均质三角形边框刚体对其质心轴的转动惯量的简明推导

Simple Derivation on the Rotation Inertia of a Homogeneous Triangular Frame Rigid Body to the Axis through Its Mass Center

利用任意三角形的边长与顶点坐标的关系,直接推出任意三角形边框的质心到各边中点的距离与三角形各边边长的关系,从而方便地求得任意均质三角形边框刚体对其质心轴的转动惯量.

Using the relationships between the side lengths and the coordinates of the triangle points,the distances from the mass center of the triangle frame to the midpoints of each side can be deduced directly.The rotation inertia of the rigid triangle frame about the axis through its mass center is obtained very briefly.