Equivalence of the generalized Lie-Hori method and the method of averaging

DOI10.1007/BF01231091zbMath0599.70029MaRDI QIDQ3735122

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Publication date: 1984

Published in: Celestial Mechanics (Search for Journal in Brave)

zbMATH Keywords

method of averagingvan der Pol equationDuffing's equationperturbation theoriesgeneralized Lie- Hori methodnon-canonical dynamical systemsoscillator with quadratic damping

Mathematics Subject Classification ID

Qualitative theory for ordinary differential equations (34C99) Linear vibration theory (70J99) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (5)

A note about certain arbitrariness in the solution of the homological equation in Deprit's method ⋮ Application of the Hori method in the theory of nonlinear oscillations ⋮ Asymptotic stability of a pendulum with quadratic damping ⋮ A note on uniqueness of the normal form for quasi-integrable systems ⋮ Uniform global asymptotic stability for oscillators with superlinear damping

Uses Software

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Cites Work

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• A Mathematical Theory of the Orbits About an Oblate Planet
• Canonical transformation applications to optimal trajectory analysis.
• The equivalence of von Zeipel mappings and Lie transforms
• Explicit recursive algorithms for the construction of equivalent canonical transformations
• Lie transforms and the Hamiltonization of non-Hamiltonian systems
• An extended canonical perturbation method

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