Time-dependent Lagrangians invariant by a vector field

Letters in Mathematical Physics

Volumn 57, Issue 2, 2001, Pages 107-121

  Muñoz Lecanda, Miguel C ^a   Román Roy, Narciso ^a   Yániz Fernández, F Javier ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Connections; Dynamical systems; Lagrangian formalism; Symmetries; Vector fields

Indexed keywords

EID: 18044402864     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1017963123948     Document Type: Article

References (14)

1. Abraham, R, and Marsden, J. E.: Foundations of Mechaniccs, Addison-Wesley, Englewood Cliffs, 1978.
2. Choquet-Bruhat, Y.: Géométrie différentielle et systèmes extérieurs, Dunod, Paris, 1968.
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.
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.
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.
6. García, P. L.: The Poincaré-Cartan invariant in the calculus of variations, Sympos. Math. 14 (1974), 219-240.
7. Goldschmidt, H. and Sternberg, S.: The Hamilton-Cartan formalism in the calculus of variations, Ann. Inst. Fourier Grenoble 23(1) (1973), 203-267.
8. Greub, W., Halpering, S. and Vanstone, S.: Connections, Curvature and Cohomology, vol I, Academic Press, New York, 1972.
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.
11. Mangiarotti, L. and Sardanashvily, G.: Gauge Mechanics, World Scientific, Singapore, 1998.
12. Marsden, J. E. and Scheurle, J.: The reduced Euler-Lagrange equations, Fields Inst. Comm. 1 (1993), 139-164.
13. Marsden, J. E. and Weinstein, A.: Reduction of symplectic manifolds with symmetry, Rep. Math. Phys. 5 (1974), 121-130.
14. Saunders, D. J.: The Geometry of Jet Bundles, London Math. Soc. Lecture Note Ser. 142, Cambridge Univ. Press.