Conformal invariance and conserved quantities of a general holonomic system with variable mass

doi:10.1088/1674-1056/19/4/040302

中国物理B ›› 2010, Vol. 19 ›› Issue (4): 40302-040302.doi: 10.1088/1674-1056/19/4/040302

Conformal invariance and conserved quantities of a general holonomic system with variable mass

蔡建乐¹, 夏丽莉²

(1)College of Science, Hangzhou Normal University, Hangzhou 310018, China; (2)Department of Physics, Henan Institute of Education, Zhengzhou 450014, China

收稿日期:2008-08-18 修回日期:2009-09-07 出版日期:2010-04-15 发布日期:2010-04-15
基金资助:
Project supported by the Key Disciplines' Building Foundation of Henan Institute of Education，the Natural Science Foundation of Education Bureau of Henan Province, China (Grant No.~2009A140003) and the Young Core Instructor from Henan Institute of Educati

Conformal invariance and conserved quantities of a general holonomic system with variable mass

Xia Li-Li(夏丽莉)^a)^† and Cai Jian-Le(蔡建乐)^b)

^a Department of Physics, Henan Institute of Education, Zhengzhou 450014, China; ^b College of Science, Hangzhou Normal University, Hangzhou 310018, China

Received:2008-08-18 Revised:2009-09-07 Online:2010-04-15 Published:2010-04-15
Supported by:
Project supported by the Key Disciplines' Building Foundation of Henan Institute of Education，the Natural Science Foundation of Education Bureau of Henan Province, China (Grant No.~2009A140003) and the Young Core Instructor from Henan Institute of Educati

摘要/Abstract

摘要： Conformal invariance and conserved quantities of a general holonomic system with variable mass are studied. The definition and the determining equation of conformal invariance for a general holonomic system with variable mass are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition under which the conformal invariance would be the Lie symmetry of the system under an infinitesimal one-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.

Abstract: Conformal invariance and conserved quantities of a general holonomic system with variable mass are studied. The definition and the determining equation of conformal invariance for a general holonomic system with variable mass are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition under which the conformal invariance would be the Lie symmetry of the system under an infinitesimal one-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.

Key words: variable mass, conformal invariance, conformal factor, conserved quantity

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

02.20.Sv (Lie algebras of Lie groups)

夏丽莉, 蔡建乐. Conformal invariance and conserved quantities of a general holonomic system with variable mass[J]. 中国物理B, 2010, 19(4): 40302-040302.

Xia Li-Li(夏丽莉) and Cai Jian-Le(蔡建乐). Conformal invariance and conserved quantities of a general holonomic system with variable mass[J]. Chin. Phys. B, 2010, 19(4): 40302-040302.

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Conformal invariance and conserved quantities of a general holonomic system with variable mass

Conformal invariance and conserved quantities of a general holonomic system with variable mass

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