惯性矩和惯性积的图解法

A diagrammatic method to determine moment and product of inertia

以张量为工具分析了平面图形对坐标轴的惯性矩和惯性积,以及主惯性轴与主惯性矩间的对应关系,提出了一种图解方法.指出了平面图形对任意一对正交坐标轴的惯性矩和惯性积相互制约地在圆周上变化,圆周上的各点坐标就是该平面图形对任意一对正交坐标轴的惯性矩和惯性积.并用此方法确定了主惯性轴的位置和主惯性矩.用图解法求惯性矩和惯性积更直观、简单,是惯性矩和惯性积转轴公式的一种补充.

Tensor was used to analyze the moment and product of inertia of a plane figure on coordinate axes and the correspondence of principal axes and principal moment of inertia.A diagrammatic method was proposed to solve the above problems.The results show that the moment and the product of inertia of a plane figure on any pair of orthogonal axes are mutual restraints and change in a circle,and the coordinates of the points of the circle are the moment and the product of inertia,which can be used to determine the principal axis position and moment of inertia.The method is more intuitive and simple,and is a supplement to the transformation equation of the moment and product of inertia.