1474. Mass Properties of Solids Using Third Moments
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Paper
Abstract
This paper presents a mathematical method of determining all of the three-dimensional mass properties of two classes of solids. The first class is bodies of revolution – a cross-sectional area of any shape revolved about an axis through any angle up to 360 degrees. The second class is prisms – a cross-sectional area of any shape that is bounded in the third dimension by two non-parallel (in general) planes. There are no restrictions at all on the complexity of the cross-sectional area. If the cross-section defines a thin shell, then the properties of a revolved or prismatic surface can be determined. The advantages of this method are: 1) complex shapes that are usually broken into several simple parts can be done in one piece, 2) it works on about 95 percent of the shapes in the SAWE handbook, and 3) it gives results for all six moments and products of inertia. It is ideally suited to be integrated into a computerized drawing system. The method requires knowledge of all of the standard section properties of the cross-sectional area plus four new higher-order properties which I call third moments. The equations for these third moments and rules for translation and rotation will be presented. This method is essentially an extension of Pappus’ theorem for volumes of bodies of revolution.
