Mechanical systems and their associated Lagrange geometries

Abstract

The aim of this paper is to study the general rheonomic mechanical systems using the Lagrange geometry. We will construct the time-dependent Lagrange space for the mechanical system, its canonical semispray and the nonlinear connection, which are determined only by the given mechanical system.

One studies the rheonomic holonomic mechanical systems with external forces, using the geometry of the rheonomic Lagrange space endowed with the canonical semispray determined by the external forces. The geometry of the canonical semispray is the geometry of the rheonomic mechanical system.

Keywords:

• rheonomic Lagrange space
• nonlinear connection
• semispray
• mechanical system
• evolution curves
• metrical connection

2000 AMS Subject Classifications :

• 53C60
• 58B20
• 70H03

Acknowledgements

We thank the anonymous referees for fruitful suggestions and comments.