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Separability of completely integrable dynamical systems admitting alternative Lagrangian descriptions

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Abstract

It is shown that whenever a (1, 1)-type tensor field, defined through two alternative Lagrangians, implies complete integrability for a second-order Lagrangian vector field Γ on the tangent bundle of a given configuration manifold, then a bundle atlas can be found in which both Γ and a class of equivalent Lagrangians are completely separated into a sum of second-order vector fields and Lagrangians, each one corresponding to a single degree of freedom.

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References

  1. Arnol'd, V. I., Méthodes Mathématiques de la Mécanique Classique, MIR, Moscow, 1976, p. 49.

    Google Scholar 

  2. Crampin, M., J. Phys. A14, 2567 (1981); Phys. Lett. A95, 209 (1983); J. Phys. A16, 3755 (1983).

    Google Scholar 

  3. De Filippo, S., Marmo, G., and Vilasi, G., Phys. Lett. B117, 418 (1982).

    Article  Google Scholar 

  4. De Filippo, S., Salerno, M., Marmo, G., and Vilasi, G., ‘A New Characterization of Completely Integrable Systems’, Nuovo Cim. B, in press.

  5. Marmo, G., Proc. of the International Conference on Geometry and Physics, Florence, 1982.

  6. Crampin, M., Marmo, G., and Rubano, C., Phys. Lett. A97, 88 (1983).

    Article  Google Scholar 

  7. Sarlet, W., Cantrijn, F., and Crampin, M., J. Phys. A17, 1999 (1984).

    Google Scholar 

  8. De Filippo, S., Marmo, G., Salerno, M., and Vilasi, G., ‘On the Phase Manifold Geometry of Integrable Nonlinear Field Theories’, University of Salerno, preprint (1982).

  9. De Filippo, S., Salerno, M., Vilasi, G., and Marmo, G., Lett. Nuovo. Cim. 37, 105 (1983).

    Google Scholar 

  10. Ferrario, C., Lo Vecchio, G., Marmo, G., and Morandi, G., Lett. Nuovo Cim. 38, 97 (1983).

    Google Scholar 

  11. Marmo, G. and Rubano, C., Nuovo Cim. B78, 70 (1983).

    Google Scholar 

  12. Currie, D. G., Saletan, E. J., J. Math. Phys. 7, 967 (1962).

    Google Scholar 

  13. Giandolfi, F., Marmo, G., and Rubano, C., Nuovo Cim. B66, 34 (1981).

    Google Scholar 

  14. Klein, J., Ann. Inst. Fourier 13, 191 (1963); Godbillon, C., Géometrie Différentielle et Mécanique Analitique, Hermann, Paris, 1968.

    Google Scholar 

  15. Hojman, S. and Ramos, S., J. Phys. A15, 3475 (1982).

    Google Scholar 

Download references

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Authors and Affiliations

  1. Istituto di Fisica dell'Università, Ferrara, Italy

    C. Ferrario & G. Lo Vecchio

  2. Dipartimento di Fisica, Napoli, Italy

    G. Marmo

  3. INFN, Napoli, Italy

    G. Marmo

  4. Dipartimento di Fisica dell'Università, Modena, Italy

    G. Morandi

Authors
  1. C. Ferrario
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  2. G. Lo Vecchio
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  3. G. Marmo
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  4. G. Morandi
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Ferrario, C., Lo Vecchio, G., Marmo, G. et al. Separability of completely integrable dynamical systems admitting alternative Lagrangian descriptions. Lett Math Phys 9, 141–148 (1985). https://doi.org/10.1007/BF00400712

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  • DOI: https://doi.org/10.1007/BF00400712

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