Calculating with Rotations

Calculating with Rotations edit page

Rotating Vectors

Let

o = rotation.byEuler(90*degree,90*degree,0*degree)

o = rotation
 
  Bunge Euler angles in degree
  phi1  Phi phi2 Inv.
    90   90    0    0

a certain rotation. Then the rotation of the xvector is computed via

v = o * xvector

v = vector3d
  x y z
  0 1 0

The inverse rotation is computed via the backslash operator

o \ v

ans = vector3d
  x y z
  1 0 0

Let

rot1 = rotation.byEuler(90*degree,0,0);
rot2 = rotation.byEuler(0,60*degree,0);

be two rotations. Then the rotation defined by applying first rotation one and then rotation two is computed by

rot = rot2 * rot1

rot = rotation
 
  Bunge Euler angles in degree
  phi1  Phi phi2 Inv.
     0   60   90    0

Then rotational angle and the axis of rotation can be computed via then commands angle(rot) and axis(rot)

rot.angle / degree

rot.axis

ans =
  104.4775
 
ans = vector3d
         x         y         z
  0.447214 -0.447214  0.774597

If two rotations are specifies the command angle(rot1,rot2) computes the rotational angle between both rotations

angle(rot1,rot2) / degree

ans =
  104.4775

The inverse rotation you get from the command inv(rot)

inv(rot)

ans = rotation
 
  Bunge Euler angles in degree
  phi1  Phi phi2 Inv.
    90   60  180    0

There are methods to transform rotations in almost any other parameterization of rotations as they are:

[alpha,beta,gamma] = Euler(rot,'Matthies')

alpha =
    4.7124
beta =
    1.0472
gamma =
    3.1416