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On the hybrid dynamics of planar mechanisms supported by frictional contacts. II: stability of two-contact rigid body postures

This paper is concerned with the hybrid dynamics and stability of a planar rigid body supported by two frictional contacts in a gravitational field. The stability of equilibrium postures is investigated under initial perturbations which may involve sliding or separation of the contacts. The paper formulates the hybrid dynamics induced by collisions and impacts at the two contacts. The Zeno behavior of bouncing and clattering motion converging to limit points of one- or two-contact re-establishment are analyzed, and a condition guaranteeing convergence to a Zeno point is derived. Finally, this condition is combined with the results of the companion paper to derive sufficient conditions for stability of frictional two-contact equilibrium postures of a planar rigid body.