
Every set of attitude coefficients (corresponding to a line in attitude data file) is valid for its own time interval and gives the possibility to get a matrix N of tranformation from the GSE coordinate system to the S/C coordinate system as well as a matrix M of tranformation from the S/C coordinate system to the GSE coordinate system.
Every set consists of 20 parameters. There are:
1. Line number
2. Year
3. Month
4. Day
5. Beginning of the time interval (in thousands of sec)
6. Interval duration (in thousands of sec)
Parameters 720 are attitude coefficients:
711. A_{1}  A_{5}
1216. B_{1}  B_{5}
17. ω_{1}
18. ω_{2}
19. c_{1}
20. c_{2}
Using the coefficients we can get angles α, β, γ:
α is an angle between X_{S} axis and the Sun projection onto X_{S}Y_{S} plane,
β is an angle between X_{S} axis and the Sun projection onto X_{S}Z_{S} plane.
The algorithm is based on the assumption that the α,β angles can be approximated by the following functions:
α = A_{1} +
A_{2}sin ω_{1} t +
A_{3}cos ω_{1} t +
A_{4}sin ω_{2} t +
A_{5}cos ω_{2} t,
β = A_{1} +
B_{2}sin ω_{1} t +
B_{3}cos ω_{1} t +
B_{4}sin ω_{2} t +
B_{5}cos ω_{2} t.
γ is an angle between Y_{S} axis and projection of the North Pole of Ecliptic onto X_{S}Y_{S} plane.
As this direction is close to the one which is orthogonal to the spin axis the linear approximation of the γ angle is valid:
γ = c_{1} + c_{2} t
ω_{1} is the spin rate of the Sun direction around the angular momentum vector;
ω_{2} is the spin rate of the the angular momentum vector around the main axis of inertia X_{S}.
Using α, β angles the Sun direction (which coincides with X_{G} axis) cosines in the S/C coordinate system can be calculated:
The direction e of the North Pole of Ecliptic plane (which coincides with Z_{G} axis cosines in the S/C coordinate system can be calculated by formulas:
a_{x} = s_{2} cos γ + s_{3} sin γ
So we have the direction cosines of X_{G} and Z_{G} axis in the S/C coordinate system.
The third direction p is
and the matrix M of transformation from the S/C to the GSE systems (the direction cosines matrix) is:
M = 

and the matrix N of transformation from the GSE system to the S/C system is the transpose of matrix M:
N = 

Any vector V_{S/C} in the S/C coordinate system can be transformed to the GSE coordinate system using M matrix:
as well as
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