In this chapter, we discuss the representation of rotations of R 3 and R 4 in terms of quaternions. Such a representation is not only concise and elegant, it also yields a very efficient way of handling composition of rotations. It also tends to be numerically more stable than the representation in terms of orthogonal matrices. 431
Algebra, T., & Quaternions, H. (2011). The Quaternions and the Spaces S 3 , SU ( 2 ),. Science, (2), 281–300.