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Construction of Lagrangian and Hamiltonian structures starting from one constant of motion

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Abstract

The problem of the construction of Lagrangian and Hamiltonian structures starting from two first-order equations of motion is presented. This approach requires the knowledge of one (time independent) constant of motion for the dynamical system only. The Hamiltonian and Lagrangian structures are constructed, the Hamilton–Jacobi equation is then written and solved, and the second (time dependent) constant of the motion for the problem is explicitly exhibited.

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Authors and Affiliations

  1. Departamento de Ciencias, Facultad de Artes Liberales, Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago, Chile

    Sergio A. Hojman

  2. Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile

    Sergio A. Hojman

  3. Centro de Recursos Educativos Avanzados, CREA, Santiago, Chile

    Sergio A. Hojman

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  1. Sergio A. Hojman
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Correspondence to Sergio A. Hojman.

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Hojman, S.A. Construction of Lagrangian and Hamiltonian structures starting from one constant of motion. Acta Mech 226, 735–744 (2015). https://doi.org/10.1007/s00707-014-1228-8

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  • DOI: https://doi.org/10.1007/s00707-014-1228-8

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