Methods of reduction for Lagrange systems on time scales with nabla derivatives**Project supported by the National Natural Science Foundation of China (Grant Nos. 11572212 and 11272227) and the Innovation Program for Graduate Student of Jiangsu Province, China (Grant No. KYLX16-0414).

Abstract

The Routh and Whittaker methods of reduction for Lagrange system on time scales with nabla derivatives are studied. The equations of motion for Lagrange system on time scales are established, and their cyclic integrals and generalized energy integrals are given. The Routh functions and Whittaker functions of Lagrange system are constructed, and the order of differential equations of motion for the system are reduced by using the cyclic integrals or the generalized energy integrals with nabla derivatives. The results show that the reduced Routh equations and Whittaker equations hold the form of Lagrnage equations with nabla derivatives. Finally, two examples are given to illustrate the application of the results.