Related papers: Cotangent bundle reduction and Routh reduction for…
In this work, we develop a Lagrangian reduction theory for covariant field theories with gauge symmetries. These symmetries are modeled by a Lie group fiber bundle acting fiberwisely on a configuration bundle. In order to reduce the…
We prove several results on symplectic varieties with a Hamiltonian action of a reductive group having invariant Lagrangian subvarieties. Our main result states that the images of the moment maps of a Hamiltonian variety and of the…
This paper concerns the Routh reduction procedure for Lagrangians systems with symmetry. It differs from the existing results on geometric Routh reduction in the fact that no regularity conditions on either the Lagrangian $L$ or the…
Applied to field theory, the familiar symplectic technique leads to instantaneous Hamiltonian formalism on an infinite-dimensional phase space. A true Hamiltonian partner of first order Lagrangian theory on fibre bundles $Y\to X$ is…
This is the first paper of a five part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connections between initial value constraints and gauge…
This note discusses Routh reduction for hybrid time-dependent mechanical systems. We give general conditions on whether it is possible to reduce by symmetries a hybrid time-dependent Lagrangian system extending and unifying previous results…
This paper discusses Routh reduction for simple hybrid forced mechanical systems. We give general conditions on whether it is possible to perform symmetry reduction for a simple hybrid Lagrangian system subject to non-conservative external…
The problem of reduction of multisymplectic manifolds by the action of Lie groups is stated and discussed, as a previous step to give a fully covariant scheme of reduction for classical field theories with symmetries.
We consider trivializations of second iterated bundles of a Lie group that preserve lifted group structures. With such a trivialization, we elaborate Hamiltonian dynamics on cotangent, Lagrangian dynamics on tangent bundles and, both…
We study the relationship between the equations of first order Lagrangian field theory on fiber bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. The…
In this article, we analyze the Pontryagin model adopting different geometric-covariant approaches. In particular, we focus on the manner in which boundary conditions must be imposed on the background manifold in order to reproduce an…
In this paper we describe Routhian reduction as a special case of standard symplectic reduction, also called Marsden-Weinstein reduction. We use this correspondence to present a generalization of Routhian reduction for quasi-invariant…
This article concerns cotangent-lifted Lie group actions; our goal is to find local and ``semi-global'' normal forms for these and associated structures. Our main result is a constructive cotangent bundle slice theorem that extends the…
A polysymplectic structure is a vector-valued symplectic form, that is, a closed nondegenerate 2-form with values in a vector space. We first outline the polysymplectic Hamiltonian formalism with coefficients in a vector space $V$, then…
In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of…
In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian to Hamiltonian classical field theories, and then we…
This paper concerns the development and application of the multisymplectic Lagrangian and Hamiltonian formalism for nonlinear partial differential equations. In this theory, solutions of a PDE are sections of a fiber bundle $Y$ over a base…
The first part of the article is, in fact, the classical Routh method delivered in the language of contemporary theory of Lagrangian systems. But the Routh method deals only with concrete equations and, therefore, can be applied only in the…
We consider two families of commuting Hamiltonians on the cotangent bundle of the group GL(n,C), and show that upon an appropriate single symplectic reduction they descend to the spectral invariants of the hyperbolic Sutherland and of the…
The possibility of the global Lagrangian reduction of a mechanical system with symmetry is shown to be connected with the characteristic class of a principal fiber bundle of the configuration space over the factor manifold. It is proved…