Principal rotation representations of proper N × N orthogonal matrices

Abstract

Three and four parameter representations of 3 × 3 orthogonal matrices are extended to the general case of proper N × N orthogonal matrices. These developments generalize the classical Rodrigues parameters, the Euler parameters, and the recently introduced modified Rodrigues parameters to higher dimensional spaces. The developments presented are motivated by, and significantly generalize and extend the classical result known as the Cayley transformation.