Conformal Invariance and Conserved Quantity for the Nonholonomic System of Chetaev’s Type

Jian-Le, Cai

doi:10.1007/s10773-009-0193-9

Cited by 28 publications

(9 citation statements)

References 19 publications

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“…The key question to the conformal invariance of dynamics is to find out the conformal factor. Considerable progress has made over past years in the application of conformal invariance to mechanical systems [21][22][23][24][25][26]. However, the application of conformal invariance to thin elastic rod has never been investigated.…”

Section: Introductionmentioning

confidence: 99%

Conformal Invariance and Conserved Quantities for Lagrange Equation of Thin Elastic Rod

Wang

Feng

2017

Acta Phys. Pol. A

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Basing on the analytical mechanics methods, the Lagrangian equations of thin elastic rod is constructed. The definition of conformal invariance for the Lagrange mechanics of elastic rod is given. The criterions that conformal invariance of elastic rod is the Lie symmetry are obtained based on the Lie point transformation group. The structure equation and conserved quantity deduced from conformal invariance of elastic rod are constructed. Take twist rod as an example to illustrate the application of the results got in this paper.

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Section: Introductionmentioning

confidence: 99%

Conformal Invariance and Conserved Quantities for Lagrange Equation of Thin Elastic Rod

Wang

Feng

2017

Acta Phys. Pol. A

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“…In 1979, M. Lutzky [11][12][13] applied Lie's theory to the differential equations of motion for the mechanical system, and studied Lie symmetries and conserved quantities of a dynamical system. In the recent 20 years, researchers [2][3][4][5][14][15][16][17][18][19][20][21][22][23][24][25] developed the methods of Noether symmetry and Lie symmetry, and obtained many important results.…”

Section: Introductionmentioning

confidence: 99%

Lie symmetries, symmetrical perturbation and a new adiabatic invariant for disturbed nonholonomic systems

Jiang

Shao-Kai

2011

Nonlinear Dyn

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For a nonlinear nonholonomic constrained mechanical system with the action of small forces of perturbation, Lie symmetries, symmetrical perturbation, and a new type of non-Noether adiabatic invariants are presented in general infinitesimal transformation of Lie groups. Based on the invariance of the equations of motion for the system under general infinitesimal transformation of Lie groups, the Lie symmetrical determining equations, constraints restriction equations, additional restriction equations, and exact invariants of the system are given. Then, under the action of small forces of perturbation, the determining equations, constraints restriction equations, and additional restriction equations of the Lie symmetrical perturbation are obtained, and adiabatic invariants of the Lie symmetrical perturbation, the weakly Lie symmetrical perturbation, and the strongly Lie symmetrical perturbation for the disturbed nonholonomic system are obtained, respectively. Furthermore, a set of nonNoether exact invariants and adiabatic invariants are given in the special infinitesimal transformations. Finally, one example is given to illustrate the application of the method and results.

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“…In 1997, Galiullin et al had proposed concepts of conformal invariance and conformal factor of Birkhoff equations in the study of dynamics in Birkhoffian systems [23], and discussed the relationships between the invariance and the conformal invariance, Lie symmetry and the conformal invariance under the infinitesimal transformations of Pfaff action. Since entering the twenty-first century, Chinese scholars have carried out certain new researches and have gained some achievements in the study of symmetries and conserved quantities for mechanical systems by means of theories of the conformal invariance [24][25][26][27][28][29][30][31][32][33][34][35]. However, for a long time, there are fewer results to Appell equations.…”

mentioning

confidence: 99%

“…Especially at present there is no papers to present publicly the conformal invariance and conserved quantity of Mei symmetry of Appell equations expressed directly from Appell functions in nonholonomic systems of Chetaev's type. Reference [34] studied the conformal invariance and conserved quantity of Mei symmetry of Lagrange equations in nonholonomic systems of Chetaev's type. Reference [35] studied the conformal invariance and conserved quantity of Mei symmetry of Appell equations in holonomic systems.…”

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confidence: 99%

Conformal invariance and conserved quantity of Mei symmetry for Appell equations in a nonholonomic system of Chetaev’s type

et al. 2014

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For a nonholonomic system of Chetaev's type, the conformal invariance and the conserved quantity of Mei symmetry for Appell equations are investigated. First, under the infinitesimal one-parameter transformations of group and the infinitesimal generator vectors, Mei symmetry and conformal invariance of differential equations of motion for the system are defined, and the determining equation of Mei symmetry and conformal invariance for the system are given. Then, by means of the structure equation to which the gauge function is satisfied, the Mei-conserved quantity corresponding to the system is derived. Finally, an example is given to illustrate the application of the result.

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Conformal Invariance and Conserved Quantity for the Nonholonomic System of Chetaev’s Type

Cited by 28 publications

References 19 publications

Conformal Invariance and Conserved Quantities for Lagrange Equation of Thin Elastic Rod

Conformal Invariance and Conserved Quantities for Lagrange Equation of Thin Elastic Rod

Lie symmetries, symmetrical perturbation and a new adiabatic invariant for disturbed nonholonomic systems

Conformal invariance and conserved quantity of Mei symmetry for Appell equations in a nonholonomic system of Chetaev’s type

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