Symmetry of Lagrangians of nonholonomic systems

Feng-Xiang, Mei; Wu, Huibin

doi:10.1016/j.physleta.2007.11.030

Cited by 15 publications

(9 citation statements)

References 16 publications

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“…[21] Wu and Zhang generalized the results of Ref. [20] to nonholonomic systems of non-Chetaev's type [22,23] and obtained the corresponding results. In this Letter, we discuss the symmetry of Lagrangians of nonholonomic controllable mechanical systems, and try to obtain some useful results.…”

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confidence: 86%

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Symmetry of Lagrangians of Nonholonomic Controllable Mechanical Systems

Xia

Jian-Le

2010

Chinese Phys. Lett.

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confidence: 86%

“…[17], Hojman [18] and Zhao [19] extended the results, and Zhao firstly called it the symmetry of Lagrangians in his book. Mei discussed both the symmetry of Lagrangians of nonholonomic systems of Chetaev's type [20] and the symmetry of Lagrangians for a dynamical system of relative motion. [21] Wu and Zhang generalized the results of Ref.…”

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confidence: 99%

Symmetry of Lagrangians of Nonholonomic Controllable Mechanical Systems

Xia

Jian-Le

2010

Chinese Phys. Lett.

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“…Therefore we have Criterion For a generalized classical system under consideration, if two groups of dynamical functions H, R µ and H, Rµ satisfy condition (18), then corresponding invariance is a symmetry of Hamiltonian of the system.…”

Section: Definition and Criterion Of The Symmetry Of Hamiltonian For ...mentioning

confidence: 99%

Symmetry of Hamiltonian and conserved quantity for a system of generalized classical mechanics

张毅¹

2011

Chinese Phys. B

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This paper focuses on a new symmetry of Hamiltonian and its conserved quantity for a system of generalized classical mechanics. The differential equations of motion of the system are established. The definition and the criterion of the symmetry of Hamiltonian of the system are given. A conserved quantity directly derived from the symmetry of Hamiltonian of the generalized classical mechanical system is given. Since a Hamilton system is a special case of the generalized classical mechanics, the results above are equally applicable to the Hamilton system. The results of the paper are the generalization of a theorem known for the existing nonsingular equivalent Lagrangian. Finally, two examples are given to illustrate the application of the results.

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“…Although the integration theory of holonomic conservative systems is perfect enough, the integration theory of nonholonomic systems is not quite perfect, and needs to be constantly developed [1][2][3][4][5][6][7][8][9][10][11][12][13]. This paper presents a new integration method of nonholonomic systems, i.e., the method of Jacobi last multiplier.…”

Section: Introductionmentioning

confidence: 99%

The Method of Jacobi Last Multiplier for Integrating Nonholonomic Systems

Zhang

2011

Acta Phys. Pol. A

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In this paper, a new integral method of nonholonomic dynamical systems is put forward. The differential equations of motion of nonholonomic systems in phase space are established. The definition of the Jacobi last multiplier of the systems is given, and the relation between the Jacobi last multiplier and the first integrals of the systems is discussed. The researches show that the solution of the systems can be found by the last multiplier if the quantity of first integrals of the systems is sufficient. An example is given to illustrate the application of the results.

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Symmetry of Lagrangians of nonholonomic systems

Cited by 15 publications

References 16 publications

Symmetry of Lagrangians of Nonholonomic Controllable Mechanical Systems

Symmetry of Lagrangians of Nonholonomic Controllable Mechanical Systems

Symmetry of Hamiltonian and conserved quantity for a system of generalized classical mechanics

The Method of Jacobi Last Multiplier for Integrating Nonholonomic Systems

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