Analytical Solution of the Kozai Resonance and its Application |
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Authors: | Hiroshi Kinoshita Hiroshi Nakai |
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Institution: | (1) National Astronomical Observatory, 2-21-1 Osawa, Mitaka, Tokyo, Japan, e-mail |
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Abstract: | When Kozai (1962) studied the secular resonance of asteroids, he found the so-called Kozai resonance and expressed the analytical
solution with the use of Weierstrass ℘. Here we discuss the case where the disturber is outside a disturbed body and give
the analytical solution of the eccentricity, the inclination and the argument of pericenter with the use of the Jacobi elliptic
functions, which are more familiar than the Weierstrass ℘. Then we derive the Fourier expansion of the longitude of node and
the mean anomaly. The analytical expressions obtained here can be used for any value of the eccentricity and the inclination.
Finally we applied these analytical expressions to several dynamical systems – Nereid, that is a highly eccentric satellite
of Neptune, and newly discovered retrograde satellites of Uranus.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | Kozai resonance secular perturbation Nereid |
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