February 2006
Intermediate to advanced
600 pages
8h 57m
English
The visualization of the calculus of rotations requires that we perceive not only the global properties of individual isolated frames but also their infinitesimal properties, which tell us how nearby frames are related and provide a basis for the calculus of frames, angular velocities, and higher derivatives. In this chapter, we will carry out a more advanced treatment of the properties of infinitesimal rotations and their relationship to the concept of logarithms and exponentials, both for matrices, and for abstract quaternions.
Rotations in two dimensions correspond precisely to a unit-length complex vector, which in turn can always be written as the exponential
Equation 18.1.
By representing ...