Remarks on Forced Oscillations in Some Systems with Gyroscopic Forces

DOI10.20537/nd200208zbMath1459.70018arXiv1912.04076OpenAlexW3037372266MaRDI QIDQ3304726

I. Yu. Polekhin

Publication date: 3 August 2020

Published in: Nelineinaya Dinamika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.04076

zbMATH Keywords

frictionspherical pendulumforced oscillationWazewski methodgyroscopic force

Mathematics Subject Classification ID

Motion of a rigid body in contact with a solid surface (70E18) Motion of a rigid body with a fixed point (70E17)

Cites Work

• On forced oscillations in groups of interacting nonlinear systems
• Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level
• Closed magnetic geodesics on \(S^2\)
• Forced oscillations of a massive point on a compact surface with a boundary
• Periodic solutions of Lagrangian systems on a compact manifold
• On topological obstructions to global stabilization of an inverted pendulum
• On periodic solutions in the Whitney's inverted pendulum problem
• The existence of two closed geodesics on every Finsler 2-sphere
• Calculus of variations in the large, existence of trajectories in a domain with boundary, and Whitney's inverted pendulum problem
• The Hamiltonian formalism and a many-valued analogue of Morse theory
• 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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