Unified symmetry of mechano-electrical systems with nonholonomic constraints

Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomic mechanic systems with unilateral constraints are established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups are also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results.

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Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints

Li-Qun

Zhang

Jin-Chao

et al. 2009

Commun. Theor. Phys.

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Generalized Mei Conserved Quantity of Mei Symmetry for Mechanico-electrical Systems with Nonholonomic Controllable Constraints

Xia

Xi-nan

2009

Chinese Phys. Lett.

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On the basis of the total time derivative along the trajectory, we study the generalized Mei conserved quantity of Mei symmetry for mechanico-electrical systems with nonholonomic controllable constraints. Firstly, the definition and criterion of Mei symmetry for mechanico-electrical systems with nonholonomic controllable constraints are presented. Secondly, a coordination function is introduced, and the conditions of existence of generalized Mei conserved quantity as well as the forms are proposed. Lastly, an example is given to illustrate the application of the results.

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Discussion on Perturbation to Weak Noether Symmetry and Adiabatic Invariants for Lagrange Systems

Wang

Fang

Wang

2009

Chinese Phys. Lett.

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We study a new symmetric perturbation, i.e. weakly Noether symmetric perturbation (WNSP). The criterion and definition of WNSP and Noether symmetric perturbation (NSP) are given. A theorem between WNSP and adiabatic invariants is established. It is concluded that WNSP is different from NSP, the sufficient condition when WNSP is NSP can be presented, and the former is broader. We apply our results to the planar Kepler problem.

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Unified symmetry of mechano-electrical systems with nonholonomic constraints

Cited by 6 publications

References 21 publications

Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints

Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints

Generalized Mei Conserved Quantity of Mei Symmetry for Mechanico-electrical Systems with Nonholonomic Controllable Constraints

Discussion on Perturbation to Weak Noether Symmetry and Adiabatic Invariants for Lagrange Systems

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