A New Type of Conserved Quantity of Mei Symmetry for Lagrange Systems

Ding, Ning; Fang, Jianhui; Wang, Peng; Xiao-Ni, Zhang

doi:10.1088/0253-6102/48/5/007

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…In Refs. [17], [18], and [19], some new types of conserved quantities for Hamilton systems, Lagrange systems, and relativistic variable mass mechanical system in phase space were studied respectively.…”

Section: Introductionmentioning

confidence: 99%

New Type of Conserved Quantities of Lie Symmetry for Nonholonomic Mechanical Systems in Phase Space

Ting¹,

Fang²,

Peng³

et al. 2009

Commun. Theor. Phys.

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The new types of conserved quantities, which are directly induced by Lie symmetry of nonholonomic mechanical systems in phase space, are studied. Firstly, the criterion of the weak Lie symmetry and the strong Lie symmetry are given. Secondly, the conditions of existence of the new type of conserved quantities induced by the weak Lie symmetry and the strong Lie symmetry directly are obtained, and their form is presented. Finally, an Appell–Hamel example is discussed to further illustrate the applications of the results.

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Section: Introductionmentioning

confidence: 99%

New Type of Conserved Quantities of Lie Symmetry for Nonholonomic Mechanical Systems in Phase Space

Ting¹,

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

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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