# quatdivide

Divide quaternion by another quaternion

## Description

example

n = quatdivide(q,r) calculates the result of quaternion division n for two given quaternions, q and r. For more information on the input and output quaternion forms, see Algorithms.

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

## Examples

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Divide one 1-by-4 quaternions by another 1-by-4 quaternion.

q = [1 0 1 0];
r = [1 0.5 0.5 0.75];
d = quatdivide(q, r)
d = 1×4

0.7273    0.1212    0.2424   -0.6061

Divide 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 = 2×4

0.7273    0.1212    0.2424   -0.6061
1.2727    0.0121   -0.7758   -0.4606

## Input Arguments

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Numerator quaternion, specified in a m-by-4 matrix of real numbers containing m quaternions or a 1-by-4 matrix of reall numbers containing one quaternion.

Example: [1 0 1 0]

Data Types: double

Denominator quaternion, specified in a m-by-4 matrix of real numbers containing m quaternions or a 1-by-4 matrix of real numbers containing one quaternion.

Example: [1 0.5 0.5 0.75]

Data Types: double

## Output Arguments

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Quaternion quotients, returned in an m-by-4 matrix of real numbers.

## Algorithms

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

$\begin{array}{l}{t}_{0}=\frac{\left({r}_{0}{q}_{0}+{r}_{1}{q}_{1}+{r}_{2}{q}_{2}+{r}_{3}{q}_{3}\right)}{{r}_{0}^{2}+{r}_{1}^{2}+{r}_{2}^{2}+{r}_{3}^{2}}\\ {t}_{1}=\frac{\left({r}_{0}{q}_{1}-{r}_{1}{q}_{0}-{r}_{2}{q}_{3}+{r}_{3}{q}_{2}\right)}{{r}_{0}^{2}+{r}_{1}^{2}+{r}_{2}^{2}+{r}_{3}^{2}}\\ {t}_{2}=\frac{\left({r}_{0}{q}_{2}+{r}_{1}{q}_{3}-{r}_{2}{q}_{0}-{r}_{3}{q}_{1}\right)}{{r}_{0}^{2}+{r}_{1}^{2}+{r}_{2}^{2}+{r}_{3}^{2}}\\ {t}_{3}=\frac{\left({r}_{0}{q}_{3}-{r}_{1}{q}_{2}+{r}_{2}{q}_{1}-{r}_{3}{q}_{0}\right)}{{r}_{0}^{2}+{r}_{1}^{2}+{r}_{2}^{2}+{r}_{3}^{2}}.\end{array}$

## References

[1] Stevens, Brian L. and Frank L. Lewis. Aircraft Control and Simulation. 2nd ed. Wiley–Interscience, 2003.

## Version History

Introduced in R2006b