General solution of the Kozai mechanism

  • Hiroshi Kinoshita
  • Hiroshi Nakai
Open Access
Original Article


Kinoshita and Nakai (Celest. Mech. Dyn. Astr. 75, 125–147, 1999) gave the analytical solution of the Kozai mechanism. In this solution the eccentricity and the inclination of a disturbed body take any value, but the argument of the pericenter is restricted to take 0° or 90°. In this paper, we derive the general solution that can be applied for any value of the argument of the pericenter.


Kozai mechanism Analytical solution Asteroid Kozai (3040) Natural satellite S2002N3 


  1. Kinoshita H., Nakai H. (1991) Secular perturbations of fictitious satellites of Uranus. Celest. Mech. 52, 293–303CrossRefADSGoogle Scholar
  2. Kinoshita H., Nakai H. (1999) Analytical solution of the Kozai resonance and its application. Celest. Mech. Dyn. Astr. 75, 125–147MATHCrossRefADSMathSciNetGoogle Scholar
  3. Kozai Y. (1962) Secular perturbations of asteroids with high inclination and eccentricity. Astron. J. 67, 591–598CrossRefADSMathSciNetGoogle Scholar
  4. Lidov, M.L.: Evolution of the planets artificial satellites orbits under effect of the outer bodies gravity perturbations. Artifi. Satellites Earth (Moscow, USSR: Nauka Publishers) 8, 5–45 (1961) (in Russian)Google Scholar
  5. Lidov, M.L.: The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies. Planet. Space Sci. 9, 719–759 (1962) (the English translation of Lidov’s paper(1961))Google Scholar
  6. Vashkovyak M.A. (1999) Evolution of the orbits of distant satellites of uranus. Astron. Lett. 25, 476–481ADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.National Astronomical ObservatoryMitaka, TokyoJapan

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