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%.
Crisco
J J
JJ
Department of Orthopaedics, Rhode Island Hospital, Brown University, Providence 02903, USA.
McGovern
R D
RD
D001696:Biomechanical Phenomena; D003198:Computer Simulation; D008962:Models, Theoretical; D009038:Motion; D010825:Physics / Q000379:methods*