0 ° uj + (Wg cos ^ — uj sin 0 1 cot 0

E3 Transformations Between Spherieal Coordinates

Figure E-2 illustrates the spherical coordinate system on a sphere of unit radius defined by the north pole, N, and the azimuthal reference direction, R, in the equatorial plane. The coordinates of point P are ($,0). A new coordinate system is defined by the north pole, N', at ($o>0a) >n the old coordinate system. The new azimuthal reference is at an angle, <f>'0 relative to the MV great circle. The coordinates (<!>', 0') of P in the new system are given by:

cos 0'=cos 0ocos 0+sin 0Qsin 0 cos (<j> - <J>0)

sin«>' - <f>0)=sin(<|> - $0)sin 0/sin 0 '

where 9 and 9' are both defined over the range 0 to 180 deg, and and

— $o) are both in the range 0 to 180 deg or in the range 180 to 360 deg. Simplified forms of Eqs. (E-1S) in two special cases are as follows:

Hie most common spherical inertial coordinates for attitude analysis are the celestial coordinates (a,S) defined in Section 2.2. The right ascension, a, and the declination, 8, are related to 4> and 9 by a—<j>

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