.Spot.Base.Transforms.rotation_abc

Information

The function rotation_abc calculates the matrix R_abc that rotates abc variables around the {1,1,1}-axis in abc-space with arbitrary angle theta.

Using the definition

  g_k = 1/3 + (2/3)*cos(theta - k*2*pi/3),  k=0,1,2 (phases a, b, c)

                 [g_0, g_2, g_1]
  R_abc(theta) = [g_1, g_0, g_2]
                 [g_2, g_1, g_0]

  {1, 1, 1}/sqrt(3)

Coefficient matrices of the form (symmetrical systems)

      [x,  xm, xm]
  X = [xm,  x, xm]
      [xm, xm, x ]

The connection between R_abc and R_dqo is the following

  R_abc = P0'*R_dqo*P0.

up users guide

Interface

function rotation_abc
  extends Icons.Function;
  input SI.Angle theta "rotation angle";
  output Real[3, 3] R_abc "rotation matrix";
end rotation_abc;