## 206 Citations

### Lagrangian Lie Subalgebroids Generating Dynamics for Second-Order Mechanical Systems on Lie Algebroids

- Mathematics
- 2018

The study of mechanical systems on Lie algebroids permits an understanding of the dynamics described by a Lagrangian or Hamiltonian function for a wide range of mechanical systems in a unified…

### Lagrangian Lie Subalgebroids Generating Dynamics for Second-Order Mechanical Systems on Lie Algebroids

- MathematicsMediterranean Journal of Mathematics
- 2018

The study of mechanical systems on Lie algebroids permits an understanding of the dynamics described by a Lagrangian or Hamiltonian function for a wide range of mechanical systems in a unified…

### Classical field theory on Lie algebroids: Multisymplectic formalism

- Mathematics
- 2004

The jet formalism for Classical Field theories is extended to the setting of Lie algebroids. We define the analog of the concept of jet of a section of a bundle and we study some of the geometric…

### Discrete Lagrangian and Hamiltonian mechanics on Lie groupoids

- Mathematics
- 2005

The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian mechanics on Lie groupoids. From a variational principle we derive the discrete Euler–Lagrange equations and…

### Hamiltonian Mechanics on Duals of Generalized Lie Algebroids

- Mathematics
- 2011

A new description, diﬀerent by the classical theory of Hamiltonian Mechanics, in the general framework of generalized Lie algebroids is presented. In the particular case of Lie algebroids, new and…

### Calculus on Lie algebroids, Lie groupoids and Poisson manifolds

- Mathematics
- 2008

We begin with a short presentation of the basic concepts related to Lie groupoids and Lie algebroids, but the main part of this paper deals with Lie algebroids. A Lie algebroid over a manifold is a…

### Dynamical equations and Lagrange–Ricci flow evolution on prolongation Lie algebroids

- MathematicsCanadian Journal of Physics
- 2019

The approach to nonholonomic Ricci flows and geometric evolution of regular Lagrange systems (S. Vacaru. J. Math. Phys. 49, 043504 (2008); Ibid. Rep. Math. Phys. 63, 95 (2009)) is extended to include…

### Legendre Duality Between Lagrangian and Hamiltonian Mechanics

- Mathematics
- 2011

In some previous papers, a Legendre duality between Lagrangian and Hamiltonian Mechanics has been developed. The (\rho,\eta)-tangent application of the Legendre bundle morphism associated to a…

### Dirac cotangent bundle reduction

- Mathematics
- 2009

The authors' recent paper in Reports in Mathematical Physics develops Dirac reduction for cotangent bundles of Lie groups, which is called Lie--Dirac reduction . This procedure simultaneously…

## References

SHOWING 1-10 OF 44 REFERENCES

### Classical field theory on Lie algebroids: Multisymplectic formalism

- Mathematics
- 2004

The jet formalism for Classical Field theories is extended to the setting of Lie algebroids. We define the analog of the concept of jet of a section of a bundle and we study some of the geometric…

### Variational principles for Lie-Poisson and Hamilton-Poincaré equations

- Mathematics
- 2003

As is well-known, there is a variational principle for the
Euler–Poincare equations on a Lie algebra g of a Lie group G obtained by reducing Hamilton’s principle on G by the action of G by, say,…

### Lie algebroid structures on a class of affine bundles

- Mathematics
- 2002

We introduce the notion of a Lie algebroid structure on an affine bundle whose base manifold is fibered over R. It is argued that this is the framework which one needs for coming to a time-dependent…

### Lagrangian Reduction by Stages

- Mathematics
- 2001

This booklet studies the geometry of the reduction of Lagrangian systems with symmetry in a way that allows the reduction process to be repeated; that is, it develops a context for Lagrangian…

### Classical field theory on Lie algebroids: variational aspects

- Mathematics
- 2004

The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function, we study the problem of finding critical points of the action…

### Lagrangian Mechanics on Lie Algebroids

- Physics, Mathematics
- 2001

A geometric description of Lagrangian Mechanics on Lie algebroids is developed in a parallel way to the usual formalism of Lagrangian Mechanics on the tangent bundle of a manifold. The dynamical…

### Lie bialgebroids and Poisson groupoids

- Mathematics
- 1994

Lie bialgebras arise as infinitesimal invariants of Poisson Lie groups. A Lie bialgebra is a Lie algebra g with a Lie algebra structure on the dual g∗ which is compatible with the Lie algebra g in a…

### Deformation Quantization of Poisson Manifolds

- Mathematics
- 1997

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the…