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Chin. Phys. B, 2009, Vol. 18(8): 3135-3138    DOI: 10.1088/1674-1056/18/8/006
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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
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.
Keywords:  third-order ordinary differential equation      Lie symmetry      Hojman's conservation law  
Received:  05 January 2009      Revised:  18 January 2009      Accepted manuscript online: 
PACS:  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
  02.20.Sv (Lie algebras of Lie groups)  
  02.30.Hq (Ordinary differential equations)  
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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