变长平面单摆运动的精确解

变长平面单摆运动的精确解 Exact Solutions for the Nonlinear Equations Describing the Motion of A Pendulum With Variable Length 姚端正 YAO Duan\|zheng 1 1 2 3 first-author 刘绪欣 LIU Xu\|xin 2 1 2 3 武汉大学物理学系,武汉,430072 武汉大学物理学系,武汉,430072 Department of Physics,Wuhan University Department of Physics,Wuhan University 武汉市广播电视大学,武汉,430022 武汉市广播电视大学,武汉,430022 Wuhan Radio\|Telerision University Wuhan Radio\|Telerision University 武汉大学物理学系!武汉430072武汉市广播电视大学,武汉,430022 武汉大学物理学系!武汉430072武汉市广播电视大学,武汉,430022 通过在极坐标形式下选择一特定的试探解和作适当的变量代换，将变长平面单摆小球运动所满足的非线性常微分方程组的求解问题，转化为解高次代数方程的问题，进而用解代数方程的卡尔丹公式求得了其精确解． The problem solving nonlinear ordindary differential equations used to describe the motion of a pendulum with variable length has been turned to that solving an algebrac equation by choosing a trial solution of a special form and by using reasonable variable change in polar coordinates.Thus the nonlinear oridinary differential equations have been solved exactly. 平面单摆 非线性方程 精确解 a simple pendulum nonlinear oridinary differential equation exact solution O411.1 湖北省自然科学基金(2017CFA007) 1999-05-01 2021-04-01 5