Quaternion Division

Divide quaternion by another quaternion

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Libraries:
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

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

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.

Extended Capabilities

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

Version History

Introduced before R2006a