3476. A Step by Step Procedure for Determining Product of Inertia Using the Moment of Inertia Method
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Paper
Abstract
This paper builds on the generic relationship between Product of Inertia (POI) and Moment of Inertia (MOI) as presented in SAWE paper 1473 (Jodry & Boynton) to develop a step by step procedure, using six MOI measurements to calculate three POI values and the uncertainty in the results, for a given coordinate system. Since the uncertainty varies as a function of the MOI measurements, the method is most suitable where relatively large POI exists, and is least suitable for balancing applications where the desired POI is zero. The method and results are also referenced to Mohr’s Circle. This tool clearly shows the relationship between the MOI measurements, the calculated POI, and its uncertainty. Mohr’s circle may be used to identify the Principal Axes or Moments and Products of Inertia for any orthogonal two-axis coordinate system in the reference coordinate plane for which two MOIs and a POI or 3 MOIs are known. The paper further describes how to populate the Inertia Tensor with MOI and POI values to achieve the standard sign conventions for the tensor so the MOI and POI can be derived for any coordinate system. The equations used to solve for the moments and products of inertia required to generate Mohr’s circle from three Moments of Inertia about non-orthogonal axes are derived.
