一类非完整奇异系统的Lie对称性与守恒量

Yuan-Cheng, Li; Zhang, Yi; Liang, Jinghui

doi:10.7498/aps.51.2186

Cited by 12 publications

(3 citation statements)

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“…For the nonholonomic controllable mechanical systems in phase space, the Noether identity can be written in Eqs. (11) and the form…”

Section: Equations Of Motion Of Controllable Mechanical Systemsmentioning

confidence: 99%

“…Criterion For the nonholonomic controllable mechanical systems in phase space, if there exists such a gauge function G N = G N (q, p, µ r , μr , t) that infinitesimal generators τ , ξ s , and η s satisfy Eqs (10), (11) and…”

Section: Equations Of Motion Of Controllable Mechanical Systemsmentioning

confidence: 99%

“…After calculations, generators (27) satisfy the restriction equation (10) and additional restriction equation (11) and…”

Section: Illustrated Examplementioning

confidence: 99%

See 2 more Smart Citations

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

Xia¹,

Yuan-Cheng²

2007

Commun. Theor. Phys.

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In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in phase space are presented. The definition and the criterion for this system are presented. A new conserved quantity and the Noether conserved quantity deduced from the Noether-form invariance are obtained. An example is given to illustrate the application of the results.

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“…For the nonholonomic controllable mechanical systems in phase space, the Noether identity can be written in Eqs. (11) and the form…”

Section: Equations Of Motion Of Controllable Mechanical Systemsmentioning

confidence: 99%

Section: Equations Of Motion Of Controllable Mechanical Systemsmentioning

confidence: 99%

See 1 more Smart Citation

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

Xia¹,

Yuan-Cheng²

2007

Commun. Theor. Phys.

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Symmetries and perturbations of a singular nonconservative system on time scales

Liu,

Song

2024

Acta Mech

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Noether Symmetry Can Lead to Non-Noether Conserved Quantity of Holonomic Nonconservative Systems in General Lie Transformations

Shao-Kai

Li-Qun

Jian-Le³

2005

Commun. Theor. Phys.

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For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first, the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of non-Noether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.

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一类非完整奇异系统的Lie对称性与守恒量

Cited by 12 publications

References 0 publications

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

Symmetries and perturbations of a singular nonconservative system on time scales

Noether Symmetry Can Lead to Non-Noether Conserved Quantity of Holonomic Nonconservative Systems in General Lie Transformations

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