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J. Geometric Mech., 2018, Volume 10, Issue 4, Pages 411–417 (Mi jgeom1)  

On motions without falling of an inverted pendulum with dry friction

Ivan Polekhin

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

Abstract: 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. Sucient 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 di erential inclusion are right-unique and continuously depend on initial conditions, which is also shown in the paper.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under Grant No. 14-50-00005.


DOI: https://doi.org/10.3934/jgm.2018015


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Document Type: Article
Language: English

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