Convert from Direction Cosine Matrix to Euler Angles

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Description

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

Usage

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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]

Author(s)

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

See Also

EA2DCM

Examples

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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')

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