On the Distance Function Between Two Keplerian Elliptic Orbits |
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Authors: | Konstantin V Kholshevnikov Nikolay N Vassiliev |
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Institution: | (1) St. Petersburg University, e-mail, Russia;(2) St. Petersburg Branch of the Steklov, Institute of Mathematics, Russian Academy of Sciences, e-mail, Russia |
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Abstract: | The problem of finding critical points of the distance function between two Keplerian elliptic orbits is reduced to the determination
of all real roots of a trigonometric polynomial of degree 8. The coefficients of the polynomial are rational functions of
orbital parameters. Using computer algebra methods we show that a polynomial of a smaller degree with such properties does
not exist. This fact shows that our result cannot be improved and it allows us to construct an optimal algorithm to find the
minimal distance between two Keplerian orbits.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | distance function elliptic orbits critical points Gr?bner basis computer algebra |
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