Classification of symmetries for higher order Lagrangian systems.
Classification of symmetries for higher order Lagrangian systems II: The non-autonomous case.
Solving non-holonomic Lagrangian dynamics in terms of almost product structures.
Given a Lagrangian system with non-holonomic constraints we construct an almost product structure on the tangent bundle of the configuration manifold such that the projection of the Euler-Lagrange vector field gives the dynamics of the system. In a degenerate case, we develop a constraint algorithm which determines a final constraint submanifold where a completely consistent dynamics of the initial system exists.
Non-holonomic mechanical systems in jet bundles.
In this paper we present a geometrical formulation for Lagrangian systems subjected to non-holonomic constraints in terms of jet bundles. Cosymplectic geometry and almost product structures are used to obtained the constrained dynamics without using Lagrange multipliers method.
Conservation laws and symmetry in economic growth models: a geometrical approach.
The aim of the present paper is twofold. On one hand, we present a classification of infinitesimal symmetries for Lagrangian systems, and the corresponding Noether theorems. The derivation of the result is made by using the symplectic techniques. Some of the results were previously obtained by other authors (see Prince (1985) for instance), and an exhaustive presentation can be found in de León and Martín de Diego (1995, 1996). Let us note that these results are true even if the Lagrangian function...
Almost product structures and Poisson reduction of presymplectic systems.
Reduction of symplectic Lie algebroids by a Lie subalgebroid and a symmetry Lie group.
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