Noether's and Poisson's methods for solving differential equation $x_s^{\left( m \right)} = F_s \left({t,x_k^{\left( {m - 2} \right)} ,x_k^{\left( {m - 1} \right)} } \right)$
He Guang(何光)a)† and Mei Feng-Xiang(梅凤翔)b)
a School of Aerospace Science and Engineering, Beijing Institute of Technology, Beijing 100081, China; b School of Science, Beijing Institute of Technology, Beijing 100081, China
Abstract This paper studies integration of a higher-order differential equation which can be reduced to a second-order ordinary differential equation. The solution of the second-order equation can be obtained by the Noether method and the Poisson method. Then the solution of the higher-order equation can be obtained by integrating the solution of the second-order equation.
Received: 10 August 2007
Accepted manuscript online:
Fund: Project supported
by the National Natural Science Foundation of China (Grant No
10572021) and Doctoral Programme Foundation of Institution of Higher
Education of China (Grant No 20040007022).
Cite this article:
He Guang(何光) and Mei Feng-Xiang(梅凤翔) Noether's and Poisson's methods for solving differential equation $x_s^{\left( m \right)} = F_s \left({t,x_k^{\left( {m - 2} \right)} ,x_k^{\left( {m - 1} \right)} } \right)$ 2008 Chin. Phys. B 17 822
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