an:04007291
Zbl 0621.58020
Cantrijn, F.; Cari??ena, J. F.; Crampin, M.; Ibort, L. A.
Reduction of degenerate Lagrangian systems
EN
J. Geom. Phys. 3, No. 3, 353-400 (1986).
00166135
1986
j
37J99 53C15 70H03 53C80
tangent bundle geometry; degenerate Lagrangian; regularization problem; reduction
Let a degenerate Lagrangian L be given on some velocity phase space (i.e. a tangent bundle). Is it possible to construct another velocity space and a regular Lagrangian which contains the same dynamical information as L ? This important question is referred to as the ''regularization problem'' for degenerate Lagrangians. The authors find conditions which guarantee the existence of such a regularization and describe a relevant class of Lagrangians for which the above question admits an affirmative answer. The connection with the canonical approach to the regularization problem of degenerate systems (Dirac's theory) and the reduction of systems with symmetry (Marsden-Weinstein theory) is also discussed. The paper is completed with a few typical examples and applications. Two appendices are devoted to the proof of those intermediate results which are of interest on their own.
J.Szilasi