Name

CL_rot_angles2matrix — Rotation angles matrix

Calling Sequence

   M = CL_rot_angles2matrix(axes,angles)
   
   

Parameters

axes:

vecteur with rotations order (1xN, Nmax = 3 ).

angles:

Euler angles (NxP, Nmax = 3 ) [rad]

M:

frame matrix. If N = 1, and P=1 M is a (3x3) matrix; if P>1 , M is a (3x3xP) hypermatrix.

Description

  • Computes the matrix M such that M' is the rotation matrix from angle angles(1) around first axis, then angles(2) around second axis, then angles(3) around third axis.

    axes =[1],angles =[a],M=CL_rot_angles2matrix(axes,angles) -> M' is a rotation of 'a' on axe 1

    axes =[2],angles =[a],M=CL_rot_angles2matrix(axes,angles) -> M' is a rotation of 'a' on axe 2

    axes =[3],angles =[a],M=CL_rot_angles2matrix(axes,angles) -> M' is a rotation of 'a' on axe 3

    axes =[1,2],angles =[a;b],M=CL_rot_angles2matrix(axes,angles) -> M=CL_rot_angles2matrix(2,b)*CL_rot_angles2matrix(1,a)

    axes =[1,2,3],angles =[a;b;c],M=CL_rot_angles2matrix(axes,angles) -> M=CL_rot_angles2matrix(3,c)*CL_rot_angles2matrix(2,b)*CL_rot_angles2matrix(1,a)

    axes =[3,2,3],angles =[a;b;c],M=CL_rot_angles2matrix(axes,angles) -> M=CL_rot_angles2matrix(3,c)*CL_rot_angles2matrix(2,b)*CL_rot_angles2matrix(3,a)

    For example: if R is a reference frame and S a satellite frame issued from successive rotations angles =[a,b,c] then the coordinates of a unique vector v (with coordinates vR in R and vS in S) are linked by:

  • Last update : 20/11/2009

Authors

CNES - DCT/SB

See also

CL_rot_quat2matrix, CL_rot_matrix2quat

Examples

M = CL_rot_angles2matrix([1],[30*%pi/180])
M = CL_rot_angles2matrix([1,2],[%pi/3;%pi/2])
M = CL_rot_angles2matrix([1,2,3],[%pi/6;%pi/2;%pi/4])

//R is a reference frame; S is a frame obtained from R with a rotation of 10 deg on the Z axis
ang = CL_deg2rad(10)
M = CL_rot_angles2matrix([3],ang)
vR = [1;0;0]  //X axis of the R reference frame expressed on the R reference frame
vS = M*vR     //vS is the X axis of R expressed on the S frame
wR = M'*vR    //wR is vector vR rotated 10 deg on the Z axis, all expressed on the R reference frame