三线摆法是测量转动惯量的常用方法,理论上通常都是把摆线作理想处理（即摆线质量趋于0）,但在工程测量中,被测工件往往较重,摆线不再是轻质细线,摆线质量势必会对空载悬盘的转动惯量测量产生影响.本文应用哈密顿原理和变量替换,导出三线摆摆线的变张力弦振动方程,通过对摆线与悬盘连接点（x=0）的运动状态讨论,推得摆线质量不能忽略情形下的对称式三线摆的转动惯量计算式,并借助于MATLAB软件快速便利地进行计算.%Using the three wire-pendulum to measure the moment of inertia is a common practice. The cycloid is usually assumed in an ideal state theoretically (i.e the mass of the cycloid approaches 0). But actually, if the workpiece measured is heavy, the mass of the cycloid can not be neglected, we have to consider the mass of the cycloid in the moment of inertia of the empty turning wheel. This paper uses the Halmiltonian theory and the variable substitution to derive the variable tension string vibration equation of the threewire-pendulum cycloid. And from the state of the point in the junction of the cycloid and the turning wheel (x = 0), we obtain a computational formula for the moment of inertia by using the three wire-pendulum without neglecting the mass of the cycloid. In addition, we can make calculations by MATLAB.
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