Related papers: Reduction (by stages) in the whole Lagrange Poinca…
We propose a category of bundles in order to perform Lagrangian reduction by stages in covariant Field Theory. This category plays an analogous role to Lagrange-Poincar\'e bundles in Lagrangian reduction by stages in Mechanics and includes…
In this work we introduce a category of discrete Lagrange--Poincare systems LP_d and study some of its properties. In particular, we show that the discrete mechanical systems and the discrete mechanical systems obtained by the Lagrangian…
In this work we introduce a category $LDP_d$ of discrete-time dynamical systems, that we call discrete Lagrange--D'Alembert--Poincar\'e systems, and study some of its elementary properties. Examples of objects of $LDP_d$ are nonholonomic…
This paper deals with the Lagrangian analogue of symplectic or point reduction by stages. We develop Routh reduction as a reduction technique that preserves the Lagrangian nature of the dynamics. To do so we heavily rely on the relation…
In this paper, some new aspects related to Routh reduction of Lagrangian systems with symmetry are discussed. The main result of this paper is the introduction of a new concept of transformation that is applicable to systems obtained after…
The aim of this paper is to write explicit expression in terms of a given principal connection of the Lagrange-d'Alembert-Poincar\`{e} equations in several stages. This is obtained by using a reduced Lagrange-d'Alembert's Principle in…
There is a well developed and useful theory of Hamiltonian reduction for semidirect products, which applies to examples such as the heavy top, compressible fluids and MHD, which are governed by Lie-Poisson type equations. In this paper we…
Rigid body with rotors is a widespread mechanical system modeled after the direct product $SO(3)\times S^1\times S^1\times S^1$, which under mild assumptions is the symmetry group of the system. In this paper, the authors present and…
Following the analysis we have presented in a previous paper (that we refer to as [I]), we describe a Noether theorem related to symmetries, with the associated reduction procedures, for classical dynamics within the Lagrangian and the…
We consider a general approach for the process of Lagrangian and Hamiltonian reduction by symmetries in chiral gauge models. This approach is used to show the complete integrability of several one dimensional texture equations arising in…
We develop a reduction theory for $G$-invariant Lagrangian field theories defined on the higher-order jet bundle of a principal $G$-bundle, thus obtaining the higher-order Euler-Poincar\'e field equations. To that end, we transfer the…
We define a quantum version of Hamiltonian reduction by stages, producing a construction in type A for a quantum Hamiltonian reduction from the W-algebra $U(\mathfrak{g},e_1)$ to an algebra conjecturally isomorphic to $U(\mathfrak{g},e_2)$,…
The Lagrange-Poincare equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/reconstruction condition is established that relates solutions…
We define a reduction, called complete reduction, for the K and KO relations of the Hopf bundle over lens spaces introducing some numbers of interest to various theories of mathematics. Along the way, we make an interesting conjecture in…
In this paper we show that a variational reduction procedure can be defined for Lagrangian systems subject to scaling symmetries (i.e. Lagrangian systems defined by a homogenous Lagrangian function), in such a way that the trajectories of…
We extend Routh's reduction procedure to an arbitrary Lagrangian system (that is, one whose Lagrangian is not necessarily the difference of kinetic and potential energies) with a symmetry group which is not necessarily Abelian. To do so we…
In this paper, we make a generalization of Routh's reduction method for Lagrangian systems with symmetry to the case where not any regularity condition is imposed on the Lagrangian. First, we show how implicit Lagrange-Routh equations can…
Motivated by the problem of longitudinal data assimilation, e.g., in the registration of a sequence of images, we develop the higher-order framework for Lagrangian and Hamiltonian reduction by symmetry in geometric mechanics. In particular,…
Polynomial reduction is one of the main tools in computational algebra with innumerable applications in many areas, both pure and applied. Since many years both the theory and an efficient design of the related algorithm have been solidly…
In this paper, we investigate the reduction process of a contact Lagrangian system whose Lagrangian is invariant under a group of symmetries. We give explicit coordinate expressions of the resulting reduced differential equations, the…