quatmultiply

Calculate product of two quaternions

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Syntax

quatprod = quatmultiply(q,r)

Description

example

quatprod = quatmultiply(q,r) calculates the quaternion product, quatprod, for two quaternions, q and r.

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

Note

Quaternion multiplication is not commutative.

Examples

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Determine the Product of Two Quaternions

Open Live Script

This example shows how to determine the product of two 1-by-4 quaternions.

q = [1 0 1 0];
r = [1 0.5 0.5 0.75];
mult = quatmultiply(q, r)

mult = 1×4

    0.5000    1.2500    1.5000    0.2500

Determine Product of a Quaternion with Itself

Open Live Script

This example shows how to determine the product of a 1-by-4 quaternion with itself.

q = [1 0 1 0];
mult = quatmultiply(q)

mult = 1×4

     0     0     2     0

Determine the Product of Two Different Quaternions

Open Live Script

This example shows how to determine the product of 1-by-4 with two 1-by-4 quaternions.

q = [1 0 1 0];
r = [1 0.5 0.5 0.75; 2 1 0.1 0.1];
mult = quatmultiply(q, r)

mult = 2×4

    0.5000    1.2500    1.5000    0.2500
    1.9000    1.1000    2.1000   -0.9000

Input Arguments

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`q` — First quaternion
m-by-4 matrix | 1-by-4 quaternion | real

First quaternion or set of quaternions, specified as an m-by-4 matrix or 1-by-4 quaternion. Each element must be real.

q must have its scalar number as the first column.

Data Types: double | single

`r` — Second quaternion
m-by-4 matrix | 1-by-4 quaternion | real

Second quaternionor set of quaternions, specified as an m-by-4 matrix or 1-by-4 quaternion. Each element must be real.

r must have its scalar number as the first column.

Data Types: double | single

Output Arguments

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`quatprod` — Output quaternion product
m-by-4 matrix

Output quaternion product, returned as a m-by-4 matrix.

More About

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q and r

Input quaternions q and r have the form:

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

and

$r = r_{0} + i r_{1} + j r_{2} + k r_{3}$

quatprod

Output quaternion product quatprod has the form of

$n = q \times r = n_{0} + i n_{1} + j n_{2} + k n_{3}$

where

$\begin{array}{l} n_{0} = (r_{0} q_{0} - r_{1} q_{1} - r_{2} q_{2} - r_{3} q_{3}) \\ n_{1} = (r_{0} q_{1} + r_{1} q_{0} - r_{2} q_{3} + r_{3} q_{2}) \\ n_{2} = (r_{0} q_{2} + r_{1} q_{3} + r_{2} q_{0} - r_{3} q_{1}) \\ n_{3} = (r_{0} q_{3} - r_{1} q_{2} + r_{2} q_{1} + r_{3} q_{0}) \end{array}$