小行星运动中的轨道扩散性质

周礼勇; 孙义燧; 周济林

小行星运动中的轨道扩散性质

南京大学天文系, 南京 210093

基金项目: 国家自然科学基金资助项目(19633010;19903001)

详细信息

作者简介:
周礼勇(1973- ),男,江苏人,讲师,博士.

中图分类号: P136;P134.2
计量
- 文章访问数: 2317
- HTML全文浏览量: 201
- PDF下载量: 571
- 被引次数: 0
出版历程
- 收稿日期: 2000-03-31
- 修回日期: 2001-02-13
- 刊出日期: 2001-07-15

Diffusion Characters of the Orbits in the Asteroid Motion

Department of Astronomy, Nanjing University, Nanjing 210093, P. R. China

摘要

摘要: 在详细讨论一个辛映射的过程中,我们注意到轨道在相空间不同区域有着不同的扩散规律:在充分发展的混沌区,残余的轨道数目随时间按指数律衰减;在混合区域,则是代数律.在相空间中特定的区域,扩散还可以用对数律描述.在一个稳定的岛屿附近,逃逸时间的对数随着离开岛屿的距离的增大而线性下降;而当逼近岛屿的时候,逃逸时间极迅速地上升,与不变曲线的超指数稳定性一致.利用此映射研究小行星运动时,它的不动点及其稳定性可解释小行星的分布.此外,本文还讨论了在4:3,3:2和2:1共振处小行星轨道的扩散速度.
- 扩散 /
- 辛映射 /
- 小行星
Abstract: A symplectic mapping is studied carefully. The exponential diffusion law in developed chaotic region and algebraic law in mixed region were observed. An area was found where the diffusion follows a logarithmic law. It is shown in the vicinity of an island, the logarithm of the escape time decreases linearily as the initial position moves away from the island. But when approaching close to the island, the escape time goes up very quickly, consistent with the superexponential stability of the invariant curve. When applied to the motion of asteroid, this mapping's fixed points and their stabilities give an explanation of the distribution of asteroids. The diffusion velocities in 4:3, 3:2 and 2:1 jovian resonances are also investigated.
- diffusion /
- symplectic mapping /
- asteroid

HTML全文

参考文献(10)

[1]	Meiss J D.Symplectic maps,variational principles,and transport[J].Rev Mod Phys,1992,64(3):795-848;Contopoulos G.Analysis and Modeling of Discrete Dynamical Systems[M].Netherlands;OPA,1998,35-90;Sun Y S,Fu Y N.Diffusion characters in a four-dimensional volume-preserving map[J].Cel Mech Dyn Astron,1999,73(4):249-258.
[2]	Nesvorny D,Ferraz-Mello S.On the asteroidal population of the first-order jovian resonances[J].Icarus,1997,130(2):247-258.
[3]	Froeschle C,Lega E.Analysis and Modeling of Discrete Dynamical Systems[M].Netherlands,OPA,1998,3-54;Hadjidemetriou J D.Analysis and Modeling of Discrete Dynamical Systems[M].Netherlands:OPA,1998:249-282.
[4]	Duncan M,Quiun T,Tremaine S.The long-term evolution of orbits in the solar system:a mapping approach[J].Icarus,1989,82(3):402-418.
[5]	Henon M,Petit J M.Series expansions for encounter-type solution of hills problem[J].Cel Mech,1986,38(2):67-100.
[6]	Hadjidemetriou J D.Predictability,Stability and Chaos in n-Body Dynamical Systems[M].Netherlands:Plenum Press,1991,157-175.
[7]	Lai Y C,Grebogi C,Blumel R.Algebraic decay and phase-space metamporphoses in microwave ionization of hydrogen rydberg[J].Phys Rev A,1992,45(12):8284-8287.
[8]	Morbidelli A,Giorgilli A.Chaos and diffusion in hamiltonian systems[M].France:Editions Frontiers,1995,65-112.
[9]	Evans N W,Tabachnik S.Possible long-lived asteroid belts in the inner solar system[J].Nature,1999,399:41-43.
[10]	Ferraz-Mello S,Michtchenko T A,Roig F.Determinant role of Jupiter's great inequality in the depletion of the hecuba gap[J].Astron J,1998,116(3):1491-1500.