Noether's and Poisson's methods for solving  differential equation xs(m)= Fs（t,xk(m-2),xk(m-1)

doi:10.1088/1674-1056/17/3/015

中国物理B ›› 2008, Vol. 17 ›› Issue (3): 822-824.doi: 10.1088/1674-1056/17/3/015

Noether's and Poisson's methods for solving differential equation x_s^(m)= F_s（t,x_k^(m-2),x_k^(m-1)

何光¹, 梅凤翔²

(1)School of Aerospace Science and Engineering, Beijing Institute of Technology, Beijing 100081, China; (2)School of Science, Beijing Institute of Technology, Beijing 100081, China

收稿日期:2007-08-10 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 10572021) and Doctoral Programme Foundation of Institution of Higher Education of China (Grant No 20040007022).

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

Received:2007-08-10 Online:2008-03-04 Published:2008-03-04
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: Noether's method, Poisson's method, higher order ordinary differential equation, integration

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.

Key words: Noether's method, Poisson's method, higher order ordinary differential equation, integration

中图分类号: (Ordinary differential equations)

02.30.Hq

02.30.Jr (Partial differential equations)

何光, 梅凤翔. Noether's and Poisson's methods for solving differential equation x_s^(m)= F_s（t,x_k^(m-2),x_k^(m-1)[J]. 中国物理B, 2008, 17(3): 822-824.

He Guang(何光) and Mei Feng-Xiang(梅凤翔). Noether's and Poisson's methods for solving differential equation $x_s^{\left( m \right)} = F_s \left({t,x_k^{\left( {m - 2} \right)} ,x_k^{\left( {m - 1} \right)} } \right)$[J]. Chin. Phys. B, 2008, 17(3): 822-824.

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Noether's and Poisson's methods for solving differential equation x_s^(m)= F_s（t,x_k^(m-2),x_k^(m-1)

Noether's and Poisson's methods for solving differential equation $x_s^{\left( m \right)} = F_s \left({t,x_k^{\left( {m - 2} \right)} ,x_k^{\left( {m - 1} \right)} } \right)$

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