POINTING IN REAL EUCLIDEAN-SPACE

We treat the following problem. Given two vectors of the same length, find an orthogonal transformation that transforms one to the other. Th is problem arises in many different engineering fields. In particular, it arises in aerospace engineering, where it is called the pointing p roblem. We establish the theoretical background of the pointing proble m in n and thus also in three-dimensional space. We give a straightfor ward solution to this problem, but because it is not unique, we widen the scope of the problem, define the notions of minimal pointing and o ptimal pointing, and require that the sought matrix be not only orthog onal but also a minimal, or an optimal, pointing. We then give an illu strative solution in three dimensions and then extend the solution to n dimensions using two different approaches, which we present and prov e. Several examples are given in three and four dimensions. The three- dimensional examples are used to illustrate the characteristics of the solution.