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

Library

Utilities/Axes Transformations

Description

The Wind Angles to Direction Cosine Matrix block converts three wind rotation angles into a 3-by-3 direction cosine matrix (DCM). 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.

Dialog Box

Inputs and Outputs

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

Output	Dimension Type	Description
First	3-by-3 direction cosine matrix	Transforms earth vectors to wind vectors.

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 to Rotation Angles

Direction Cosine Matrix to Wind Angles

Rotation Angles to Direction Cosine Matrix

WGS84 Gravity Model

Wind Angular Rates

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