Computation of periodic solutions to pendulum type systems with a small parameter

DOI10.1134/S0965542520120167zbMath1459.34107OpenAlexW3120467269MaRDI QIDQ828132

Victor P. Varin

Publication date: 8 January 2021

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542520120167

zbMATH Keywords

periodic solutionsvariational equationscomputer algebra methodsformal differentiation

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Periodic solutions to ordinary differential equations (34C25) Theoretical approximation of solutions to ordinary differential equations (34A45) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Nonautonomous smooth dynamical systems (37C60)

Cites Work

• Integration of ordinary differential equations on Riemann surfaces with unbounded precision
• Asymptotic methods for solving the Hamilton equations by the parametrization of canonical transformations
• Research of the periodic solutions of the Hénon-Heiles nonintegrable Hamiltonian system by the Lindstedt-Poincaré method
• Periodic solutions of the N-body problem
• Degeneracies of periodic solutions to the Beletsky equation
• Normal form methods for symbolic creation of approximate solutions of nonlinear dynamical systems
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