Some results on the existence of forced oscillations in mechanical systems

DOI10.1134/S0081543820050193zbMath1475.70020arXiv1912.03987OpenAlexW3111520953MaRDI QIDQ2214297

I. Yu. Polekhin

Publication date: 8 December 2020

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.03987

zbMATH Keywords

periodic solutionsgeodesicinverted pendulumforced oscillationsNagumo conditionWażewski methodLefschetz-Hopf theorem

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Forced motions for nonlinear problems in mechanics (70K40)

Cites Work

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• On forced oscillations in groups of interacting nonlinear systems
• Forced oscillations of a massive point on a compact surface with a boundary
• Lectures on algebraic topology.
• On topological obstructions to global stabilization of an inverted pendulum
• On periodic solutions in the Whitney's inverted pendulum problem
• Two-point boundary value problems. Lower and upper solutions
• Calculus of variations in the large, existence of trajectories in a domain with boundary, and Whitney's inverted pendulum problem
• Periodic and bounded solutions in blocks for time-periodic nonautonomous ordinary differential equations
• Examples of topological approach to the problem of inverted pendulum with moving pivot point

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