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Lidov-Kozai perturbation in the motion of Jupiter Trojans

The Lidov-Kozai perturbation was investigated in the region of Jupiter Trojans. These asteroids move in the mean-motion commensurability 1:1 with Jupiter. The study was carried out by means of numerical integration of equations of motion of real asteroids. The simplest dynamical model was used with Jupiter as an only perturbing body moving in a fixed elliptical orbit. After eliminating classical secular perturbations from osculating elements, it becomes possible to determine the influence of the Lidov-Kozai mechanism on the orbital inclination and eccentricity. As a result, it was found that for L 4 -trojans the maximum eccentricity, and, accordingly, the minimum inclination is achieved with perihelion argument values ω = 30º and 210º. For L 5 -trojans the maximum eccentricity is located at the points ω = 150º, 330º.