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Quaternion Rotation

Rotate vector by quaternion

Library

Utilities/Math Operations

Description

The Quaternion Rotation block rotates a vector by a quaternion.

The quaternion has the form of

q=q0+iq1+jq2+kq3.

The vector has the form of

v=iv1+jv2+kv3.

The rotated vector has the form of

v=[v1v2v3]=[(12q222q32)2(q1q2+q0q3)2(q1q3q0q2)2(q1q2q0q3)(12q122q32)2(q2q3+q0q1)2(q1q3+q0q2)2(q2q3q0q1)(12q122q22)][v1v2v3]

For more information, see Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors.

Inputs and Outputs

InputDimension TypeDescription

First

Quaternion or vectorContains quaternions in the form of [q0, r0, ..., q1, r1, ... , q2, r2, ... , q3, r3, ...].

Second

VectorContains vector or vector of vectors in the form of [v1, u1, ... , v2, u2, ... , v3, u3, ...].

OutputDimension TypeDescription

First

Rotated quaternion or vectorContains rotated vector or vector of rotated vectors.

References

Stevens, Brian L., Frank L. Lewis, Aircraft Control and Simulation, Wiley–Interscience, 2nd Edition.

Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors

Introduced before R2006a

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