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dcm2alphabeta

Convert direction cosine matrix to angle of attack and sideslip angle

Description

example

[alpha beta] = dcm2alphabeta(dcm) calculates the angle of attack (alpha) and sideslip angle (beta) for the direction cosine matrix, dcm. The function transforms the coordinates from a vector in body axes into a vector in wind axes.

[alpha beta] = dcm2alphabeta(dcm,action) performs action if the dcm is not orthogonal.

[alpha beta] = dcm2alphabeta(___,tolerance) uses a tolerance level to evaluate if the direction cosine matrix, dcm, is orthogonal. Specify tolerance after all other input arguments.

Examples

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Determine the angle of attack and sideslip angle from a direction cosine matrix:

dcm = [ 0.8926    0.1736    0.4162; ...
       -0.1574    0.9848   -0.0734; ...
       -0.4226         0    0.9063]; 
[alpha, beta] = dcm2alphabeta(dcm)
alpha =

    0.4363


beta =

    0.1745

Determine the angle of attack and sideslip angle from multiple direction cosine matrices:

dcm = [ 0.8926    0.1736    0.4162; ...
       -0.1574    0.9848   -0.0734; ...
       -0.4226         0    0.9063]; 
dcm(:,:,2) = [ 0.9811    0.0872    0.1730; ...
              -0.0859    0.9962   -0.0151; ...
              -0.1736         0    0.9848]; 
[alpha, beta] = dcm2alphabeta(dcm)
alpha =

    0.4363
    0.1745


beta =

    0.1745
    0.0873

Determine the angle of attack and sideslip angle from multiple direction cosine matrices. Return a warning if the dcm exceeds a tolerance of 0.1:

dcm = [ 0.8926    0.1736    0.4162; ...
       -0.1574    0.9848   -0.0734; ...
       -0.4226         0    0.9063]; 
dcm(:,:,2) = [ 0.9811    0.0872    0.1730; ...
              -0.0859    0.9962   -0.0151; ...
              -0.1736         0    0.9848]; 
[alpha, beta] = dcm2alphabeta(dcm,'Warning',0.1)
alpha =
    0.4363
    0.1745

beta =
    0.1745
    0.0873

Input Arguments

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Direction cosine matrices, specified as a 3-by-3-by-m matrix, where m is the number of direction cosine matrices. dcm contains m orthogonal direction cosine matrices.

Action for invalid direction cosine matrices, specified as:

  • 'Warning' — Displays warning and indicates that the direction cosine matrix is invalid.

  • 'Error' — Displays error and indicates that the direction cosine matrix is invalid.

  • 'None' — Does not display warning or error.

Data Types: char | string

Tolerance level to evaluate if the direction cosine matrix, dcm, is orthogonal, specified as a scalar.

The function considers the direction cosine matrix valid if these conditions are true:

  • The transpose of the direction cosine matrix times itself equals 1 within the specified tolerance (transpose(n)*n == 1±tolerance)

  • The determinant of the direction cosine matrix equals 1 within the specified tolerance (det(n) == 1±tolerance).

Data Types: double

Output Arguments

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Angles of attack, returned as an array of m angles of attack, in radians.

Sideslip angles, returned as an m array of sideslip angles, in radians.

Introduced in R2006b