Geometric properties of Lagrangian mechanical systems
Differential Geometry
2009-09-14 v1
Abstract
The geometry of a Lagrangian mechanical system is determined by its associated evolution semispray. We uniquely determine this semispray using the symplectic structure and the energy of the Lagrange space and the external force field. We study the variation of the energy and Lagrangian functions along the evolution and the horizontal curves and give conditions by which these variations vanish. We provide examples of mechanical systems which are dissipative and for which the evolution nonlinear connection is either metric or symplectic.
Keywords
Cite
@article{arxiv.math/0609818,
title = {Geometric properties of Lagrangian mechanical systems},
author = {Ioan Bucataru and Radu Miron},
journal= {arXiv preprint arXiv:math/0609818},
year = {2009}
}