# Quaternion Inverse

Calculate inverse of quaternion

• Library:
• Aerospace Blockset / Utilities / Math Operations

## Description

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

## Ports

### Input

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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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Quaternion inverse or vector of quaternion inverses.

Data Types: `double`

## Algorithms

The quaternion has the form of

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

The quaternion inverse has the form of

`${q}^{-1}=\frac{{q}_{0}-i{q}_{1}-j{q}_{2}-k{q}_{3}}{{q}_{0}^{2}+{q}_{1}^{2}+{q}_{2}^{2}+{q}_{3}^{2}}.$`

## References

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