The Quaternion Subtraction (q = q1 - q2) calculator computes the resulting quaternion (q) from the difference of two (q1 and q2).
INSTRUCTIONS: Enter the following:
The calculator will return the quaternion that is the difference of the two input quaternions.
Quaternions can be represented in several ways. One of the ways is similar to the way complex numbers are represented:
q ≡ q4 + q1i + q2j + q3k,
in which q1 , q2 , q3 and q4 , are real numbers, and i, j, and k, are unit “vectors” which obey similar rules to the vectors of the same names found in vector analysis, but with an additional similarity to the i of complex arithmetic which equals − 1 . The multiplication rules for i , j , and k are depicted
conceptually as follows:
That is, i j = + k, j k = + i, etc. , from figure 1(a) , and j i = - k, i k = -j , etc., from figure 1(b) . Expressed
in this form, the multiplication rules are very easy to remember. Note that the cross products of i, j , and
k obey the rules of vector cross product multiplication, where, for example, given the orthogonal axes,
x, y, and z: x × y = z, y × z = x , and z × x = y .