中国物理B ›› 2006, Vol. 15 ›› Issue (1): 8-12.doi: 10.1088/1009-1963/15/1/002

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Momentum-dependent symmetries and non-Noether conserved quantities for nonholonomic nonconservative Hamilton canonical systems

陈立群1, 傅景礼2, 陈向炜3   

  1. (1)Department of Mechanics, Shanghai University, Shanghai 200072, China;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; (2)Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;Shangqiu Teachers College, Shangqiu 476000, China; (3)Shangqiu Teachers College, Shangqiu 476000, China
  • 收稿日期:2004-12-06 修回日期:2005-12-06 出版日期:2006-01-20 发布日期:2006-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10372053) and the Natural Science Foundation of Henan Province, China (Grant Nos 0311011400 and 0511022200) and the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences.

Momentum-dependent symmetries and non-Noether conserved quantities for nonholonomic nonconservative Hamilton canonical systems

Fu Jing-Li (傅景礼)acd, Chen Li-Qun (陈立群)bc, Chen Xiang-Wei (陈向炜)d   

  1. a Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; b Department of Mechanics, Shanghai University, Shanghai 200072, China; c Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, Chinad Shangqiu Teachers College, Shangqiu 476000, China
  • Received:2004-12-06 Revised:2005-12-06 Online:2006-01-20 Published:2006-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10372053) and the Natural Science Foundation of Henan Province, China (Grant Nos 0311011400 and 0511022200) and the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences.

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摘要： This paper investigates the momentum-dependent symmetries for nonholonomic nonconservative Hamilton canonical systems. The definition and determining equations of the momentum-dependent symmetries are presented, based on the invariance of differential equations under infinitesimal transformations with respect to the generalized coordinates and generalized momentums. The structure equation and the non-Noether conserved quantities of the systems are obtained. The inverse issues associated with the momentum-dependent symmetries are discussed. Finally, an example is discussed to further illustrate the applications.

关键词: nonholonomic nonconservative Hamiltonian system, momentum-dependent symmetry, infinitesimal transformation, Lie group

Abstract: This paper investigates the momentum-dependent symmetries for nonholonomic nonconservative Hamilton canonical systems. The definition and determining equations of the momentum-dependent symmetries are presented, based on the invariance of differential equations under infinitesimal transformations with respect to the generalized coordinates and generalized momentums. The structure equation and the non-Noether conserved quantities of the systems are obtained. The inverse issues associated with the momentum-dependent symmetries are discussed. Finally, an example is discussed to further illustrate the applications.

Key words: nonholonomic nonconservative Hamiltonian system, momentum-dependent symmetry, infinitesimal transformation, Lie group

中图分类号:  (General theory of classical mechanics of discrete systems)

  • 45.05.+x
02.20.Qs (General properties, structure, and representation of Lie groups)