The Symmetries of Equivalent Lagrangian Systems and Constants of Motion

Author
N. Elyasi
Amirkabir University of Technology
Abstract
In this paper Mathematical structure of time-dependent Lagrangian systems and their symmetries are extended and the explicit relation between constants of motion and infinitesimal symmetries of time-dependent Lagrangian systems are considered. Starting point is time-independent Lagrangian systems ,then we extend mathematical concepts of these systems such as equivalent lagrangian systems to the case of time-dependent Lagrangian systems. Also some new theorems and corollaries will be proved. Finally we make a 1-1 correspondence between the symmetries of equivalent time-dependent lagrangian systems and constants of motion by the new geometric concept of Galilean space-time.
Keywords
Infinitesimal symmetries
Lagrangian system
Symmetries of Lagrangian systems
Hamiltonian system
Constant of motion