【摘要】 物理学中的单摆问题,在摆角大于5°时候,其动力学方程是非线性的,这一非线性方程可用奇异摄动法来求得近似解,鉴于奇异摄动法求解过程比较复杂,尝试将单摆的动力学非线性方程进行线化,然后采用摄动理论中的直接展开法来求得线化后的方程的近似解,使得求解过程大大简化。与精确解比较表明:一阶近似解也具有相当高的精度。更多还原

【Abstract】 In physics,the single pendulum dynamic equation is nonlinear when the pendulum angle is more than 5 degrees.Its approximate solution can be obtained by using singular perturbation method,but the process of solution is a little complex.In this paper,the nonlinear equation is linearized.The solution of linear equation is obtained by method of regular perturbation.The process becomes simple.Comparing with accurate solution,the result indicates that its first order approximate solution is also of high accuracy.更多还原