Two kinds of generalized gradient representations for holonomic mechanical systems

Feng-Xiang, Mei; Wu, Huibin

doi:10.1088/1674-1056/25/1/014502

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…Recently, the important achievements for the relation between gradient system and constrained mechanical system have been made, such as those given in Refs. [19]- [22].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a simple rheonomic nonholonomic constrained system

Liu

Mei

2016

Chinese Phys. B

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It is a difficult problem to study the stability of the rheonomic and nonholonomic mechanical systems. Especially it is difficult to construct the Lyapunov function directly from the differential equation. But the gradient system is exactly suitable to study the stability of a dynamical system with the aid of the Lyapunov function. The stability of the solution for a simple rheonomic nonholonomic constrained system is studied in this paper. Firstly, the differential equations of motion of the system are established. Secondly, a problem in which the generalized forces are exerted on the system such that the solution is stable is proposed. Finally, the stable solutions of the rheonomic nonholonomic system can be constructed by using the gradient systems.

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“…Recently, the important achievements for the relation between gradient system and constrained mechanical system have been made, such as those given in Refs. [19]- [22].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a simple rheonomic nonholonomic constrained system

Liu

Mei

2016

Chinese Phys. B

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“…There are three kinds of symmetries: Noether symmetry, Lie symmetry, and Mei symmetry. [1][2][3][4][5][6][7][8][9][10][11][12] The symmetry theory has been approved to be a powerful tool to solve differential equations, to study constrained mechanical systems, to discuss controllable dynamical systems, to investigate mechanicoelectrical systems and to establish the properties of their solution space. [13][14][15][16][17][18][19][20][21][22][23][24][25] In recent years, the fractional Noether symmetry theories have been described in many of the references.…”

Section: Introductionmentioning

confidence: 99%

Lie symmetry theorem of fractional nonholonomic systems

Sun¹,

Chen²,

Fu³

2014

Chinese Phys. B

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The Lie symmetry theorem of fractional nonholonomic systems in terms of combined fractional derivatives is established, and the fractional Lagrange equations are obtained by virtue of the d'Alembert-Lagrange principle with fractional derivatives. As the Lie symmetry theorem is based on the invariance of differential equations under infinitesimal transformations, by introducing the differential operator of infinitesimal generators, the determining equations are obtained. Furthermore, the limit equations, the additional restriction equations, the structural equations, and the conserved quantity of Lie symmetry are acquired. An example is presented to illustrate the application of results.

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Gradient systems and mechanical systems

Feng-Xiang

2016

Acta Mech. Sin.

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Two kinds of generalized gradient representations for holonomic mechanical systems

Cited by 3 publications

References 14 publications

Stability analysis of a simple rheonomic nonholonomic constrained system

Stability analysis of a simple rheonomic nonholonomic constrained system

Lie symmetry theorem of fractional nonholonomic systems

Gradient systems and mechanical systems

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