Methods of reduction for Lagrange systems on time scales with nabla derivatives  

作　　者：Shi-Xin Jin Yi Zhang 金世欣;张毅(School of Science, Nanjing University of Science and Technology, Nanjing 210009, China College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China)

机构地区：[1]School of Science, Nanjing University of Science and Technology, Nanjing 210009, China [2]College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

出　　处：《Chinese Physics B》2017年第1期243-249,共7页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11572212 and 11272227);the Innovation Program for Graduate Student of Jiangsu Province,China(Grant No.KYLX16-0414)

摘　　要：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.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.

关 键 词：reduction of dynamical system cyclic integral energy integral time scales 

分 类 号：O241.8[理学—计算数学]