Rotation parameters - A survey of techniques

A number of parameterizations of rotations in three-dimensional space are c ompared with respect to their formulas and qualitative characteristics rele vant for practical use. The number and uniqueness of parameters, singularit ies. visualization, and constraint equations within one parameter set are c onsidered. Formulas are given fur the transformation to and from rotation m atrices and symmetric Euler parameters as well as fur the rotation of a vec tor. the inverse rotation, the combination of two rotations, and the kinema tic differential equations. The list of parameters includes the five-parame tric Hopf parameters. Symmetric rotation matrices are treated separately. A ll properties are given in comprehensive tables with formulas ready for pro gramming.