Sandwich product of Quaternion normalizes rotating point

[Mayitzin]

Class: Quaternion

A vector x in 3D can be rotated with the methods rotate() and to_DCM() as:

q = Quaternion([1.0, 2.0, 3.0, 4.0])
x = [1.0, 2.0, 3.0]
# Build rotation R from q and multiply it with x
x1 = q.toDCM()@x    # returns [1.8, 2., 2.6]
# Simplifies the operation above:
x2 = q.rotate(x)    # also returns [1.8, 2., 2.6]

A product q*x*q.conj() is called a sandwich product and it also rotates x by a given q, but cannot be performed because they are different types of data. So, multiply with x as a pure quaternion.

x3 = q*Quaternion(x)*q.conj()   # returns [0.4811, 0.5345, 0.6949]

This product is, however, normalized. As a solution, the two first methods are preferred, but a seamless sandwich product would be nice to have.