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 th...

A recent study (Muriel and Romero (2010a)) on the linearization of ordinary differential equations through generalized Sundman transformations suggests considering the problem of linearization through nonlocal transformations from the point of view of the λ−symmetries admitted by the equation and their associated first integrals. The systematic methods to calculate λ−symmetries and associated f...