中国物理B ›› 2010, Vol. 19 ›› Issue (9): 90303-090303.doi: 10.1088/1674-1056/19/9/090303

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Conformal invariance and Hojman conserved quantities for holonomic systems with quasi-coordinates

罗一平, 傅景礼   

  1. Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China
  • 收稿日期:2009-10-14 修回日期:2010-04-07 出版日期:2010-09-15 发布日期:2010-09-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10672143 and 60575055).

Conformal invariance and Hojman conserved quantities for holonomic systems with quasi-coordinates

Luo Yi-Ping(罗一平)† and Fu Jing-Li(傅景礼)   

  1. Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China
  • Received:2009-10-14 Revised:2010-04-07 Online:2010-09-15 Published:2010-09-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10672143 and 60575055).

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摘要： We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators for holonomic systems with quasi-coordinates are described in detail. The conformal factor in the determining equations of the Lie symmetry is found. The necessary and sufficient conditions of conformal invariance, which are simultaneously of Lie symmetry, are given. The conformal invariance may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Finally, an illustration example is introduced to demonstrate the application of the result.

Abstract: We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators for holonomic systems with quasi-coordinates are described in detail. The conformal factor in the determining equations of the Lie symmetry is found. The necessary and sufficient conditions of conformal invariance, which are simultaneously of Lie symmetry, are given. The conformal invariance may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Finally, an illustration example is introduced to demonstrate the application of the result.

Key words: quasi-coordinates, conformal invariance, conformal factor, conserved quantity

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