2018/06/04 by Ivan Polekhin, Polekhin, Ivan
Computer Science · Engineering · Mathematics · #Aerospace Engineering and Control Systems #Classical Analysis and ODEs (math.CA) #Control and Dynamics of Mobile Robots #Dynamical Systems (math.DS) #Educational Technology and Optimization #FOS: Mathematics #math.CA #math.DS
paper · pdf · doi:10.48550/arxiv.1806.01075
arxiv created 2018/06/04 · openalex publication_date 2018/06/04 · arxiv updated 2018/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 horizontal positions 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.