CHARACTERIZATION AND APPLICATION OF QUATERNIONS FOR ENHANCED COMPUTER PROCESSING ALGORITHMS

THE QUATERNION OPERATOR HAS LONG BEEN REGARDED AS AN EFFICIENT ROTATION OPERATOR BUT ONE THAT IS NOT WELL KNOWN IN THE PRACTICING AEROSPACE ENGINEERING COMMUNITY. SO, FIRST WE METRICIZE 'HOW MUCH BETTER' THE QUATERNION OPERATOR ACTUALLY IS FOR A VARIETY OF APPLICATIONS. THEN, A PLAN FOR RIGOROUSLY INTRODUCING QUATERNION ALGEBRA AND QUATERNION CALCULUS IS PRESENTED. THIS PLAN EXPLOITS THE INTRINSIC GEOMETRIC PROPERTIES OF THE QUATERNION OPERATOR IN ORDER TO ACHIEVE AN ENGAGING 'DO-IT-YOURSELF' PEDAGOGY. LIBERAL USE OF PICTORIAL REPRESENTATIONS OF THIS GEOMETRY AND ALSO OF THE VARIOUS APPLICATIONS WILL APPEAL TO THE INTUITION AND HENCE MAKE THE QUATERNION OPERATOR EASIER TO UNDERSTAND AND MORE READILY ACCESSIBLE TO ALL PRACTITIONERS.