77 citations · 818 across the 61 of their papers we have counts for
10 papers · 1 filter
The nonholonomic bracket on contact mechanical systems
Manuel De León, Víctor M. Jiménez
In this paper we study contact nonholonomic mechanical sys\-tems. We construct a general framework for non-holonomic constraints in contact geometry and, in this framework, we defi…
On Non-autonomous Hamiltonian Dynamics, Dual Spaces, and Kinetic Lifts
Begüm Ateşli, Oğul Esen, Manuel de León +1
Vlasov kinetic theory is the dynamics of a bunch of particles flowing according to symplectic Hamiltonian dynamics. More recently, this geometry has been extended to contact Hamilt…
New notions of uniformity and homogeneity of Cosserat media
V. M. Jiménez, M. De León
In this paper, we study internal properties of a Cosserat media. In fact, by using groupoids and smooth distributions, we obtain a three canonical equations. The \textit{non-holono…
On Locally Conformally Cosymplectic Hamiltonian Dynamics and Hamilton-Jacobi Theory
Begüm Ateşli, Oğul Esen, Manuel de León +1
Cosymplectic geometry has been proven to be a very useful geometric background to describe time-dependent Hamiltonian dynamics. In this work, we address the globalization problem o…
Reviewing the Geometric Hamilton-Jacobi Theory concerning Jacobi and Leibniz identities
O. Esen, M. de León, M. Lainz +2
In this survey, we review the classical Hamilton Jacobi theory from a geometric point of view in different geometric backgrounds. We propose a Hamilton Jacobi equation for differen…
Lie groupoids and algebroids applied to the study of uniformity and homogeneity of Cosserat media
V. M. Jiménez, M. de León, M. Esptein
A Lie groupoid, called \textit{second-order non-holonomic material Lie groupoid}, is associated in a natural way to any Cosserat media. This groupoid is used to give a new definiti…
Lie groupoids and algebroids applied to the study of uniformity and homogeneity of material bodies
V. M. Jiménez, M. de León, M. Epstein
A Lie groupoid, called \textit{material Lie groupoid}, is associated in a natural way to any elastic material. The corresponding Lie algebroid, called \textit{material algebroid},…
Lagrangian submanifolds in k-symplectic settings
M. de León, S. Vilariño
In this paper we extend the well-know normal form theorem for Lagrangian submanifolds proved by A. Weinstein in symplectic geometry to the setting of k-symplectic manifolds.
Unambiguous Formalism for Higher-Order Lagrangian Field Theories
Cedric M. Campos, Manuel de Leon, David Martin de Diego +1
The aim of this paper is to propose an unambiguous intrinsic formalism for higher-order field theories which avoids the arbitrariness in the generalization of the conventional desc…
Nonholonomic Constraints: a New Viewpoint
J. Grabowski, M. de Leon, J. C. Marrero +1
The purpose of this paper is to show that, at least for Lagrangians of mechanical type, nonholonomic Euler-Lagrange equations for a nonholonomic linear constraint D may be viewed a…