Non-Noether symmetrical conserved quantity for nonholonomic Vacco dynamical systems with variable mass

doi:10.1088/1009-1963/13/11/003

中国物理B ›› 2004, Vol. 13 ›› Issue (11): 1790-1795.doi: 10.1088/1009-1963/13/11/003

Non-Noether symmetrical conserved quantity for nonholonomic Vacco dynamical systems with variable mass

乔永芬¹, 赵淑红², 李仁杰³

(1)Department of Mechanical Engineering and Automation, Zhejiang Institute of Science and Technology, Hangzhou 310027, China; Faculty of Science, Laiyang Agricultural College, Laiyang 265200, China; Engineering College of Northeast Agricultural University, Harbin 150030, China; (2)Engineering College of Northeast Agricultural University, Harbin 150030, China; (3)Faculty of Science, Laiyang Agricultural College, Laiyang 265200, China

收稿日期:2003-10-16 修回日期:2004-04-07 出版日期:2004-11-20 发布日期:2005-06-20
基金资助:
Project supported by the Heilongjiang Natural Science Foundation, China (Grant No 9507).

Non-Noether symmetrical conserved quantity for nonholonomic Vacco dynamical systems with variable mass

Qiao Yong-Fen (乔永芬)^abc, Li Ren-Jie (李仁杰)^b, Zhao Shu-Hong (赵淑红)^c

^a Department of Mechanical Engineering and Automation, Zhejiang Institute of Science and Technology, Hangzhou 310027, China^b Faculty of Science, Laiyang Agricultural College, Laiyang 265200, China; ^c Engineering College of Northeast Agricultural University, Harbin 150030, China

Received:2003-10-16 Revised:2004-04-07 Online:2004-11-20 Published:2005-06-20
Supported by:
Project supported by the Heilongjiang Natural Science Foundation, China (Grant No 9507).

摘要/Abstract

摘要： Using a form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the nonholonomic Vacco dynamical system with variable mass is studied. The differential equations of motion of the systems are established. The definition and criterion of the form invariance of the system under special infinitesimal transformations are studied. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The Hojman theorem is established. Finally an example is given to illustrate the application of the result.

关键词: variable mass, nonholonomic constraint, Vacco dynamical system, non-Noether conserved quantity

Abstract: Using a form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the nonholonomic Vacco dynamical system with variable mass is studied. The differential equations of motion of the systems are established. The definition and criterion of the form invariance of the system under special infinitesimal transformations are studied. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The Hojman theorem is established. Finally an example is given to illustrate the application of the result.

Key words: variable mass, nonholonomic constraint, Vacco dynamical system, non-Noether conserved quantity

中图分类号: (Computational methods in classical mechanics)

45.10.-b

45.20.Jj (Lagrangian and Hamiltonian mechanics) 02.30.Hq (Ordinary differential equations) 02.20.Sv (Lie algebras of Lie groups)

乔永芬, 李仁杰, 赵淑红. Non-Noether symmetrical conserved quantity for nonholonomic Vacco dynamical systems with variable mass[J]. 中国物理B, 2004, 13(11): 1790-1795.

Qiao Yong-Fen (乔永芬), Li Ren-Jie (李仁杰), Zhao Shu-Hong (赵淑红). Non-Noether symmetrical conserved quantity for nonholonomic Vacco dynamical systems with variable mass[J]. Chinese Physics, 2004, 13(11): 1790-1795.

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Non-Noether symmetrical conserved quantity for nonholonomic Vacco dynamical systems with variable mass

Non-Noether symmetrical conserved quantity for nonholonomic Vacco dynamical systems with variable mass

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