quatmod

Calculate modulus of quaternion

Syntax

n = quatmod(q)

Description

n = quatmod(q) calculates the modulus n for a given quaternion, q. For more information on the quaternion and quaternion modulus forms, see Algorithms.

Aerospace Toolbox uses quaternions that are defined using the scalar-first convention.

Examples

Comparing Quaternion Modulus Values

This example computes and prints the modulus of a quaternion.

q = quaternion([1, 2, 3, 4]);
qm = quatmod(q);
fprintf('Modulus of the quaternion: %.3f\n', qm);

Modulus of the quaternion: 5.477

Determine Modulus of Quaternion

Determine the modulus of q = [1 0 0 0].

mod = quatmod([1 0 0 0])

mod = 
1

Input Arguments

q — Quaternion

m-by-4 matrix of real numbers

Quaternion, specified in a m-by-4 matrix of real numbers containing m quaternions.

Example: [1 0 0 0]

Data Types: double

Output Arguments

n — Moduli

column vector of m elements

Moduli, returned as a column vector of m elements.

Algorithms

The quaternion has the form of

$$q=q_0+i{q}_1+j{q}_2+k{q}_3.$$

The quaternion modulus has the form of

$$\left|q\right|=\sqrt{q_0^2+q_1^2+q_2^2+q_3^2}.$$

References

[1] Stevens, Brian L. and Frank L. Lewis. Aircraft Control and Simulation. 2nd ed. Wiley–Interscience, 2003.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Code generation for this function requires the Aerospace Blockset™ software.

Version History

Introduced in R2006b