New Role of Null Lagrangians in Derivation of Equations of Motion for Dynamical Systems

Abstract: The space of Null Lagrangians is the least investigated territory in dynamics since they are identically sent to zero by their Euler-Lagrange operator and thereby having no effects on equations of motion. A humble effort to discover the relevance of these Null Lagrangians in dynamics is made by introducing a generalized procedure (with respect to the recent procedure introduced by the authors of this paper) that takes advantage of the null-ness of these Lagrangians to construct non-standard Lagrangians that represent a range of interesting dynamical systems. By using the generalized procedure, derivation of equations of motion for a harmonic oscillator as well as for the Bateman and Duffing oscillators is presented. The obtained results demonstrate a new role played by the null Lagrangians and their corresponding non-standard Lagrangians in describing linear and nonlinear, and dissipative and non-dissipative dynamical systems.