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Direction Cosine Matrix to Wind Angles - Convert direction cosine matrix to wind angles

Library

Utilities/Axes Transformations

Description

The Direction Cosine Matrix to Wind Angles block converts a 3-by-3 direction cosine matrix (DCM) into three wind rotation angles. The DCM matrix performs the coordinate transformation of a vector in earth axes (ox₀, oy₀, oz₀) into a vector in wind axes (ox₃, oy₃, oz₃). The order of the axis rotations required to bring this about is:

1. A rotation about oz₀ through the heading angle (χ) to axes (ox₁, oy₁, oz₁)

2. A rotation about oy₁ through the flight path angle (γ) to axes (ox₂, oy₂, oz₂)

3. A rotation about ox₂ through the bank angle (μ) to axes (ox₃, oy₃, oz₃)

Combining the three axis transformation matrices defines the following DCM.

To determine wind 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 earth vectors to wind vectors.

Output	Dimension Type	Description
First	3-by-1 vector	Contains the wind angles, in radians.

Assumptions and Limitations

This implementation generates a flight path angle that lies between ±90 degrees, and bank and heading angles that lie between ±180 degrees.

See Also

Direction Cosine Matrix Body to Wind

Direction Cosine Matrix Body to Wind to Alpha and Beta

Direction Cosine Matrix to Rotation Angles

Rotation Angles to Direction Cosine Matrix

Wind Angles to Direction Cosine Matrix

Direction Cosine Matrix to Rotation Angles

Discrete Wind Gust Model

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