Lagrangian reduction of discrete mechanical systems by stages

In this work we introduce a category of discrete Lagrange{Poincare systems £ β d and study some of its properties. In particular, we show that the discrete mechanical systems and the discrete dynamical systems obtained by the Lagrangian reduction of symmetric discrete mechanical systems are objects in We introduce a notion of symmetry group for objects of £ βd as well as a reduction procedure that is closed in the category Furthermore, under some conditions, we show that the reduction in two steps (first by a closed normal subgroup of the symmetry group and then by the residual symmetry group) is isomorphic in LPd to the reduction by the full symmetry group.Facultad de Ciencias Exacta

Lagrangian reduction of forced discrete mechanical systems

In this paper we propose a process of Lagrangian reduction and reconstruction for symmetric discrete-time mechanical systems acted on by external forces, where the symmetry group action on the configuration manifold turns it into a principal bundle. We analyze the evolution of momentum maps and Poisson structures under different conditions

Lagrangian reduction of discrete mechanical systems by stages

In this work we introduce a category of discrete Lagrange{Poincare systems £ β d and study some of its properties. In particular, we show that the discrete mechanical systems and the discrete dynamical systems obtained by the Lagrangian reduction of symmetric discrete mechanical systems are objects in We introduce a notion of symmetry group for objects of £ βd as well as a reduction procedure that is closed in the category Furthermore, under some conditions, we show that the reduction in two steps (first by a closed normal subgroup of the symmetry group and then by the residual symmetry group) is isomorphic in LPd to the reduction by the full symmetry group.Facultad de Ciencias Exacta

Reducción lagrangiana de sistemas mecánicos discretos con vínculos no holónomos

El propósito de esta tesis es avanzar en el estudio de la reducción de sistemas mecánicos discretos con vínculos no holónomos. En este tipo de sistemas los vínculos variacionales no se deducen de los vínculos cinemáticos, es por esto que consideramos que la reducción de sistemas mecánicos discretos no holónomos es la contraparte discreta de la reducción de sistemas no holónomos generalizados tratada por Cendra, Ferraro y Grillo en [8].Tesis digitalizada en SEDICI gracias a la Biblioteca del Departamento de Matemática de la Facultad de Ciencias Exactas (UNLP).Doctor en Ciencias Exactas, área MatemáticaUniversidad Nacional de La PlataFacultad de Ciencias Exacta

Curvatura escalar Riemanniana en un gas de electrones unidimensional

En este trabajo, nos enfocaremos en sistemas unidimensionales no ideales. Siguiendo esta línea, y para considerar el efecto de la interacción entre electrones en la curvatura escalar, usamos el modelo de Tomonaga-Luttinger. En general, este modelo hace una buena descripción de las exaltaciones de baja energía en líquidos de Fermi cuasi dimensionales conocidos como cables o hilos cuánticos. Los líquidos unidimensionales de Fermi son un sistema singular porque las excitaciones elementales están caracterizadas por fluctuaciones bosónicas colectivas de carga. (Párrafo extraído del texto a modo de resumen)Facultad de Ingenierí