Lie transforms and the Hamiltonization of non-Hamiltonian systems

DOI10.1007/BF01231400zbMath0234.34069MaRDI QIDQ5642892

Ahmed Aly Kamel

Publication date: 1971

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

Mathematics Subject Classification ID

Hamilton's equations (70H05) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (9)

The uniqueness of normal forms via Lie transforms and its applications to Hamiltonian systems ⋮ Equivalence of the generalized Lie-Hori method and the method of averaging ⋮ An extended canonical perturbation method ⋮ [https://portal.mardi4nfdi.de/wiki/Publication:4118118 Perturbations des syst�mes diff�rentiels et r�sultats de g�om�trie diff�rentielle] ⋮ A new radial, natural, higher-order intermediary of the main problem four decades after the elimination of the parallax ⋮ An accelerated elimination technique for the solution of perturbed Hamiltonian systems ⋮ A First Order Automated Lie Transform ⋮ Multiple-parameter Lie transform ⋮ Quadratic analytical solution of general systems through formal hamiltonization

Cites Work

• Canonical transformations depending on a small parameter
• Expansion formulae in canonical transformations depending on a small parameter
• Equivalence of the perturbation theories of Hori and Deprit
• A new algorithm for the Lie transformation
• The equivalence of von Zeipel mappings and Lie transforms
• On a perturbation theory using Lie transforms
• Explicit recursive algorithms for the construction of equivalent canonical transformations
• Perturbation method in the theory of nonlinear oscillations

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