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Memorandum N 2 24.06.997 |

Arrangement on storing coordinate values and operations on them |

x=(x_{1};x_{2};x_{3}).
Stored in the form of the one-dimensional array of three numbers. Basic
coordinate system - ICRS (international celestial reference system), more
exactly ICRF (international celestial reference frame) as a system of
three coordinate axes with high accuracy (~10^{–3} angular
seconds) binded to motionless extragalactic sources of the electromagnetic
radiation. This system is close to the orthonormal trihedron, in which
the first vector is directed to the mean 0 Aries at the epoch J2000, and
third - to the mean celestial pole at the same epoch. No need to to convert
vector values to calculate their components in other reference systems,
since here the vector calculation system of all necessary Cartesian and
angular values has adopted. Instead of vector components the orthonormal
trihedrons of coordinate systems are subjected to transformations.
x× y=x_{1}y_{1}+x_{2}y_{2}+x_{3}y_{3}.
x´
y=(x_{2}y_{3}–x_{3}y_{2})1+(x_{3}y_{1}–x_{1}y_{3})2+(x_{1}y_{2}–x_{2}y_{1})3=(x_{2}y_{3}–x_{3}y_{2};
x_{3}y_{1}–x_{1}y_{3}; x_{1}y_{2}–x_{2}y_{1}).
_{1}=x×
1
x}=(x_{1}/l_{x};x_{2}/l_{x};x_{3}/l_{x})
x}×
{y}).
q=arccos({ x}× 3)
x}–({x}×
3)3} with the first and second elements of reference frame
are calculated. First innerproduct is equal to a_{1}=cosj,
second — a_{2}=sinj. According
these two values using the function arctan azimuth angle is calculated
within the range of [0, 2p]: j=atan2(a_{2};a_{1}).
R _{3}(e)x=(x_{1}cose–x_{2}sine;x_{1}sine+x_{2}cose;x_{3})
R _{3}(e)x=(x_{3}sine+x_{1}cose;x_{2};x_{3}cose–x_{1}sine)
R _{3}(e)x=(x_{1};x_{2}cose–x_{3}sine;x_{3}cose+x_{2}sine) |