3,080 research outputs found
Leibniz algebroid associated with a Nambu-Poisson structure
The notion of Leibniz algebroid is introduced, and it is shown that each
Nambu-Poisson manifold has associated a canonical Leibniz algebroid. This fact
permits to define the modular class of a Nambu-Poisson manifold as an
appropiate cohomology class, extending the well-known modular class of Poisson
manifolds
The inhomogeneous Suslov problem
We consider the Suslov problem of nonholonomic rigid body motion with
inhomogeneous constraints. We show that if the direction along which the Suslov
constraint is enforced is perpendicular to a principal axis of inertia of the
body, then the reduced equations are integrable and, in the generic case,
possess a smooth invariant measure. Interestingly, in this generic case, the
first integral that permits integration is transcendental and the density of
the invariant measure depends on the angular velocities. We also study the
Painlev\'e property of the solutions.Comment: 10 pages, 5 figure
A new geometric setting for classical field theories
A new geometrical setting for classical field theories is introduced. This
description is strongly inspired in the one due to Skinner and Rusk for
singular lagrangians systems. For a singular field theory a constraint
algorithm is developed that gives a final constraint submanifold where a
well-defined dynamics exists. The main advantage of this algorithm is that the
second order condition is automatically included.Comment: 22 page
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). Several examples illustrate the interest of these developments.Comment: 42 pages, Section with examples improve
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