University of TehranJournal of Sciences, Islamic Republic of Iran1016-110422120110301The Symmetries of Equivalent Lagrangian
Systems and Constants of MotionThe Symmetries of Equivalent Lagrangian
Systems and Constants of Motion6313222214ENN.ElyasiAmirkabir University of TechnologyJournal Article19700101In 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.https://jsciences.ut.ac.ir/article_22214_95e14ab8a13e141de4deda070f30dd1b.pdf