A Beginners guide to 6-D vectors (part 1)

A Beginner's guide to the use of six-dimensional (6-D) vectors to describe its motions and the forces acting upon it is presented. 6-D vectors come in various forms. The particular kind presented here is called spatial vectors. Other kinds of 6-D vector include screws, motors, and Lie algebras. The obvious advantage of 6-D vectors is that they cut the volume of algebra. They have their own physical meanings and mathematical properties. Spatial vectors have their own physical interpretations, their own equations and formulae, and their own rules of use; and the best way to use them is to think directly in 6-D. Spatial vectors are closely related to screw theory, to motor algebra, and the Lie algebra. The 6-D vector makes 6N-dimensional vectors and 6N 36N matrices that describe properties of a whole rigid-body system comprising N bodies.