标题： 线性微分方程求解非线性力学问题：一种新方法 显示英文标题

标题： Linear differential equations to solve nonlinear mechanical problems: A novel approach

摘要： 通常，非线性力学问题被表述为非线性微分方程。 如果已知一个给定的非线性微分方程的一个解，引入一种新方法来找出非线性微分方程的新解。 利用已知的非线性微分方程的解，建立线性微分方程。 这些线性微分方程的解使用标准技术找到。 然后将这些线性微分方程的解代入非线性微分方程，并检查这些解是否也是原始非线性微分方程的解。 发现许多线性微分方程的解也是原始非线性微分方程的解。 显示英文摘要

摘要： Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations are set up. The solutions of these linear differential equations are found using standard techniques. Then the solutions of the linear differential equations are put into non-linear differential equations and checked whether these solutions are also solutions of the original non-linear differential equation. It is found that many solutions of the linear differential equations are also solutions of the original non-linear differential equation.