The center of mass (CM) is the mean location of all the system mass, and is typically expressed as a vector in a selected coordinate system. When combining CM data defined in multiple coordinate systems, coordinate transformations are performed using well-known vector transformation algorithms to bring data into a common coordinate system for summation or comparison. CM uncertainties (also known as dispersions) are typically expressed as a set of plus (+) and minus (-) values around the nominal value. CM uncertainties may be visualized as a volume of possible CM locations surrounding the mean value. Uncertainty coordinate transformation is not a well-defined process because it involves transforming boundaries of a volumetric region without a defined shape. There is currently no standard, well-documented method for transforming the coordinates of CM uncertainties. This situation has resulted in CM uncertainty data being handled inconsistently and incorrectly when coordinate transformations are applied. This paper proposes methods and algorithms for performing coordinate transformations on CM uncertainty data, and describes the pros and cons of the various approaches.
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