Methods of reduction for Lagrange systems on time scaleswith nabla derivatives

doi:10.1088/1674-1056/26/1/014501

中国物理B ›› 2017, Vol. 26 ›› Issue (1): 14501-014501.doi: 10.1088/1674-1056/26/1/014501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Methods of reduction for Lagrange systems on time scaleswith nabla derivatives

Shi-Xin Jin(金世欣), Yi Zhang(张毅)

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

收稿日期:2016-08-16 修回日期:2016-12-12 出版日期:2017-01-05 发布日期:2017-01-05
通讯作者: Yi Zhang E-mail:zhy@mail.usts.edu.cn
基金资助:
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).

Methods of reduction for Lagrange systems on time scaleswith nabla derivatives

Shi-Xin Jin(金世欣)¹, Yi Zhang(张毅)^1,2

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

Received:2016-08-16 Revised:2016-12-12 Online:2017-01-05 Published:2017-01-05
Contact: Yi Zhang E-mail:zhy@mail.usts.edu.cn
Supported by:
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).

摘要/Abstract

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.

关键词: reduction of dynamical system, cyclic integral, energy integral, time scales

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.

Key words: reduction of dynamical system, cyclic integral, energy integral, time scales

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

89.75.Da (Systems obeying scaling laws) 71.10.Pm (Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.))

金世欣, 张毅. Methods of reduction for Lagrange systems on time scaleswith nabla derivatives[J]. 中国物理B, 2017, 26(1): 14501-014501.

Shi-Xin Jin(金世欣), Yi Zhang(张毅). Methods of reduction for Lagrange systems on time scaleswith nabla derivatives[J]. Chin. Phys. B, 2017, 26(1): 14501-014501.

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Methods of reduction for Lagrange systems on time scaleswith nabla derivatives

Methods of reduction for Lagrange systems on time scaleswith nabla derivatives

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