins University, 21218-2689, Baltimore, MD, USA

    Jong-Shi Pang & Jeffrey C. Trinkle

  2. Department of Computer Science, Texas A&M University, 77843-3112, College Station, TX, USA

    Jong-Shi Pang & Jeffrey C. Trinkle

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  1. Jong-Shi Pang
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  2. Jeffrey C. Trinkle
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Correspondence to Jeffrey C. Trinkle.

Additional information

The research of this author was based on work supported by the National, Science Foundation under grants DDM-9104078 and CCR-9213739.

The research of this author was partially supported by the National Science Foundation under grant IRI-9304734, by the Texas Advanced Research Program grant 999903-078, and by the Texas Advanced Technology Program under grant 999903-095.

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Pang, JS., Trinkle, J.C. Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with coulomb friction. Mathematical Programming 73, 199–226 (1996). https://doi.org/10.1007/BF02592103

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  • DOI: https://doi.org/10.1007/BF02592103

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