中国物理B ›› 2006, Vol. 15 ›› Issue (8): 1662-1664.doi: 10.1088/1009-1963/15/8/002

• GENERAL • 上一篇    下一篇

Hamilton--Jacobi method for solving ordinary differential equations

梅凤翔, 吴惠彬, 张永发   

  1. Faculty of Science, Beijing Institute of Technology, Beijing 100081, China
  • 修回日期:2005-12-31 出版日期:2006-08-20 发布日期:2006-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10272021, 10572021) and the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 0040007022).

Hamilton--Jacobi method for solving ordinary differential equations

Mei Feng-Xiang(梅凤翔)†, Wu Hui-Bin(吴惠彬), and Zhang Yong-Fa(张永发)   

  1. Faculty of Science, Beijing Institute of Technology, Beijing 100081, China
  • Revised:2005-12-31 Online:2006-08-20 Published:2006-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10272021, 10572021) and the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 0040007022).

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摘要： The Hamilton--Jacobi method for solving ordinary differential equations is presented in this paper. A system of ordinary differential equations of first order or second order can be expressed as a Hamilton system under certain conditions. Then the Hamilton--Jacobi method is used in the integration of the Hamilton system and the solution of the original ordinary differential equations can be found. Finally, an example is given to illustrate the application of the result.

Abstract: The Hamilton--Jacobi method for solving ordinary differential equations is presented in this paper. A system of ordinary differential equations of first order or second order can be expressed as a Hamilton system under certain conditions. Then the Hamilton--Jacobi method is used in the integration of the Hamilton system and the solution of the original ordinary differential equations can be found. Finally, an example is given to illustrate the application of the result.

Key words: differential equation, integration, Hamilton--Jacobi method

中图分类号:  (Ordinary differential equations)

  • 02.30.Hq
45.20.Jj (Lagrangian and Hamiltonian mechanics) 02.30.Ik (Integrable systems)