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Direction Cosine Matrix Body to Wind to Alpha and Beta - Convert direction cosine matrix to angle of attack and sideslip angle

Library

Utilities/Axes Transformations

Description

The Direction Cosine Matrix Body to Wind to Alpha and Beta block converts a 3-by-3 direction cosine matrix (DCM) into angle of attack and sideslip angle. The DCM matrix performs the coordinate transformation of a vector in body axes (ox₀, oy₀, oz₀) into a vector in wind axes (ox₂, oy₂, oz₂). The order of the axis rotations required to bring this about is:

1. A rotation about oy₀ through the angle of attack (α) to axes (ox₁, oy₁, oz₁)

2. A rotation about oz₁ through the sideslip angle (β) to axes (ox₂, oy₂, oz₂)

Combining the two axis transformation matrices defines the following DCM.

To determine angles from the DCM, the following equations are used:

Dialog Box

Inputs and Outputs

Input	Dimension Type	Description
First	3-by-3 direction cosine matrix	Transforms body-fixed vectors to wind-fixed vectors.

Output	Dimension Type	Description
First	2-by-1 vector	Contains angle of attack and sideslip angle, in radians.

Assumptions and Limitations

This implementation generates angles that lie between ±90 degrees.

Reference

Stevens, B. L., and F. L. Lewis, Aircraft Control and Simulation, John Wiley & Sons, New York, 1992.

See Also

Direction Cosine Matrix Body to Wind

Direction Cosine Matrix to Rotation Angles

Direction Cosine Matrix to Wind Angles

Rotation Angles to Direction Cosine Matrix

Wind Angles to Direction Cosine Matrix

Direction Cosine Matrix Body to Wind

Direction Cosine Matrix ECEF to NED

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