Higher-Order Cayley Transforms with Applications to Attitude Representations
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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.
author list (cited authors)
Tsiotras, P., Junkins, J. L., & Schaub, H.