转动惯量与惯量积二者平行轴定理的统一处理

将相对于刚体内某定点O的惯量张量分解为两部分:一为相对于刚体质心C*的惯量张量;另一为相对于O点的惯量张量,但假定刚体的所有质量都集中在C*点。如此的分解,能使转动惯量平行轴定理或惯量积平行轴定理均极其便于表述。这样获得的两个定理中,前者已熟知后者尚陌生,且前者只不过是后者的特例。通过惯量张量本身即可统一处理此二定理,而且它们的表达式将全部概括在单个公式之中。

Unified treatment of the theorem of parallel axes for both moments and products of inertia

The inertia tensor, relative to some fixed point O in the rigid body, is decomposed into two parts. One is the inertia tensor relative to C*, the mass center of the body; and the other is that relative to O with the whole mass of the body supposed to be concentrated at C*. Such a decomposition greatly facilitates the formulation of the theorem of parallel axes for the moments or for the products of inertia. Of the two theorems thus obtained, the former is already well-known while the latter remains unfamiliar. Moreover, the former is merely a particular case of the latter. Subsequently, it is further expounded that, via the inertia tensor itself, these two theorems can be treated unifiedly, and that all the expressions for both of them will be totally summarized in a single formula.