Articles you may be interested inThe Hamiltonian framework on symplectic and cosymplectic manifolds is extended in order to consider classical field theories. To do this, the notion of k-cosymplectic manifold is introduced, and a suitable Hamiltonian formalism is developed so that the field equations for scalar and vector Hamiltonian functions are derived.

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.

In this note we revisit E. Cartan's address at the 1928 International Congress of Mathematicians at Bologna, Italy. The distributions considered here will be of the same class as those considered by Cartan, a special type which we call strongly or maximally non-holonomic. We set up the groundwork for using Cartan's method of equivalence (a powerful tool for obtaining invariants associated to geometrical objects), to more general non-holonomic distributions.

No abstract

One can develop a symplectic reduction procedure for higher order Lagrangian systems with symmetry. The reconstruction procedure of the dynamics is also studied and an application (spinning particle) is given at the end of the work.

We introduce the notion of almost s-tangent structures of higher order by abstracting the geometric structure of the space of /c-jets J k (R, M). These structures are a natural extension of almost tangent structures of higher order. The notion of almost tangent structure of higher order is due to Eliopoulos [7]. An almost tangent structure of order A: on a ((k+l)n)-dimensional manifold is defined by abstracting the geometric structure of the tangent bundle of order k of an n-dimensional manifold. Tangent bundles of higher order are the natural framework to develop the Lagrangian dynamics of higher order (see [14,4]

Given a regular Lagrangian L of order k on M we show that there exists a canonical connection F L on T 2k-tM whose paths are the solutions of the Euler-Lagrange equations for L. IfL is the kinetic energy defined by a Riernannian metric then F L is the Riemannian connection.

No abstract