Singular Lagrangian Systems on Jet Bundles

Lie algebroid structures and Lagrangian systems on affine bundles

As a continuation of previous papers, we study the concept of a Lie algebroid structure on an affine bundle by means of the canonical immersion of the affine bundle into its bidual. We pay particular attention to the prolongation and various lifting procedures, and to the geometrical construction of Lagrangian-type dynamics on an affine Lie algebroid.

0 On Holomorphic Jet Bundles

Horizontal forms on jet bundles

We give an elementary proof that, if the order of a horizontal sform on a jet bundle does not increase under the operation of the horizontal differential, then the coefficients of the form must be polynomial of degree s in the highest-order coordinates. M.S.C. 2000: 58E99.

Singular Lagrangian Systems and Variational Constrained Mechanics on Lie Algebroids

The purpose of this paper is describe Lagrangian Mechanics for constrained systems on Lie algebroids, a natural framework which covers a wide range of situations (systems on Lie groups, quotients by the action of a Lie group, standard tangent bundles...). In particular, we are interested in two cases: singular Lagrangian systems and vakonomic mechanics (variational constrained mechanics). Sever...

Lagrangian reductive structures on gauge-natural bundles

A reductive structure is associated here with Lagrangian canonically defined conserved quantities on gauge-natural bundles. Infinitesimal parametrized transformations defined by the gauge-natural lift of infinitesimal principal automorphisms induce a variational sequence such that the generalized Jacobi morphism is naturally self-adjoint. As a consequence, its kernel defines a reductive split s...