Direct method of finding first integral of two-dimensional autonomous systems in polar coordinates

doi:10.1088/1009-1963/15/5/002

中国物理B ›› 2006, Vol. 15 ›› Issue (5): 895-898.doi: 10.1088/1009-1963/15/5/002

Direct method of finding first integral of two-dimensional autonomous systems in polar coordinates

汪文珑¹, 楼智美²

(1)Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China; (2)Department of Physics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China

收稿日期:2005-08-27 修回日期:2005-12-08 出版日期:2006-05-20 发布日期:2006-05-20

Direct method of finding first integral of two-dimensional autonomous systems in polar coordinates

Lou Zhi-Mei (楼智美)^a, Wang Wen-Long (汪文珑)^b

^a Department of Physics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China; ^b Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China

Received:2005-08-27 Revised:2005-12-08 Online:2006-05-20 Published:2006-05-20

摘要/Abstract

摘要： A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained. An example is given to illustrate the application of the results.

关键词: direct method, autonomous systems, first integral, polar coordinates

Abstract: A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained. An example is given to illustrate the application of the results.

Key words: direct method, autonomous systems, first integral, polar coordinates

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

45.05.+x (General theory of classical mechanics of discrete systems)

楼智美, 汪文珑. Direct method of finding first integral of two-dimensional autonomous systems in polar coordinates[J]. 中国物理B, 2006, 15(5): 895-898.

Lou Zhi-Mei (楼智美), Wang Wen-Long (汪文珑). Direct method of finding first integral of two-dimensional autonomous systems in polar coordinates[J]. Chinese Physics, 2006, 15(5): 895-898.

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Direct method of finding first integral of two-dimensional autonomous systems in polar coordinates

Direct method of finding first integral of two-dimensional autonomous systems in polar coordinates

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