TABLE OF CONTENTS Attitude coordinates (sometimes also referred to as attitude parameters) are sets of coordinates { x 1, x 2, ..., x n} that completely describe the orientation of a rigid body relative to some reference frame. There is an infinite number of attitude coordinates to choose from. Each set has strengths and weaknesses compared to the other sets. This is analogous to choosing among the infinite sets of translational coordinates such as Cartesian, polar, or spherical coordinates to describe a spatial position of a point. However, describing the attitude of an object relative to some reference frame does differ in a fundamental way from describing the corresponding relative spatial position of a point. In Cartesian space, the linear displacement between two spatial positions can grow arbitrarily large. On the other hand, two rigid body (or coordinate frame) orientations can differ at most by a 180 deg rotation, a finite rotational displacement. If an object rotates past 180 deg, then its orientation actually starts to approach the starting angular position again. This concept of two orientations differing only by finite rotations is important when designing control laws. A smart choice in attitude coordinates can exploit this fact and produce a control law that can intelligently handle very large orientation errors.
The quest for "the best rigid body orientation description" is a very fundamental and important one. It has been studied by such great scholars as Euler, Jacobi, Hamilton, Cayley, Klein, Rodrigues, and Gibbs and has led to...
