摘要
利用拉格朗日方程,导出了多节摆系统的运动微分方程.根据三对角阵的性质,给出了振动系统的特征多项式和特征矢量的递推公式.并以三节摆为例,说明了结果的应用,用此方法验证了《力学与实践》2002年第24期《多自由度振动系统的简正坐标和简正振动模式》一文中的结果.
The differential equation of motion of the system with many identical pendulums is derived by using Lagrange＇ equation.Based on properties of three diagonal matrixes,the recursion expressions of characteristic polynomial and mode vectors of the vibration system are given.Moreover,taking three identical pendulums as examples,we show the application of the result and confirm the result in the reference [3] with this method.
出处
《大学物理》
北大核心
2011年第4期12-15,共4页
College Physics
关键词
多节摆
自由振动
三对角阵
特征多项式
特征矢量
many identical pendulums
free vibration
three diagonal matrixes
characteristic polynomial
mode vectors
