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Chin. Phys., 2004, Vol. 13(11): 1790-1795    DOI: 10.1088/1009-1963/13/11/003
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Non-Noether symmetrical conserved quantity for nonholonomic Vacco dynamical systems with variable mass

Qian Yong-Fena, Zhao Shu-Hongb, Li Ren-Jiec
a 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; b Engineering College of Northeast Agricultural University, Harbin 150030, China; c Faculty of Science, Laiyang Agricultural College, Laiyang 265200, China
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.
Keywords:  variable mass      non-Noether conserved quantity      nonholonomic constraint      Vacco dynamical system  
Received:  16 October 2003      Revised:  07 April 2004      Published:  20 June 2005
PACS:  45.10.-b (Computational methods in classical mechanics)  
  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
  02.30.Hq (Ordinary differential equations)  
  02.20.Sv (Lie algebras of Lie groups)  
Fund: Project supported by the Heilongjiang Natural Science Foundation, China (Grant No 9507).

Cite this article: 

Qian Yong-Fen, Li Ren-Jie, Zhao Shu-Hong Non-Noether symmetrical conserved quantity for nonholonomic Vacco dynamical systems with variable mass 2004 Chin. Phys. 13 1790

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