Efficient calculation of mass moments of inertia for segmented homogeneous three-dimensional objects

The equations for the volume, centroid, and mass moments of inertia of a three-dimensional object are derived using Green's theorem. The object is assumed to be homogeneous and described as a stack of two-dimensional cross-sections. Given these assumptions, our approach using Green's theorem dramatically decreases data manipulation and computation as compared to the classical mass element summation technique employed for three-dimensional discrete objects. Although numerous factors influence accuracy, we chose to evaluate two representative objects in two orientations to determine the influence of the number of two-dimensional cross-sections on the accuracy of the calculations. For these shapes, 15 cross-sections per object were required to achieve relative error below 1%.