A new type of conserved quantity of Mei symmetry for relativistic nonholonomic mechanical system in phase space

Xiao-Ni, Zhang; Fang, Jianhui; Ting, Pang; Peng, Lin

doi:10.1088/1674-1056/17/2/007

Chinese Phys. B

2008

DOI: 10.1088/1674-1056/17/2/007

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A new type of conserved quantity of Mei symmetry for relativistic nonholonomic mechanical system in phase space

Zhang Xiao-Ni

Jianhui Fang

Pang Ting

et al.

Abstract: In this paper, a new type of conserved quantity induced directly from the Mei symmetry for a relativistic nonholonomic mechanical system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions for the existence and form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

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Cited by 3 publications

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Noether theorem for nonholonomic nonconservative mechanical systems in phase space on time scales

Qihang

Zhu

2016

Journal of Mathematical Physics

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The paper focuses on studying the Noether theorem for nonholonomic nonconservative mechanical systems in phase space on time scales. First, the Hamilton equations of nonholonomic nonconservative systems on time scales are established, which is based on the Lagrange equations for nonholonomic systems on time scales. Then, based upon the quasi-invariance of Hamilton action of systems under the infinitesimal transformations with respect to the time and generalized coordinate on time scale, the Noether identity and the conserved quantity of nonholonomic nonconservative systems on time scales are obtained. Finally, an example is presented to illustrate the application of the results.

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Noether theorem for nonholonomic nonconservative mechanical systems in phase space on time scales

Qihang

Zhu

2016

Journal of Mathematical Physics

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Conformal Invariance and a New Type of Conserved Quantities of Mechanical Systems with Variable Mass in Phase Space

Zhang¹,

Fang²,

Peng³

et al. 2009

Commun. Theor. Phys.

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Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry under the infinitesimal transformations is provided. Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.

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A New type of conserved quantity deduced from Mei symmetry of nonholonomic systems in terms of quasi-coordinates

et al. 2009

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This paper studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the existence of the new conserved quantities as well as their forms are proposed. Some special cases are given to illustrate the generalized significance of the new type conserved quantity. Finally, an illustrated example is given to show the application of the nonholonomic system's results.

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A new type of conserved quantity of Mei symmetry for relativistic nonholonomic mechanical system in phase space

Cited by 3 publications

References 18 publications

Noether theorem for nonholonomic nonconservative mechanical systems in phase space on time scales

Noether theorem for nonholonomic nonconservative mechanical systems in phase space on time scales

Conformal Invariance and a New Type of Conserved Quantities of Mechanical Systems with Variable Mass in Phase Space

A New type of conserved quantity deduced from Mei symmetry of nonholonomic systems in terms of quasi-coordinates

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