Geometric properties of Lagrangian mechanical systems

Details Geometric properties of Lagrangian mechanical systems Geometric properties of Lagrangian mechanical systems

2006-09-28

arxiv.org/abs/math/0609818v1

Reports on Mathematical Physics, 59 (2007), no. 3, 225--241.

Mathematics

Differential Geometry

Scientific paper

10.1016/S0034-4877(07)00013-4

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.

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