无阻尼单摆运动微分方程的反正切分式变换精确解  

Exact solution of arctangent fractional transformation of motion differential equation of single pendulum without damping

作　　者：张广平[1] 

机构地区：[1]陇东学院电气工程学院,甘肃庆阳745000

出　　处：《大学物理》2012年第2期16-18,共3页College Physics

摘　　要：无阻尼单摆运动微分方程是一种具有物理背景的非线性常微分方程,研究其精确解和解法是非线性科学中的一个重要内容.在F展开法的基础上,应用反正切分式变换正弦函数方法,并引入Riccati辅助方程,得到了4种无阻尼单摆方程精确解的结果.达到了丰富此类方程求解技巧和精确解的目的.总结得出此类方程应用反正切分式变换方法具有一定普适性的结论.The differential equation of motion of single pendulum without damping is a kind of nonlinear ordinary differential equation with the physical background and the study of exact solutions in nonlinear science is an important work. In order to lay the foundation for studying nonlinear behavior of these issues, four kinds of exact solutions are obtained by using the arctangent fractional transformation method of sine function and introducing Riccati auxiliary equation based on the F-expansion method. The arctangent fractional transformation method applied in such equation is a universal conclusion.

关 键 词：无阻尼单摆 非线性方程 F展开法 反正切分式变换 RICCATI方程 精确解 

分 类 号：O322[理学—一般力学与力学基础]