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Direction Cosine Matrix Body to Wind

Convert angle of attack and sideslip angle to direction cosine matrix

Library

Utilities/Axes Transformations

Description

The Direction Cosine Matrix Body to Wind block converts angle of attack and sideslip angle into a 3-by-3 direction cosine matrix (DCM). 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.

Dialog Box

Inputs and Outputs

InputDimension TypeDescription

First

2-by-1 vectorContains the angle of attack and sideslip angle, in radians.

OutputDimension TypeDescription

First

3-by-3 direction cosine matrixTransforms body-fixed vectors to wind-fixed vectors.

Reference

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

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