This paper is a summary of a comprehensive study of the problem of predicting the accelerations of a set of rigid, three‐dimensional bodies in contact in the presence of Coulomb friction. We begin with a brief introduction of this problem and its governing equations. This is followed by the introduction of complementarity formulations for the contact problem under two friction laws: Coulomb's Law of quadratic friction and an approximated pyramid law. Existence and uniqueness results for the complementary problems are presented. Algorithms for solving these problems are proposed and their convergence properties are discussed. Computational results are presented and conclusions are drawn.

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