Using Rotations to Build Aerospace Coordinate Systems

Presented here are the main techniques necessary to understand rotations in three dimensions, for use with global visualisation and aerospace simulations. Relevant techniques can be extremely difficult to find in textbooks, so some useful examples are collected here to highlight these techniques. The three standard aerospace coordinate systems are described and built using rotations. The mathematics of rotations is described, using both matrices and quaternions. The necessary calculations are given for analysing standard scenarios that involve the Global Positioning Satellite system for finding line- of-sight directions on Earth, as well as for visualising the world from a cockpit, and for converting to and from the standard software protocol for distributed interactive simulation environments. Appendices then discuss combining rotations, conversions with a particular type of Euler angle convention, the dangers of confusing Euler angles with incremental rotations for software writers, and finally there is a short discussion of interpolation of rotations in computing.