导出变系数非线性动力学系统拉格朗日函数的两种方法

TWO METHODS TO DERIVE LAGRANGIAN FOR A NONLINEAR DYNAMICAL SYSTEM WITH VARIABLE COEFFICIENTS

利用从运动微分方程出发和从第一积分出发导出拉格朗日函数的两种直接方法,构造变系数非线性动力学系统¨x+b(x)x^2+c(x)x=0的拉格朗日函数和c(x)=0特殊情况的拉格朗日函数族.另外,讨论了这种非保守系统广义能量守恒的物理意义.

By using two direct methods to derive Lagrangian from the equation of motion and from the first inte- gral respectively, the Lagrangian for a nonlinear dynamical system with variable coefficients x＋ b（x）x^2 ＋ c（x）x = 0 and a family of Lagrangians for the special case that c （x） = 0 are constructed. In addition, the physical sig- nificance of conservation of general energy for the non - conservative systems is also discussed.