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
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.
Received: 27 August 2005
Revised: 08 December 2005
Accepted manuscript online:
(General theory of classical mechanics of discrete systems)
Cite this article:
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 2006 Chinese Physics 15 895
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