Bounds on the Friction-Dominated Motion of a Pushed Object

We consider the friction-dominated, or quasistatic, motion of a rigid body being pushed over a horizontal plane in situations where the precise frictional interaction cannot be determined. Consequently, the complete set of motions corresponding to all possible friction distributions must be found. We demonstrate that if the contact region between the body and the support ing plane has one or two components, the set of all possible motions coincides with the set of motions arising for friction distributions restricted to two-point contact in the boundary of the contact region. These two-point problems are solved analytically. In previous formulations of the problem, general friction support had only been reduced to the case of tripods, which does not have an analytic solution. Various examples are presented, and an effective numerical scheme based on a dissipation function is implemented.

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