用Gauss原理求非线性振动微分方程的近似解

本文将Ｇａｕｓｓ原理用于求解某些非线性振动微分方程的近似解，其结果与非线性振动理论中常用的摄动法（如：Ｌｉｎｄｓｔｅｄｔ－Ｐｏｉｎｃａｒｅ法，ＫＢＭ法等）所得结果完全一致，而与其它数值近似解法（如最小二乘法等）相比．不仅原理及方法简单，而且也较为精确．

Approximate Solution of Nonlinear Vibration Differential Equations by Gauss's Principle

In this paper the approximate solution of nonlinear vibration differential equations is given by Gauss's principle. This is the same conclusion of approximate solution of nonlinear vibration differential equation as is obtained by perturbation methods (such as: Lindstedt - Poincare method, KBM method ) which are usually employed in nonlinear vibration theory. The prillciple and method of this solutioll are not Only simpler but also accurater than the other numerical approximate solution (such as the least square method ).