Quaternion Division

Divide quaternion by another quaternion

Library:
Aerospace Blockset / Utilities / Math Operations

Description

The Quaternion Division block divides a given quaternion by another. Aerospace Blockset™ uses quaternions that are defined using the scalar-first convention. The output is the resulting quaternion from the division or vector of resulting quaternions from division. For the quaternion forms used, see Algorithms.

Ports

Input

expand all

`q` — Dividend quaternion
quaternion | vector of quaternions

Dividend quaternions in the form of [q₀, p₀, ..., q₁, p₁, ... , q₂, p₂, ... , q₃, p₃, ...], specified as a quaternion or vector of quaternions.

Data Types: double

`r` — Divisor quaternion
quaternion | vector of quaternions

Divisor quaternions in the form of [s₀, r₀, ..., s₁, r₁, ... , s₂, r₂, ... , s₃, r₃, ...], specified as a quaternion or vector of quaternions.

Data Types: double

Output

expand all

`q/r` — Output quaternion
quaternion | vector

Output quaternion or vector of resulting quaternions from division.

Data Types: double

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

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

References

[1] Stevens, Brian L., Frank L. Lewis. Aircraft Control and Simulation, Second Edition. Hoboken, NJ: Wiley–Interscience.

Documentation

Quaternion Division

Description

Ports

Input

`q` — Dividend quaternion
quaternion | vector of quaternions

`r` — Divisor quaternion
quaternion | vector of quaternions

Output

`q/r` — Output quaternion
quaternion | vector

Algorithms

References

Extended Capabilities

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

See Also

Aerospace Blockset Documentation

Support

Documentation

Quaternion Division

Description

Ports

Input

q — Dividend quaternion quaternion | vector of quaternions

r — Divisor quaternion quaternion | vector of quaternions

Output

q/r — Output quaternion quaternion | vector

Algorithms

References

Extended Capabilities

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

See Also

Aerospace Blockset Documentation

Support

`q` — Dividend quaternion
quaternion | vector of quaternions

`r` — Divisor quaternion
quaternion | vector of quaternions

`q/r` — Output quaternion
quaternion | vector

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