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

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.