First-Order Approximate Mei Symmetries and Invariants of the Lagrangian

Abstract

In this article, the formulation of first-order approximate Mei symmetries and Mei invariants of the corresponding Lagrangian is presented. Theorems and determining equations are given to evaluate approximate Mei symmetries, as well as approximate first integrals corresponding to each symmetry of the associated Lagrangian. The formulated procedure is explained with the help of the linear equation of motion of a damped harmonic oscillator (DHO). The Mei symmetries corresponding to the Lagrangian and Hamiltonian of DHO are compared.