Abstract
The author's theory of Trojan asteroids (Érdi, 1988) is developed further. The motion of the Trojans is considered in the framework of the three-dimensional elliptic restricted three-body problem of the Sun-Jupiter-asteroid system including also the secular changes of Jupiter's orbital eccentricity and the apsidal motion of Jupiter's elliptic orbit. An asymptotic solution is derived, by applying the multiple-timescale method, for the cylindrical coordinates of the asteriods and for the perturbations of the orbital elements. This solution is used for the analysis of the long-time dynamical behaviour of the perihelion and the eccentricity of the Trojans.
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