Quaternion Calculator 9

Last modified by KurtHeckman on 2018/07/26 17:04
Equations in "Quaternion Calculator Collection"
Quaternion Addition Quaternion Subtraction
Quaternion Magnitude Quaternion Conjugate
Quaternion Multiplication Quaternion Versor
Quaternion Inverse Quaternion of Rotation
V3 - Vector Rotation

The Quaternion Calculator includes functions associated with quaternion mathematics.  These include the following:V3 - Vector Rotation.pngQUATERNION ROTATIONS

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:quaternionCycle.png

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 .

Note: Quaternions are not commutative, and the following should be noted:

            q1*q2 ≠ q2 * q1
                   q1*q2 ≠ -q2 * q1
, but
      (q1 * q2) * q3 = q1 * (q2 * q3)

Equations

  • Quaternion Addition by vCalc
  • Quaternion Subtraction by vCalc
  • Quaternion Magnitude by vCalc
  • Quaternion Conjugate by vCalc
  • Quaternion Multiplication by vCalc
  • Quaternion Versor by vCalc
  • Quaternion Inverse by vCalc
  • Quaternion of Rotation by vCalc
  • V3 - Vector Rotation by vCalc