Biomedical Engineering Reference
In-Depth Information
where
is the identity matrix,
the transposed vector of
and
the matrix whose multiplication by a vector gives
the same result as the cross product:
0
0
0
.
Figure 3.5.
Rotation vector representing movement of the hip
Finally, spatial rotation can be represented by a unitary
quaternion
(mathematic theory developed by Hamilton in
1843), in the form of a four-dimensional (4D) vector:
or in the form of a hypercomplex number (3D number in
space, with analogous properties as complex numbers in the
plane):
=
