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Singular Lagrangians: some geometric structures along the Legendre map

Xavier Gràcia1 and Josep M Pons2

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New geometric structures that relate the Lagrangian and Hamiltonian formalisms defined upon a singular Lagrangian are presented. Several vector fields are constructed in velocity space that give new and precise answers to several topics such as the projectability of a vector field to a Hamiltonian vector field, the computation of the kernel of the presymplectic form of a Lagrangian formalism, the construction of the Lagrangian dynamical vector fields and the characterization of dynamical symmetries.


PACS

45.20.Jj Lagrangian and Hamiltonian mechanics

02.40.Vh Global analysis and analysis on manifolds

MSC

70Hxx Hamiltonian and Lagrangian mechanics (See also 37Jxx)

57N16 Geometric structures on manifolds (See also 57M50)

Subjects

Mathematical physics

Dates

Issue 14 (13 April 2001)

Received 20 October 2000



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