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

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.