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