A tutorial on vectors and attitude [Focus on Education]

We examine vectors and attitude in Engineering with greater attention to detail than in earlier works on the subject. This tutorial is an expansion of part of a survey of attitude representations. The most salient characteristic of this work is a greater emphasis on the distinction between physical vectors and their representation as column vectors. The need for such a treatment arises most strongly in attitude estimation, but logically, the need is present also in attitude dynamics and control. Attitude is estimated by comparing two different column-vector representations of the same physical vector. Thus, from the beginning, the distinction between physical vectors and column vectors requires explicit treatment in attitude estimation. In works on attitude dynamics and control, however, this distinction is often overlooked or presented only in attitude statics, with the transition to attitude dynamics being made as much through verbal arguments as by mathematical development.