quatmultiply

Calculate product of two quaternions

Description

example

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

Note

Quaternion multiplication is not commutative.

Examples

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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

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

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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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

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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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=q0+iq1+jq2+kq3

and

r=r0+ir1+jr2+kr3

quatprod

Output quaternion product quatprod has the form of

n=q×r=n0+in1+jn2+kn3

where

n0=(r0q0r1q1r2q2r3q3)n1=(r0q1+r1q0r2q3+r3q2)n2=(r0q2+r1q3+r2q0r3q1)n3=(r0q3r1q2+r2q1+r3q0)

References

[1] Stevens, Brian L., Frank L. Lewis. Aircraft Control and Simulation, 2nd Edition. Hoboken, NJ: John Wiley & Sons, 2003.

Extended Capabilities

Introduced in R2006b