Quaternion Multiplication

Calculate product of two quaternions

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Libraries:
Aerospace Blockset / Utilities / Math Operations

Description

The Quaternion Multiplication block calculates the product for two given quaternions. Aerospace Blockset™ uses quaternions that are defined using the scalar-first convention. For more information on the quaternion forms, see Algorithms.

Examples

HL-20 with Flight Instrument Blocks and Visualization Using Unreal Engine

Model NASA HL-20 lifting body and controller modeled in Simulink^® and Aerospace Blockset, using Unreal Engine^® for visualization.

• Open Live Script

Ports

Input

q — First quaternion

quaternion | vector of quaternions

First quaternion, specified as a vector or vector of quaternions. A vector of quaternions has this form, where q and p are quaternions:

[ q 0 , p 0 , ..., q 1 , p 1 , ... , q 2 , p 2 , ... , q 3 , p 3 , ...]

Data Types: double

r — Second quaternion

quaternion | vector of quaternions

Second quaternion, specified as a vector or vector of quaternions. A vector of quaternions has this form, where s and r are quaternions:

[ s 0 , r 0 , ..., s 1 , r 1 , ... , s 2 , r 2 , ... , s 3 , r 3 , ...]

Data Types: double

Output

q*r — Product

vector | vector of quaternion products

Product of two quaternions, output as a vector or vector of quaternion products.

Data Types: double

Algorithms

This block uses quaternions of 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 quaternion product has the form of

$$t=q\times r=t_0+i{t}_1+j{t}_2+k{t}_3,$$

where

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

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