平面对称图形静矩与惯性矩的关系研究

定义平面图形K绕Ox轴、Oy轴的静矩与惯性矩关系系数分别为px、py,通过对矩形、椭圆等典型图形px、py的计算发现,具有双重垂直对称平面图形K存在px=py=常数的关系;通过对等腰三角形、对称四边形等典型图形px、py的计算发现,具有单重对称平面图形存在px=常数1、py=常数2的关系,且在这两种情况下,px、py均具有标度变换不变性等性质。

Research on Coefficient of the Relationship between Static Moment and Moment of Inertia

Given definition px and py to the coefficient of relationship between static moment and moment of inertia for a plane figure K rotating along Ox-axis and Oy-axis,it can be found after calculation of a rectangle and an oval that px is equal to py and equal to a constant for a symmetrical plane figure K which has two symmetry axis perpendicular to each other.After calculation of a risosceles triangle and a symmetric quadrilateral,it also can be found that for a symmetrical plane figure K which has only one symmetry axis px is equal to constant 1 and py equal to constant 2.These two cases tell that px and py has many features such as the feature of invariance of the scale conversion.