Higher-order Cayley transforms with applications to attitude representations

We generalize previous results on attitude representations by using Cayley transforms. First, we show that proper orthogonal matrices, which naturally represent rotations, can be generated by a form of conformal analytic mappings in the space of matrices. Using a natural parallelism between the elements of the complex plane and the real matrices, we generate higher-order Cayley transforms and discuss some of their properties. These higher-order Cayley transforms are shown to parameterize proper orthogonal matrices into higher-order Rodrigues parameters.

Higher-order Cayley transforms with applications to attitude representations Academic Article