Quaternion Normalize

Normalize quaternion

Libraries:
Aerospace Blockset / Utilities / Math Operations

Description

The Quaternion Normalize block calculates a normalized quaternion for a given quaternion. Aerospace Blockset™ uses quaternions that are defined using the scalar-first convention. For the equations used for the quaternion and normalized quaternion, see Algorithms.

Examples

Quaternion Estimate from Measured Rates

Estimate a quaternion and model the equations.

Open Script

Ports

Input

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q — Quaternion
quaternion | vector of quaternions

Quaternions in the form of [ q ₀ , r ₀ , ..., q ₁ , r ₁ , ... , q ₂ , r ₂ , ... , q ₃ , r ₃ , ...], specified as a quaternion or vector of quaternions.

Data Types: double

Output

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normal(q) — Normalized quaternion
normalized quaternion | vector of normalized quaternions

Normalized quaternion or vector of normalized quaternions.

Data Types: double

Algorithms

The quaternion has the form of

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

The normalized quaternion has the form of

$n o r m a l (q) = \frac{q_{0} + i q_{1} + j q_{2} + k q_{3}}{\sqrt{q_{0}^{2} + q_{1}^{2} + q_{2}^{2} + q_{3}^{2}}} .$

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