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## Unusual Lidov–Kozai Perturbation in the Hilda Group

Transactions of IAA RAS, issue 54, 3–10 (2020)

Keywords: celestial mechanics, asteroids, secular perturbations

### Abstract

The Lidov–Kozai mechanism was investigated in the region of the Hilda group. The asteroids in this region move in commensurability of the mean motions 3:2 with Jupiter. The study was carried out mainly by means of numerical integration of the equations of real asteroids motion. The simplest dynamic model was used with Jupiter as the only perturbing body moving in a fixed elliptical orbit. After eliminating the classical secular perturbations, it becomes possible to determine the influence of the Lidov–Kozai mechanism on the orbital elements. As a result, it was found that the maximum eccentricity, and, accordingly, the minimum inclination is observed when the argument of perihelion ω = 0º, 180º, whilst usually it takes place at ω = 90º, 270º. On the contrary, there is a minimum eccentricity and a maximum inclination at ω = 90º, 270º. The character of the elements change, which is typical for the Lidov–Kozai perturbation, is preserved for only asteroids with a large amplitude of the semi-major axis libration.

### Citation

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T. A. Vinogradova. Unusual Lidov–Kozai Perturbation in the Hilda Group // Transactions of IAA RAS. — 2020. — Issue 54. — P. 3–10. @article{vinogradova2020, abstract = {The Lidov–Kozai mechanism was investigated in the region of the Hilda group. The asteroids in this region move in commensurability of the mean motions 3:2 with Jupiter. The study was carried out mainly by means of numerical integration of the equations of real asteroids motion. The simplest dynamic model was used with Jupiter as the only perturbing body moving in a fixed elliptical orbit. After eliminating the classical secular perturbations, it becomes possible to determine the influence of the Lidov–Kozai mechanism on the orbital elements. As a result, it was found that the maximum eccentricity, and, accordingly, the minimum inclination is observed when the argument of perihelion ω = 0º, 180º, whilst usually it takes place at ω = 90º, 270º. On the contrary, there is a minimum eccentricity and a maximum inclination at ω = 90º, 270º. The character of the elements change, which is typical for the Lidov–Kozai perturbation, is preserved for only asteroids with a large amplitude of the semi-major axis libration.}, author = {T.~A. Vinogradova}, doi = {10.32876/ApplAstron.54.3-10}, issue = {54}, journal = {Transactions of IAA RAS}, keyword = {celestial mechanics, asteroids, secular perturbations}, pages = {3--10}, title = {Unusual Lidov–Kozai Perturbation in the Hilda Group}, url = {http://iaaras.ru/en/library/paper/2056/}, year = {2020} } TY - JOUR TI - Unusual Lidov–Kozai Perturbation in the Hilda Group AU - Vinogradova, T. A. PY - 2020 T2 - Transactions of IAA RAS IS - 54 SP - 3 AB - The Lidov–Kozai mechanism was investigated in the region of the Hilda group. The asteroids in this region move in commensurability of the mean motions 3:2 with Jupiter. The study was carried out mainly by means of numerical integration of the equations of real asteroids motion. The simplest dynamic model was used with Jupiter as the only perturbing body moving in a fixed elliptical orbit. After eliminating the classical secular perturbations, it becomes possible to determine the influence of the Lidov–Kozai mechanism on the orbital elements. As a result, it was found that the maximum eccentricity, and, accordingly, the minimum inclination is observed when the argument of perihelion ω = 0º, 180º, whilst usually it takes place at ω = 90º, 270º. On the contrary, there is a minimum eccentricity and a maximum inclination at ω = 90º, 270º. The character of the elements change, which is typical for the Lidov–Kozai perturbation, is preserved for only asteroids with a large amplitude of the semi-major axis libration. DO - 10.32876/ApplAstron.54.3-10 UR - http://iaaras.ru/en/library/paper/2056/ ER -