The Lie symmetries and Noether conserved quantities  of discrete mechanical systems with variable mass

doi:10.1088/1674-1056/17/3/003

中国物理B ›› 2008, Vol. 17 ›› Issue (3): 754-758.doi: 10.1088/1674-1056/17/3/003

The Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass

施沈阳¹, 傅景礼², 张晓波², 黄晓虹³, 陈立群⁴

(1)Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China；Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; (2)Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; (3)School of Physics and Electronic Information, Wenzhou University, Wenzhou 325000, China; (4)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

收稿日期:2007-05-21 修回日期:2007-08-01 出版日期:2008-03-04 发布日期:2008-03-04
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 10672143).

The Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass

Shi Shen-Yang(施沈阳)^a)b)†, Fu Jing-Li(傅景礼)^a), Huang Xiao-Hong(黄晓虹)^c),Chen Li-Qun(陈立群)^b), and Zhang Xiao-Bo(张晓波)^a)

^a Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; ^b Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; ^c School of Physics and Electronic Information, Wenzhou University, Wenzhou 325000, China

Received:2007-05-21 Revised:2007-08-01 Online:2008-03-04 Published:2008-03-04
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 10672143).

摘要/Abstract

摘要： This paper studies the Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass. The discrete Euler--Lagrange equation and energy evolution equation are derived by using a total variational principle. The invariance of discrete equations under infinitesimal transformation groups is defined to be Lie symmetry. The condition of obtaining the Noether conserved quantities from the Lie symmetries is also presented. An example is discussed for applications of the results.

关键词: discrete mechanics, variable mass system, Lie symmetry, Noether conserved quantity

Abstract: This paper studies the Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass. The discrete Euler--Lagrange equation and energy evolution equation are derived by using a total variational principle. The invariance of discrete equations under infinitesimal transformation groups is defined to be Lie symmetry. The condition of obtaining the Noether conserved quantities from the Lie symmetries is also presented. An example is discussed for applications of the results.

Key words: discrete mechanics, variable mass system, Lie symmetry, Noether conserved quantity

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

45.05.+x

施沈阳, 傅景礼, 黄晓虹, 陈立群, 张晓波. The Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass[J]. 中国物理B, 2008, 17(3): 754-758.

Shi Shen-Yang(施沈阳), Fu Jing-Li(傅景礼), Huang Xiao-Hong(黄晓虹), Chen Li-Qun(陈立群), and Zhang Xiao-Bo(张晓波) . The Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass[J]. Chin. Phys. B, 2008, 17(3): 754-758.

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The Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass

The Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass

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