Quaternion Rotation

Rotate vector by quaternion

Library:
Aerospace Blockset / Utilities / Math Operations

Description

The Quaternion Rotation block rotates a vector by a quaternion. Aerospace Blockset™ uses quaternions that are defined using the scalar-first convention. For the equations used for the quaternion, vector, and rotated vector, see Algorithms.

Ports

Input

expand all

`q` — Quaternion
quaternion | vector

Quaternions in the form of [q₀, r₀, ..., q₁, r₁, ... , q₂, r₂, ... , q₃, r₃, ...], specified as a quaternion or vector of quaternions.

Data Types: double

`vec` — Vector
vector | vector of vectors

Vector or vector of vectors in the form of [v₁, u₁, ... , v₂, u₂, ... , v₃, u₃, ...].

Data Types: double

Output

expand all

`vec_rot` — Rotated quaternion
rotated quaternion | vector of rotated quaternions

Rotated vector or vector of rotated vectors.

Data Types: double

Algorithms

The quaternion has the form of

$q = q_{0} + i q_{1} + j q_{2} + k q_{3} .$

The vector has the form of

$v = i v_{1} + j v_{2} + k v_{3} .$

The rotated vector has the form of

$v^{'} = [\begin{matrix} v_{1}^{'} \\ v_{2}^{'} \\ v_{3}^{'} \end{matrix}] = [\begin{matrix} (1 - 2 q_{2}^{2} - 2 q_{3}^{2}) & 2 (q_{1} q_{2} + q_{0} q_{3}) & 2 (q_{1} q_{3} - q_{0} q_{2}) \\ 2 (q_{1} q_{2} - q_{0} q_{3}) & (1 - 2 q_{1}^{2} - 2 q_{3}^{2}) & 2 (q_{2} q_{3} + q_{0} q_{1}) \\ 2 (q_{1} q_{3} + q_{0} q_{2}) & 2 (q_{2} q_{3} - q_{0} q_{1}) & (1 - 2 q_{1}^{2} - 2 q_{2}^{2}) \end{matrix}] [\begin{matrix} v_{1} \\ v_{2} \\ v_{3} \end{matrix}]$

References

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

[2] Diebel, James. "Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors." Stanford University, Stanford, California, 2006.

Documentation

Quaternion Rotation

Description

Ports

Input

`q` — Quaternion
quaternion | vector

`vec` — Vector
vector | vector of vectors

Output

`vec_rot` — Rotated quaternion
rotated quaternion | vector of rotated quaternions

Algorithms

References

Extended Capabilities

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

See Also

Aerospace Blockset Documentation

Support

Documentation

Quaternion Rotation

Description

Ports

Input

q — Quaternion quaternion | vector

vec — Vector vector | vector of vectors

Output

vec_rot — Rotated quaternion rotated quaternion | vector of rotated quaternions

Algorithms

References

Extended Capabilities

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

See Also

Aerospace Blockset Documentation

Support

`q` — Quaternion
quaternion | vector

`vec` — Vector
vector | vector of vectors

`vec_rot` — Rotated quaternion
rotated quaternion | vector of rotated quaternions

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