On the dynamics of Armbruster Guckenheimer Kim galactic potential in a rotating reference frame

被引：0
作者：
A. A. Elmandouh
机构：
[1] King Faisal University,Department of Mathematics and Statistics, Faculty of Science
[2] Mansoura University,Department of Mathematics, Faculty of Science
来源：
Astrophysics and Space Science | 2016年 / 361卷
关键词：
Galactic dynamics; Integrability; Equilibrium positions and stability; Periodic solutions;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this article, we are interested in studying some dynamics aspects for the Armbruster Guckenheimer Kim galactic potential in a rotating reference frame. We introduce a non-integrability condition for this problem using Painlevé analysis. The equilibrium positions are given and their stability is studied. Furthermore, we prove the force resulting from the rotation of the reference frame can be used to stabilize the unstable maximum equilibrium positions. The periodic solutions near the equilibrium positions are constructed by applying Lyapunov method. The permitted region of motion is determined.
引用
收藏
相关论文
共 62 条
  • [1] Ablowitz M.J.(1980)A connection between non-linear evaluation equations and ordinary differential equations of P-type J. Math. Phys. 21 715-721
  • [2] Ramani A.(2013)Periodic orbits for a class of galactic potentials Astrophys. Space Sci. 344 39-44
  • [3] Segur H.(1989)Chaotic dynamics in systems with square symmetry Phys. Lett. A 140 416-420
  • [4] Alfaro F.(1975)Dynamics of early type galaxies, I: the rotation curve of the elliptical galaxy NGC 4697 Astrophys. J. 200 439-445
  • [5] Llibre J.(1982)Integrable Hamiltonian systems and the Painlevé property Phys. Rev. A 25 1257-1264
  • [6] Pérez-Chavela E.(1995)Investigating non-integrability and chaos in complex time Physica D 86 256-267
  • [7] Alfaro F.(1993)Chaotic Friedmann-Roberston-Walker cosmology Class. Quantum Gravity 10 1825-1841
  • [8] Armbruster D.(1989)A mapping for the study of the 1:1 resonance in a galactic type Hamiltonian Celest. Mech. Dyn. Astron. 47 87-96
  • [9] Guckenheimer J.(1990)Exact periodic orbits and chaos in polynomial potentials Astrophys. Space Sci. 167 305-313
  • [10] Kim S.(1990)Global stochastically in a time-dependent galactic model Astron. Astrophys. 227 54-60
1234567