Symmetries and perturbations of a singular nonconservative system on time scales

The symmetries and perturbations of a singular nonconservative Lagrangian system on time scales are studied. The differential equations of motion are given. The definitions and criteria of the Noether, Lie, and Mei symmetries of the system are presented, and the corresponding conserved quantities deduced from these symmetries are obtained. In addition, the perturbations to each symmetry and the corresponding adiabatic invariants were studied. In the end, three examples are used to illustrate the applications of the results.