Page 75 - Satellite Communications, Fourth Edition

Orbits and Launching Methods 55

Figure 2.9 Geocentric-equatorial coordinate system (IJK frame).

texts on engineering mathematics. Many programmable calculators and
computer programs have a built-in matrix multiplication function). The
transformation matrix in this case is 3 2, given by Eq. (2.33b) and the
PQW components form a 2 1 matrix. The components of r in the IJK
frame appear as a 3 1 matrix given by

r I
~
≥ r ¥ R c r P d (2.33a)
J
r Q
r K
~
where the transformation matrix R is given by

(cos cos sin sin cos i)( cos sin sin cos cos i)
~
R 5 ≥(sin cos cos sin cos i)( sin sin cos cos cos i)¥
(sin sin i) (cos sin i)

(2.33b)
It should be noted that the angles Ω and w take into account the
rotations resulting from the earth’s equatorial bulge, as described in
Sec. 2.8.1. The matrix multiplication is most easily carried out by
computer.