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Separability structures corresponding to conservative dynamical systems

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Sommario

Si presenta un metodo di integrazione delle equazioni di Hamilton-Jacobi che corrispondono ad una hamiltoniana quadratica con potenziale e che soddisfano le condizioni di separabilità secondo Levi-Civita.

Si dimostra in modo costruttivo l'esistenza di opportuni sistemi di coordinate (dette coordinate separabili normali) e si determina la forma generale dell'equazione di Hamilton-Jacobi in tali coordinate.

Summary

We discuss a method of integration of the Hamilton-Jacobi equation corresponding to a quadratic Hamiltonian with a potential function and satisfying the Levi-Civita separability conditions.

We prove the existence of suitable coordinates (called normal separable coordinates) by direct construction and we establish the general form of the Hamilton-Jacobi equation in such coordinates.

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Authors and Affiliations

  1. Istituto di Fisica Matematica ≪J.L. Lagrange≫, Università di Torino, Italy

    Sergio Benenti & Giorgio Pidello

Authors
  1. Sergio Benenti
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  2. Giorgio Pidello
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Benenti, S., Pidello, G. Separability structures corresponding to conservative dynamical systems. Meccanica 19, 275–281 (1984). https://doi.org/10.1007/BF01556323

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  • DOI: https://doi.org/10.1007/BF01556323

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