%0 Journal Article
%T The Symmetries of Equivalent Lagrangian
Systems and Constants of Motion
%J Journal of Sciences, Islamic Republic of Iran
%I University of Tehran
%Z 1016-1104
%A Elyasi, N.
%D 2011
%\ 03/01/2011
%V 22
%N 1
%P 63-132
%! The Symmetries of Equivalent Lagrangian
Systems and Constants of Motion
%K Infinitesimal symmetries
%K Lagrangian system
%K Symmetries of Lagrangian systems
%K Hamiltonian system
%K Constant of motion
%R
%X 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.
%U https://jsciences.ut.ac.ir/article_22214_95e14ab8a13e141de4deda070f30dd1b.pdf