Liu, "Pitt's inequality and the uncertainty principle associated with the
quaternion fourier transform," Journal of Mathematical Analysis and Applications, vol.
Throughout the paper, we denote the real number field by R, the set of all m x n matrices over the
quaternion algebra
Quaternion analysis offers another possibility of generalizing complex function theory to higher dimension, and it has wide applications in mathematical physics, Dirichlet BVPs of higher-order partial differential equations, and other fields.
[delta][[theta].sub.1] is the attitude error computed from the error
quaternion [delta]Q which is defined as
Consider the
quaternion group [Q.sub.16] = (x, y|x = [y.sup.2], xyx = y) of order 16.
Simplifying, we can notice that the rotation's definition of vector v post by
quaternion is calculated as qvq-1 where q-1 is the conjugate of the
quaternion q.
A
quaternion moment-based scheme is suggested in [17] where Tsougenis et al.
where [cross product] denotes the
quaternion product which can be determined using the Hamilton rule [25]:
Shoemake, "Animating rotation with
quaternion curves," in Proceedings of the 12th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '85), pp.
Unit
quaternion is a 4D parameterization, which allows such singularities to be avoided [22].