Minimum-Parameter Representations of NDimensional Principal Rotations,” The

Classic techniques have been established to characterize SO(N) using the N-dimen-sional Euler’s theorem and the Cayley transform. These techniques provide separate descriptions of N-dimensional orientation in terms of the constituent principal rota-tions or a minimum-parameter representation. The two descriptions can be linked by the canonical form of the extended Rodrigues parameters. This form is developed into a minimum-parameter representation that directly links to the principal rotations. The new representation can be solved analytically for N = 3 and numerically for higher dimensions. The new parameters represent a projection of the principal rotations onto the planes formed by the body coordinates