Chapter 18. More on Logarithms and Exponentials
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.
2D Rotations
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 ...
Get The Morgan Kaufmann Series in Interactive 3D Technology: Visualizing Quaternions now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
