The energetic/variational interpretation of Poincaré's criterion for the orbital stability of limit cycles of autonomous systems

DOI10.1016/0020-7225(87)90122-4zbMath0618.70011OpenAlexW2083955871MaRDI QIDQ1089147

John G. Papastavridis

Publication date: 1987

Published in: International Journal of Engineering Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0020-7225(87)90122-4

zbMATH Keywords

limit cyclesnonlinear oscillationscharacteristic exponentsautonomous systemsorbital stabilityphase-space methodsHamiltonian variational principlesPoincaré criterion

Mathematics Subject Classification ID

Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Lagrange's equations (70H03) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

Cites Work

• Generalization of the method of slowly varying amplitude and phase to non-linear oscillatory systems with two degrees of freedom
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