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.

example

Examples

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Determine Division of Two 1-by-4 Quaternions

Open Live Script

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

Open Live Script

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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`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

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`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

quatdivide

Syntax

Description

Examples

Determine Division of Two 1-by-4 Quaternions

Determine Division of 2-by-4 Quaternion

Input Arguments

q — Numerator quaternion m-by-4 matrix of real numbers | 1-by-4 matrix of real numbers

r — Denominator quaternion m-by-4 matrix of real numbers | 1-by-4 matrix of real numbers

Output Arguments

n — Quaternion quotients m-by-4 matrix of real numbers

Algorithms

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

Version History

See Also

`q` — Numerator quaternion
m-by-4 matrix of real numbers | 1-by-4 matrix of real numbers

`r` — Denominator quaternion
m-by-4 matrix of real numbers | 1-by-4 matrix of real numbers

`n` — Quaternion quotients
m-by-4 matrix of real numbers

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.