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. 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

Determine Division of Two 1-by-4 Quaternions

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

Determine Division of 2-by-4 Quaternion

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

q — Numerator quaternion

m-by-4 matrix of real numbers | 1-by-4 matrix of real numbers

Numerator 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 1 0]

Data Types: double

r — Denominator quaternion

m-by-4 matrix of real numbers | 1-by-4 matrix of real numbers

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

n — Quaternion quotients

m-by-4 matrix of real numbers

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

$$t=\frac{q}{r}=r^{-q}=t_0+i{t}_1+j{t}_2+k{t}_3.$$

where

$$\begin{array}{l}{t}_0=\frac{(r_0{q}_0+r_1{q}_1+r_2{q}_2+r_3{q}_3)}{r_0^2+r_1^2+r_2^2+r_3^2}\\ t_1=\frac{(r_0{q}_1-r_1{q}_0-r_2{q}_3+r_3{q}_2)}{r_0^2+r_1^2+r_2^2+r_3^2}\\ t_2=\frac{(r_0{q}_2+r_1{q}_3-r_2{q}_0-r_3{q}_1)}{r_0^2+r_1^2+r_2^2+r_3^2}\\ t_3=\frac{(r_0{q}_3-r_1{q}_2+r_2{q}_1-r_3{q}_0)}{r_0^2+r_1^2+r_2^2+r_3^2}.\end{array}$$

References

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

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Code generation for this function requires the Aerospace Blockset™ software.

Version History

Introduced in R2006b