On motions without falling of an inverted pendulum with dry friction. (English) Zbl 1411.70030

Summary: An inverted planar pendulum with horizontally moving pivot point is considered. It is assumed that the law of motion of the pivot point is given and the pendulum is moving in the presence of dry friction. Sufficient conditions for the existence of solutions along which the pendulum never falls below the horizon are presented. The proof is based on the fact that solutions of the corresponding differential inclusion are right-unique and continuously depend on initial conditions, which is also shown in the paper.


70K40 Forced motions for nonlinear problems in mechanics
37B55 Topological dynamics of nonautonomous systems
34A60 Ordinary differential inclusions
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