Skip to main content
SpringerLink
Log in

Time-Dependent Lagrangians Invariant by a Vector Field

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

We study the reduction of nonautonomous regular Lagrangian systems by symmetries, which are generated by vector fields associated with connections in the configuration bundle of the system Q × \(\mathbb{R}\) → \(\mathbb{R}\). These kind of symmetries generalize the idea of ‘time-invariance’ (which corresponds to taking the trivial connection in the above trivial bundle).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abraham, R. and Marsden, J. E.: Foundations of Mechaniccs, Addison-Wesley, Englewood Cliffs, 1978.

    Google Scholar 

  2. Choquet-Bruhat, Y.: Géométrie différentielle et systèmes extérieurs, Dunod, Paris, 1968.

    Google Scholar 

  3. Echeverría-Enríquez, A., Muñoz-Lecanda, M. C. and Román-Roy, N.: Geometrical setting of time-dependent regular systems. Alternative models, Rev. Math. Phys. 3(3) (1991), 301-330.

    Google Scholar 

  4. Echeverría-Enríquez, A., Muñoz-Lecanda, M. C. and Román-Roy, N.: Non-standard connections in classical mechanics, J. Phys. A: Math. Gen. 28 (1995), 553-5567.

    Google Scholar 

  5. Echeverría-Enríquez, A., Muñoz-Lecanda, M. C. and Román-Roy, N.: Reduction of presymplectic manifolds with symmetry, Rev. Math. Phys. 11(10) (1999), 1209-1247.

    Google Scholar 

  6. García, P. L.: The Poincaré-Cartan invariant in the calculus of variations, Sympos. Math. 14 (1974), 219-240.

    Google Scholar 

  7. Goldschmidt, H. and Sternberg, S.: The Hamilton-Cartan formalism in the calculus of variations, Ann. Inst. Fourier Grenoble 23(1) (1973), 203-267.

    Google Scholar 

  8. Greub, W., Halpering, S. and Vanstone, S.: Connections, Curvature and Cohomology, vol I, Academic Press, New York, 1972.

    Google Scholar 

  9. De León, M., Marín, J., Marrero, J. C., Muñoz-Lecanda, M. and Román-Roy, N.: Singular Lagrangian systems on jet bundles, math-ph/0105012 (2001).

  10. Libermann, P. and Marle, C. M.: Symplectic Geometry and Analytical Dynamics, D. Reidel Publ. Co., Dordrecht, 1987.

    Google Scholar 

  11. Mangiarotti, L. and Sardanashvily, G.: Gauge Mechanics, World Scientific, Singapore, 1998.

    Google Scholar 

  12. Marsden, J. E. and Scheurle, J.: The reduced Euler-Lagrange equations, Fields Inst. Comm. 1 (1993), 139-164.

    Google Scholar 

  13. Marsden, J. E. and Weinstein, A.: Reduction of symplectic manifolds with symmetry, Rep. Math. Phys. 5 (1974), 121-130.

    Google Scholar 

  14. Saunders, D. J.: The Geometry of Jet Bundles, London Math. Soc. Lecture Note Ser. 142, Cambridge Univ. Press.

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática Aplicada IV, Edificio C-3, Campus Norte UPC, C/, Jordi Girona 1, E-08034, Barcelona, Spain

    Miguel C. Muñoz-Lecanda, Narciso Román-Roy & F. Javier Yániz-Fernández

Authors
  1. Miguel C. Muñoz-Lecanda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Narciso Román-Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. Javier Yániz-Fernández
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Muñoz-Lecanda, M.C., Román-Roy, N. & Yániz-Fernández, F.J. Time-Dependent Lagrangians Invariant by a Vector Field. Letters in Mathematical Physics 57, 107–121 (2001). https://doi.org/10.1023/A:1017963123948

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1017963123948

Search

Navigation