664. Transformations and Invariants of the Inertia Tensor


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R L Johnson: 664. Transformations and Invariants of the Inertia Tensor. In: 27th Annual Conference, New Orleans, Louisiana, May 13-16, pp. 12, Society of Allied Weight Engineers, Inc., New Orleans, Louisiana, 1968.



The reader who has been required to develop the mass properties of an inclined body has probably discovered that information in this area is scarce and generally discussed too esoterically for the average man. While it is true that a complete understanding of of the theory involved requires a knowledge of tensor analysis and advanced classical mechanics, a background of matrix algebra and trigonometry is sufficient to follow this treatise.
Starting with basic notions and definitions the direction cosine matrix and its relation to coordinate transformations will be demonstrated. With this development the generation of mass properties of a body around an arbitrary set of coordinate axes is readily accomplished.


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