Hojman's theorem of the third-order ordinary differential equation

doi:10.1088/1674-1056/18/8/006

中国物理B ›› 2009, Vol. 18 ›› Issue (8): 3135-3138.doi: 10.1088/1674-1056/18/8/006

Hojman's theorem of the third-order ordinary differential equation

吕洪升¹, 张宏彬², 顾书龙²

(1)Department of Mathematics, Chaohu College, Chaohu 238000, China; (2)Department of Physics, Chaohu College, Chaohu \rm 238000, China

收稿日期:2009-01-05 修回日期:2009-01-18 出版日期:2009-08-20 发布日期:2009-08-20
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 10872037) and the Natural Science Foundation of Anhui Province of China (Grant No 070416226).

Hojman's theorem of the third-order ordinary differential equation

ü Hong-Sheng(吕洪升)^a), Zhang Hong-Bin(张宏彬)^b)^†, and Gu Shu-Long(顾书龙)^b)

^a Department of Mathematics, Chaohu College, Chaohu 238000, China; ^b Department of Physics, Chaohu College, Chaohu \rm 238000, China

Received:2009-01-05 Revised:2009-01-18 Online:2009-08-20 Published:2009-08-20
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 10872037) and the Natural Science Foundation of Anhui Province of China (Grant No 070416226).

摘要/Abstract

摘要： This paper extends Hojman's conservation law to the third-order differential equation. A new conserved quantity is constructed based on the Lie group of transformation generators of the equations of motion. The generators contain variations of the time and generalized coordinates. Two independent non-trivial conserved quantities of the third-order ordinary differential equation are obtained. A simple example is presented to illustrate the applications of the results.

Abstract: This paper extends Hojman's conservation law to the third-order differential equation. A new conserved quantity is constructed based on the Lie group of transformation generators of the equations of motion. The generators contain variations of the time and generalized coordinates. Two independent non-trivial conserved quantities of the third-order ordinary differential equation are obtained. A simple example is presented to illustrate the applications of the results.

Key words: third-order ordinary differential equation, Lie symmetry, Hojman's conservation law

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

02.20.Sv (Lie algebras of Lie groups) 02.30.Hq (Ordinary differential equations)

吕洪升, 张宏彬, 顾书龙. Hojman's theorem of the third-order ordinary differential equation[J]. 中国物理B, 2009, 18(8): 3135-3138.

ü Hong-Sheng(吕洪升), Zhang Hong-Bin(张宏彬), and Gu Shu-Long(顾书龙) . Hojman's theorem of the third-order ordinary differential equation[J]. Chin. Phys. B, 2009, 18(8): 3135-3138.

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Hojman's theorem of the third-order ordinary differential equation

Hojman's theorem of the third-order ordinary differential equation

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