Noether's theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws

doi:10.1088/1674-1056/23/11/114501

中国物理B ›› 2014, Vol. 23 ›› Issue (11): 114501-114501.doi: 10.1088/1674-1056/23/11/114501

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

Noether's theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws

龙梓轩^a, 张毅^b

a College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;
b College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

收稿日期:2014-04-02 修回日期:2014-05-02 出版日期:2014-11-15 发布日期:2014-11-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10972151 and 11272227) and the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province, China (Grant No. CXLX11_0961).

Noether's theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws

Long Zi-Xuan (龙梓轩)^a, Zhang Yi (张毅)^b

a College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;
b College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

Received:2014-04-02 Revised:2014-05-02 Online:2014-11-15 Published:2014-11-15
Contact: Zhang Yi E-mail:weidiezh@gmail.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10972151 and 11272227) and the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province, China (Grant No. CXLX11_0961).

摘要/Abstract

摘要：

This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by El-Nabulsi. First, the El-Nabulsi dynamical model which is based on a fractional integral extended by periodic laws is introduced, and El-Nabulsi-Hamilton's canonical equations for non-conservative Hamilton system with holonomic or nonholonomic constraints are established. Second, the definitions and criteria of El-Nabulsi-Noether symmetrical transformations and quasi-symmetrical transformations are presented in terms of the invariance of El-Nabulsi-Hamilton action under the infinitesimal transformations of the group. Finally, Noether's theorems for the non-conservative Hamilton system under the El-Nabulsi dynamical system are established, which reveal the relationship between the Noether symmetry and the conserved quantity of the system.

关键词: Noether', s theorem, non-conservative Hamilton system, El-Nabulsi dynamical model, fractional integral extended by periodic laws

Abstract:

Key words: Noether', s theorem, non-conservative Hamilton system, El-Nabulsi dynamical model, fractional integral extended by periodic laws

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

11.30.Na (Nonlinear and dynamical symmetries (spectrum-generating symmetries)) 02.30.Xx (Calculus of variations)

龙梓轩, 张毅. Noether's theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws[J]. 中国物理B, 2014, 23(11): 114501-114501.

Long Zi-Xuan (龙梓轩), Zhang Yi (张毅). Noether's theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws[J]. Chin. Phys. B, 2014, 23(11): 114501-114501.

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Noether's theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws

Noether's theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws

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