Representing a Projection-based SRF Vector in Terms of a CLTP

• x, y and z refer to the projection-based SRFwhile X,Y and Z refer to the CLTP

• Counter-clockwise rotations are takento be positive

• ? is the COM (Convergence Of the Meridian)and determines the true North direction

• Let V be a unit vector in a projection-basedSRF = (xc, yc, zc)

• Rotations are about the Z-axis so that it issufficient to consider only the planar rotations

• The X-Y system is the planar part of the CLTP

• The vector V can be represented in the X-Ysystem by a rotation of the components of V

• Since vectors are not position dependent, therotation can be viewed as occurring at theprojection-based SRF origin

• A counter-clockwise rotation from x-y to X-Ysuffices. That is:

XC = xc?cos(?) + yc?sin(?)YC = -xc?sin(?) + yc?cos(?)ZC = zc

• The vector V = (XC, YC, ZC) is therepresentation of V in the CLTP.