To the problem of nonlinear oscillations near triangular libration points

封面

如何引用文章

全文:

开放存取 开放存取
受限制的访问 ##reader.subscriptionAccessGranted##
受限制的访问 订阅或者付费存取

详细

A spatial restricted problem of three bodies attracted by Newton's law is studied. The orbits of the main attracting bodies are assumed to be ellipses of small eccentricity. An approximate mathematical model describing nonlinear oscillations of a passively gravitating body near a Lagrangian triangular libration point is obtained using the normal form method. A detailed study of these oscillations is given in a particular case of third-order resonance. This research was carried out within the framework of the state assignment (registration No. 124012500443-0) at the Ishlinsky Institute for Problems in Mechanics RAS.

全文:

受限制的访问

作者简介

A. Markeev

Ishlinsky Institute for Problems in Mechanics of the RAS

编辑信件的主要联系方式.
Email: anat-markeev@mail.ru
俄罗斯联邦, Moscow

参考

  1. Lagrange J.L. Essai sur le Proble`me des Trois Corps // Oeuvres de Lagrange, J., vol. 6. Paris: Gauthier Villars, 1873. pp. 229–324.
  2. Lyapunov A.M. On the stability of motion in one particular case of the three-body problem // in: Сoll. Works. Vol. 1, Moscow;Leningrad: USSR Acad. of Sci. Pub. House, 1956. pp. 327–401.
  3. Danby J.M.A. Stability of the triangular points in the elliptic restricted problem of three bodies // Astron. J., 1964, vol. 69, no. 2, pp. 165–172.
  4. Giacaglia G.E.O. Characteristics exponents at L4 and L5 in the elliptic restricted problem of three bodies // Celest. Mech. & Dyn. Astron., 1971, vol. 4, no. 3/4, pp. 468–489.
  5. Nayfeh A.H., Kamel A.A. Stability of the triangular points in the elliptic restricted problem of three bodies // AIAA J., 1970, vol. 8, no. 2, pp. 221–223.
  6. Duboshin G.N. Celestial mechanics. Analytical and Qualitative Methods. Moscow: Nauka, 1978. 456 p. (in Russian)
  7. Markeev A.P. Libration Points in Celestial Mechanics and Cosmodynamics. Moscow: Nauka, 1978. 312 p. (in Russian)
  8. Yumagulov M.G., Belikova O.N. Bifurcation of 4π-periodic solutions of the planar, restricted, elliptical three-body problem // Astron. Rep., 2009, vol. 86, no. 2, pp. 148–152.
  9. Kovacs T. Stability chart of the triangular points in the elliptic restricted problem of three bodies // Mon. Not. R. Astron. Soc., 2013, vol. 430, no. 4, pp. 2755–2760.
  10. Isanbaeva N.R. On the construction of the boundaries of stability regions of triangular libration points of a planar bounded elliptic three-body problem // Vestn. Bashk. univ. Matem. i Mekh., 2017, vol. 22, no. 1, pp. 5–9. (in Russian)
  11. Markeev A.P. On normal coordinates in the vicinity of the Lagrangian libration points of the restricted elliptic three-body problem // Vestn. Udmurt. univ. Matem. Mekh. Komp’yut. Nauki, 2020, vol. 30, no. 4, pp. 657–671. (in Russian)
  12. Markeev A.P. On the stability of Lagrange solutions in the spatial near-circular restricted three-body problem // Mech. of Solids, 2021, vol. 56, no. 8, pp. 1541–1549.
  13. Markeev A.P. On the metric stability and the Nekhoroshev estimate of the velocity of Arnold diffusion in a special case of the three-body problem // R.&C. Dyn., 2021, vol. 26, no. 4, pp. 321–330.
  14. Markeev A.P. On resonance values of parameters in the problem of stability of Lagrange solutions in a restricted three-body problem close to a circle // Mech. of Solids, 2023, vol. 58, no. 7, pp. 2531–2543.
  15. Giacaglia G.E.O. Perturbation Methods in Non-Linear Systems. N.Y.: Springer, 1972. 369 p.
  16. Nayfeh A.X. Perturbation Methods. N.Y.: Wiley, 1973. 425 p.

补充文件

附件文件
动作
1. JATS XML
下载
2. Fig. 1

下载 (100KB)
索引源数据
3. Fig. 2

下载 (82KB)
索引源数据
4. Fig. 3

下载 (107KB)
索引源数据
5. Fig. 4

下载 (90KB)
索引源数据

版权所有 © Russian Academy of Sciences, 2025