By useing two direct methods to derive Lagrangian from the equation of motion andfrom the first integral respectively, the Lagrangian for a nonlinear dynamical system with variable coefficients x+b(x)x2+c(x)x=0 and a family of Lagrangians for the special case that c(x)=0 are constructed. In addition, the physical significance of conservation of general energy for the non-conservative systems is also discussed.
丁光涛.导出变系数非线性动力学系统拉格朗日函数的两种方法[J].动力学与控制学报,2017,15(1):10~14; Ding Guangtao. Two methods to derive lagrangian for a nonlinear dynamical system with variable coefficients[J]. Journal of Dynamics and Control,2017,15(1):10-14.
