Lidov–Kozai mechanism in Hildas and Jupiter Trojans

In this paper, the Lidov–Kozai mechanism was studied in the region of the Hilda group and Jupiter Trojans. Asteroids of these populations move in 3:2 and 1:1 orbital resonances with Jupiter. The study was carried out using numerical integration of real asteroids’ equations of motion. A simplified dynamical model was adopted. Perturbations from only Jupiter moving in a fixed elliptical orbit were taken into account. Classical secular perturbations were excluded from osculating elements at every print step, and derived orbital inclinations and eccentricities were plotted versus a perihelion argument \(\omega \) $\omega$ . As a result, it was found that usual positions of a maximum of the eccentricity and, accordingly, a minimum of the inclination ( \(\omega = 90^{\circ }\) $\omega ={90}^{\circ }$ , \(270^{\circ }\) ${270}^{\circ }$ ) are shifted in these resonant regions. For Hildas, the maximum of the eccentricity is achieved with perihelion argument values \(\omega =0^{\circ }\) $\omega =0^{\circ }$ , \(180^{\circ }\) ${180}^{\circ }$ . For L4 Trojans, it is achieved with \(\omega = 30^{\circ }\) $\omega ={30}^{\circ }$ , \(210^{\circ }\) ${210}^{\circ }$ , and for L5 Trojans—with \(\omega = 150^{\circ }\) $\omega ={150}^{\circ }$ , \(330^{\circ }\) ${330}^{\circ }$ .