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

Abstract

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.

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

Received: 02 April 2014
Revised: 02 May 2014
Accepted manuscript online:

PACS:	45.20.Jj	(Lagrangian and Hamiltonian mechanics)
	11.30.Na	(Nonlinear and dynamical symmetries (spectrum-generating symmetries))
	02.30.Xx	(Calculus of variations)

Fund:

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).

Corresponding Authors: Zhang Yi
E-mail: weidiezh@gmail.com

Cite this article:

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 2014 Chin. Phys. B 23 114501

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

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