中国物理B ›› 2006, Vol. 15 ›› Issue (10): 2197-2201.doi: 10.1088/1009-1963/15/10/002

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New non-Noether conserved quantities of mechanical system in phase space

闫向宏, 方建会   

  1. College of Physics Science and Technology, University of Petroleum,Dongying 257061, China
  • 收稿日期:2006-04-15 修回日期:2006-04-26 出版日期:2006-10-20 发布日期:2006-10-20

New non-Noether conserved quantities of mechanical system in phase space

Yan Xiang-Hong (闫向宏), Fang Jian-Hui (方建会)   

  1. College of Physics Science and Technology, University of Petroleum, Dongying 257061, China
  • Received:2006-04-15 Revised:2006-04-26 Online:2006-10-20 Published:2006-10-20

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摘要： This paper focuses on studying non-Noether conserved quantities of Lie symmetry and of form invariance for a mechanical system in phase space under the general infinitesimal transformation of groups. We obtain a new non-Noether conserved quantity of Lie symmetry of the system, and Hojman and Mei's results are of special cases of our conclusion. We find a condition under which the form invariance of the system will lead to a Lie symmetry, and, further, obtain a new non-Noether conserved quantity of form invariance of the system. An example is given finally to illustrate these results.

关键词: non-Noether conserved quantity, Lie symmetry, form invariance, phase space

Abstract: This paper focuses on studying non-Noether conserved quantities of Lie symmetry and of form invariance for a mechanical system in phase space under the general infinitesimal transformation of groups. We obtain a new non-Noether conserved quantity of Lie symmetry of the system, and Hojman and Mei's results are of special cases of our conclusion. We find a condition under which the form invariance of the system will lead to a Lie symmetry, and, further, obtain a new non-Noether conserved quantity of form invariance of the system. An example is given finally to illustrate these results.

Key words: non-Noether conserved quantity, Lie symmetry, form invariance, phase space

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj
45.20.da (Forces and torques)