# DCM2EA: Convert from Direction Cosine Matrix to Euler Angles In RSpincalc: Conversion Between Attitude Representations of DCM, Euler Angles, Quaternions, and Euler Vectors

## Description

`DCM2EA` converts from Direction Cosine Matrix (DCM) to Euler Angles (EA).

## Usage

 ```1 2``` ```DCM2EA(DCM, EulerOrder='zyx', tol = 10 * .Machine\$double.eps, ichk = FALSE, ignoreAllChk = FALSE) ```

## Arguments

 `DCM` Direction Cosine Matrix (DCM) is a rotation matrix 3x3 (N=1) or an array 3x3xN `EulerOrder` Euler Angles (EA) is a vector [psi, theta, phi] `tol` Tolerance from deviations from unity for the determinant of rotation matrices or the the vector length for unitary vectors. `ichk` Logical, FALSE=disables near-singularity warnings. `ignoreAllChk` Logical, TRUE=disables all warnings and error checks (use with caution!).

## Details

Euler Angles (EA) xyz <=> x(roll) y(pitch) z(yaw) Type 1 Rotations (Tait-Bryan angles): xyz - xzy - yxz - yzx - zyx - zxy Singular if second rotation angle is -90 or 90 degrees. Type 2 Rotations (proper Euler angles): xyx - xzx - yxy - yzy - zxz - zyz Singular if second rotation angle is 0 or 180 degrees.

Euler angles [psi, theta, phi] range from -90 to 90 degrees. Tait-Bryan angles [psi, theta, phi] range from 0 to 180 degrees. Angles about Euler vectors range from 0 to 180 degrees.

## Value

Euler Angles (EA) vector [psi, theta, phi]

Jose Gama

## References

by John Fuller, 14 Jul 2008 SpinCalc, Function to Convert between DCM, Euler angles, Quaternions, and Euler vectors. http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm–euler-angles–quaternions–and-euler-vectors

Paolo de Leva, 01 May 2013 SpinConv, Conversion from a rotation representation type to another. http://www.mathworks.com/matlabcentral/fileexchange/41562-spinconv

`EA2DCM`

## Examples

 ```1 2 3``` ```DCM <- matrix(c(-0.3573404, -0.1515663, 0.9215940, 0.6460385, 0.6724915, 0.3610947, -0.6744939, 0.7244189, -0.1423907),3,3,byrow=TRUE) DCM2EA(DCM,'xyz') ```

### Example output

```          [,1]      [,2]      [,3]
[1,] -1.764881 -0.740279 -2.076036
```

RSpincalc documentation built on May 2, 2019, 10:59 a.m.