刚体的转动惯性旋心

Rotation inertia center of rigid body

转动惯量是刚体转动惯性的度量,转动惯性旋心是刚体的特殊转动中心,刚体对旋心的转动惯量张量是一个二阶球形张量,刚体对过旋心的任意轴的转动惯量都相等,过旋心的任意轴都是刚体的惯量主轴.提出并证明了转动惯性旋心定理:当刚体对质心的三个主转动惯量均相等时,质心是刚体唯一的旋心;当刚体对质心的三个主转动惯量当中仅较小的两个主转动惯量相等时,刚体有且仅有两个旋心,均在主转动惯量较大的中心惯量主轴上且关于质心对称分布,两个旋心到质心的距离均等于刚体对质心的较大与较小主转动惯量差值与刚体质量比值的平方根;当刚体对质心的三个主转动惯量互不相等或者仅其中较大的两个主转动惯量相等时,刚体不存在转动惯性旋心.

The moment of inertia is the measure of the rotational inertia of the rigid body,and the rotational inertia center is the special rotational center of the rigid body.The inertia tensor to the rotation center is a second-order spherical tensor.The moment of inertia of a rigid body is equal to any axis passing through the rotational inertia center,and any axis passing through the rotation center is the principal axis of inertia.The theorem for the rotation inertia center is proposed and proved,namely,when the three principal moments of inertia to the center of mass are equal,the center of mass is the only rotation center;When only two smaller principal moments of inertia are equal,the rigid body has only two rotation centers,both on the principal axis of larger principal moment and symmetrically distributed with respect to the center of mass,and the distance from the two rotation centers to the center of mass is equal to the square root of the ratio of the difference between the larger and smaller principal moment of inertia to the mass of the rigid body;When the three principal moments of inertia are not equal to each other or only two larger of them are equal,there is no rotation inertia center.