dcm2alphabeta

Convert direction cosine matrix to angle of attack and sideslip angle

Syntax

[alpha beta] = dcm2alphabeta(dcm)

[alpha beta] = dcm2alphabeta(dcm,action)

[alpha beta] = dcm2alphabeta(___,tolerance)

Description

[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

collapse all

Determine Angle of Attack and Sideslip Angle from Direction Cosine Matrix

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 Angle of Attack and Sideslip Angle from Multiple Direction Cosine Matrices

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 Angle of Attack and Sideslip Angle from Multiple Direction Cosine Matrices within Tolerance

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

collapse all

`dcm` — Direction cosine matrices
3-by-3-by-m matrix

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` — Action
`'None'` (default) | `'Error'` | `'Warning'`

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` — Relative tolerance
`eps(2)` (default) | scalar

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