quatdivide

Divide quaternion by another quaternion

Syntax

n = quatdivide(q,r)

Description

n = quatdivide(q,r) calculates the result of quaternion division, n, for two given quaternions, q and r. Inputs q and r can each be either an m-by-4 matrix containing m quaternions, or a single 1-by-4 quaternion. n returns an m-by-4 matrix of quaternion quotients. Each element of q and r must be a real number.

Aerospace Toolbox uses quaternions that are defined using the scalar-first convention.

The quaternions have the form of

$q = q_{0} + i q_{1} + j q_{2} + k q_{3}$

and

$r = r_{0} + i r_{1} + j r_{2} + k r_{3}$

The resulting quaternion from the division has the form of

$t = \frac{q}{r} = t_{0} + i t_{1} + j t_{2} + k t_{3}$

where

$\begin{array}{l} t_{0} = \frac{(r_{0} q_{0} + r_{1} q_{1} + r_{2} q_{2} + r_{3} q_{3})}{r_{0}^{2} + r_{1}^{2} + r_{2}^{2} + r_{3}^{2}} \\ t_{1} = \frac{(r_{0} q_{1} - r_{1} q_{0} - r_{2} q_{3} + r_{3} q_{2})}{r_{0}^{2} + r_{1}^{2} + r_{2}^{2} + r_{3}^{2}} \\ t_{2} = \frac{(r_{0} q_{2} + r_{1} q_{3} - r_{2} q_{0} - r_{3} q_{1})}{r_{0}^{2} + r_{1}^{2} + r_{2}^{2} + r_{3}^{2}} \\ t_{3} = \frac{(r_{0} q_{3} - r_{1} q_{2} + r_{2} q_{1} - r_{3} q_{0})}{r_{0}^{2} + r_{1}^{2} + r_{2}^{2} + r_{3}^{2}} \end{array}$

Examples

Determine the division of two 1-by-4 quaternions:

q = [1 0 1 0];
r = [1 0.5 0.5 0.75];
d = quatdivide(q, r)


d =

    0.7273    0.1212    0.2424   -0.6061

Determine the division of a 2-by-4 quaternion by a 1-by-4 quaternion:

q = [1 0 1 0; 2 1 0.1 0.1];
r = [1 0.5 0.5 0.75];
d = quatdivide(q, r)


d =

    0.7273    0.1212    0.2424   -0.6061
    1.2727    0.0121   -0.7758   -0.4606