Parameterization of rotation

The effective description of rotations has led to the development of numerous parameterization techniques presenting various properties and advantages, as described in the following review papers [239, 240, 241, 242, 243, 244, 245].Whether originating from geometric, algebraic, or matrix approaches, parameterization of rotation is most naturally categorized into two classes: vectorial and non-vectorial parameterizations. The former refers to parameterization in which a set of parameters, sometimes called rotational “quasi-coordinates,” define a geometric vector, whereas the latter cannot be cast in the form of a vector. These two types of parameterizations are sometimes denoted as invariant and non-invariant parameterization, respectively