26 citations · 50 across the 7 of their papers we have counts for
7 papers
Dirac Structures and Hamilton-Jacobi Theory for Lagrangian Mechanics on Lie Algebroids
Melvin Leok, Diana Sosa
This paper develops the notion of implicit Lagrangian systems on Lie algebroids and a Hamilton--Jacobi theory for this type of system. The Lie algebroid framework provides a natura…
Hamilton-Jacobi Theory for Degenerate Lagrangian Systems with Holonomic and Nonholonomic Constraints
Melvin Leok, Tomoki Ohsawa, Diana Sosa
We extend Hamilton-Jacobi theory to Lagrange-Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians a…
Variational Constrained Mechanics on Lie Affgebroids
Juan Carlos Marrero, David Martin de Diego, Diana Sosa
In this paper we discuss variational constrained mechanics (vakonomic mechanics) on Lie affgebroids. We obtain the dynamical equations and the aff-Poisson bracket associated with a…
Singular lagrangian systems and variational constrained mechanics on Lie algebroids
D. Iglesias, J. C. Marrero, D. Martin de Diego +1
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 gr…
A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
D. Iglesias, J. C. Marrero, D. Martin de Diego +1
This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomi…
The Hamilton-Jacobi equation on Lie affgebroids
Juan Carlos Marrero, Diana Sosa
The Hamilton-Jacobi equation for a Hamiltonian section on a Lie affgebroid is introduced and some examples are discussed.