Pseudo-Reversing Theorem for Rotation and its Application to Orientation Theory.

摘要

We state and prove a useful theorem on manipulating rotation order which, while not new, is barely present in the literature. This theorem allows the order of a sequence of rotations to be reversed, provided that the sense of the axes of rotation is changed from 'body' to 'space fixed' or vice versa. We use the theorem to aid calculations in geodesy (constructing a local northeast down coordinate system) and aerospace theory (relating yaw pitch roll rates to vehicle angular velocity). The new notation here sheds light generally on the field of orientation theory, as well as giving insight to standard terms relating to wind direction used for treating ship motion. Although we present our analyses in the style of a tutorial in the general subject of spatial orientation theory, there is new notation here, along with alternative and novel ways of treating problems that are often seen as difficult or obscure by practitioners. This report follows on from the 2005 DSTO report DSTOTN0640, but is completely self contained, and DSTOTN0640 need not be read beforehand.