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.
Received: 05 January 2009
Revised: 18 January 2009
Accepted manuscript online:
Fund: 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).
Cite this article:
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 2009 Chin. Phys. B 18 3135
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