Nonlocal criteria for the existence and stability of periodic oscillations in autonomous Hamiltonian systems

DOI10.1016/0021-8928(86)90056-0zbMath0618.70012OpenAlexW2067357719MaRDI QIDQ1089148

Alexandr A. Zevin

Publication date: 1986

Published in: Journal of Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8928(86)90056-0

zbMATH Keywords

nonlinear oscillationsequilibrium configurationvariational methodsorbital stabilityfirst approximationLyapunov theoremoscillation periodsisoenergetic surfaceBilateral estimatesHessian of a Hamilton functionsingle-parameter families of periodic solutionsstring with lumped asses

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Stability for nonlinear problems in mechanics (70K20) Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (1)

Nonlocal generalization of the Lyapunov theorem

Cites Work

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• Some conditions for the existence and stability of periodic oscillations in non-linear non-autonomous Hamiltonian systems
• Periodic Solutions of Hamiltonian Systems: A Survey
• Gravity gradient stabilization of large space stations

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