# American Institute of Mathematical Sciences

December  2018, 10(4): 411-417. doi: 10.3934/jgm.2018015

## On motions without falling of an inverted pendulum with dry friction

 Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

* Corresponding author: Ivan Polekhin

Received  March 2017 Revised  September 2018 Published  November 2018

Fund Project: This work was supported by the Russian Science Foundation under Grant No. 14-50-00005.

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.

Citation: Ivan Polekhin. On motions without falling of an inverted pendulum with dry friction. Journal of Geometric Mechanics, 2018, 10 (4) : 411-417. doi: 10.3934/jgm.2018015
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