Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems

doi:10.1088/1674-1056/20/3/030202

中国物理B ›› 2011, Vol. 20 ›› Issue (3): 30202-030202.doi: 10.1088/1674-1056/20/3/030202

Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems

姜文安, 李状君, 罗绍凯

Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China

收稿日期:2010-09-21 修回日期:2010-10-20 出版日期:2011-03-15 发布日期:2011-03-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10372053).

Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems

Jiang Wen-An(姜文安), Li Zhuang-Jun(李状君), and Luo Shao-Kai(罗绍凯)^†

Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China

Received:2010-09-21 Revised:2010-10-20 Online:2011-03-15 Published:2011-03-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10372053).

摘要/Abstract

摘要： This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system. On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation, the determining equations, the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed. The criterions of Mei symmetries, weak Mei symmetries and strong Mei symmetries of the system are given. New types of conserved quantities, i.e. the Mei symmetrical conserved quantities, the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system, are obtained. Then, a deduction of the first-order nonholonomic system is discussed. Finally, two examples are given to illustrate the application of the method and then the results.

Abstract: This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system. On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation, the determining equations, the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed. The criterions of Mei symmetries, weak Mei symmetries and strong Mei symmetries of the system are given. New types of conserved quantities, i.e. the Mei symmetrical conserved quantities, the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system, are obtained. Then, a deduction of the first-order nonholonomic system is discussed. Finally, two examples are given to illustrate the application of the method and then the results.

Key words: higher-order nonholonomic system, Mei symmetry, Mei conserved quantity

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

11.30.-j (Symmetry and conservation laws) 03.50.Kk (Other special classical field theories) 11.10.Ef (Lagrangian and Hamiltonian approach)

姜文安, 李状君, 罗绍凯. Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems[J]. 中国物理B, 2011, 20(3): 30202-030202.

Jiang Wen-An(姜文安), Li Zhuang-Jun(李状君), and Luo Shao-Kai(罗绍凯). Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems[J]. Chin. Phys. B, 2011, 20(3): 30202-030202.

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Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems

Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems

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