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The Hamiltonian transformation in quadratic lie transforms

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Abstract

The algorithm for Hamiltonian transformation in the quadratic perturbation technique of one of the authors admits of various equivalent forms. Using as a criterion the number of inter-term multiplications required for transformation, however, the amount of effort required to obtain the transformed Hamiltonian is not equivalent among these forms. Each is considered in some detail, and general guidelines for the choice of ‘most efficient’ algorithm to be used in a given problem are provided. Their utility is demonstrated by application to Duffing's equation.

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References

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Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Notre Dame, 46556, Notre Dame, IN, USA

    R. A. Howland

  2. Department of Aerospace Engineering, University of Cincinnati, 45221, Cincinnati, OH, USA

    D. L. Richardson

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  1. R. A. Howland
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  2. D. L. Richardson
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Howland, R.A., Richardson, D.L. The Hamiltonian transformation in quadratic lie transforms. Celestial Mechanics 32, 99–107 (1984). https://doi.org/10.1007/BF01231118

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  • DOI: https://doi.org/10.1007/BF01231118

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