Lie symmetries of the relative motion systems on time scales

In this paper, the Lie symmetries and conserved quantities of the relative motion systems on time scales are proposed and studied. The Lagrange equations with delta derivatives on time scales are derived. By defining the infinitesimal transformations generators and using the invariance of differential equations under infinitesimal transformations, the determining equations of the Lie symmetries on time scales are established. Then, the structural equation and the form of conserved quantities of the Lie symmetries are given. Lie symmetries of the relative motion systems in discrete and continuous systems were discussed, respectively. Finally, an example is given to illustrate the applications of the conclusion.