A discretization scheme for contact/impact problems related to the modeling of gears is proposed. The problem is first discretized in time and then a variational formulation for the resulted one step problem is developed. A Finite Element discretization completes the discretization process. The scheme is reinterpretation of the general Simo-Laursen-Chavla algorithm in the contest of rigid body motion superimposed with small elastic deformation; it conserves precisely linear momentum and total energy, and approximately the angular momentum.

The discretization method is illustrated with two numerical examples: the standard 1D impact problem for an elastic rod, and a 2D model problem of an elastic wheel bouncing within a constraining box.

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