关于一些特殊的限制性三体问题的讨论

发布时间：2018-06-06 21:53

本文选题：限制性三体问题 + 环双星系统　；参考：《南京大学》2014年硕士论文

【摘要】：一般来说,三体问题是不可积的,因此我们需要做一些近似。其中很重要的一类就是限制性三体问题,这也是很多实际问题的很好的近似模型,例如,研究卫星的轨道演化的时候,不妨引入太阳+行星+无质量的测试粒子的模型,亦如研究太阳系主带小行星或者柯伊伯带天体的时候,也可以简化成太阳+木星或者海王星+无质量的测试粒子的模型；这些都是真实情况的很好近似。特别的,我们所感兴趣的是等级式的系统(系统可以分成内部轨道和外部轨道因而保证了系统的稳定性),大体来说,限制性等级式三体问题可以分成外限制(测试粒子在外部轨道)和内限制(测试粒子在内部轨道)两种,我们在第一章和第二章中分别做讨论。在对外限制问题的讨论中,我们利用展开了的摄动函数,得到最低阶的一个可积的系统,由此得出,这时候测试粒子的升交点经度可能会平动,并且此时伴有较高的倾角；更一般的,我们介绍了这个系统的演化特性。而后我们引入高阶影响,特别关注了此时的偏心率的演化。在近共面的情况下,我们得到此时的偏心率激发和共面情况没有(明显)差别的结论；在近极轨的条件下,我们发现,此时偏心率的激发可能会依赖初始的倾角的不同而分为两种情况,这是因为这两种不同的激发在相图中属于不同的平动区的缘故；并且,当轨道属于高激发区域时,偏心率可以从近零激发到0.3,这会极大的影响这种轨道的轨道稳定性,事实上,我们利用这种偏心率激发机制可以很好的限制环高偏心率双星的高倾角轨道的稳定性。在对内限制问题的研究中,我们关注的重点是外部天体的平运动与内部测试粒子的进动频率相当的时候所引起的近共振的影响。在共面的假设下,我们推导了含有偏心率的哈密顿量,并利用此时发生倍周期分叉临界点可以得出关于稳定性边界的限制。我们也推导了高阶的描述倾斜轨道的演化的哈密顿量。
[Abstract]:Generally speaking, the problem of trisomy is not integrable, so we need to do some approximation. One of the most important classes is the restrictive three body problem, which is also a good approximation model for many practical problems. For example, when the orbit evolution of the satellite is studied, the model of the sun + planet + non mass test particle can be introduced, as well as the research too. It can be simplified into a model of the sun + Jupiter or Neptune + non mass test particles when the main body of an asteroid or the Kuiper belt, which is a good approximation of the real situation. In particular, we are interested in hierarchical systems (systems can be divided into internal orbits and external orbits so that the system is guaranteed. " In general, the restrictive hierarchical trisomy problem can be divided into two kinds of external constraints (testing particles in the external orbit) and internal constraints (testing particles in the internal orbit). We discuss separately in the first and second chapters. In the discussion of the problem of external constraints, we use the extended perturbation function to get the lowest order. The integrable system thus concludes that the longitude of the intersection point of the test particle may be translational at this time, and it is accompanied by a higher dip at this time; more generally, we introduce the evolutionary characteristics of the system. Then we introduce the higher order effect, and we pay special attention to the evolution of the eccentricity at this time. In the case of near coplane, we get the deviation of this time. There is no (obvious) difference between heart rate excitation and coplanar condition; in the condition of the near polar orbit, we find that the excitations of eccentricity may be divided into two cases depending on the initial angle of inclination, because these two different excitations belong to different translational areas in the phase diagram; and when the orbit is highly excited. In the region, the eccentricity can be excited from near zero to 0.3, which will greatly affect the orbital stability of this orbit. In fact, we can use this eccentricity excitation mechanism to limit the stability of high inclination orbit with high eccentricity. In the study of the internal constraints, we focus on the level of the external body. Under the assumption of coplanar, we derive the Hamiltonian with eccentricity, and the limit of the stability boundary can be obtained by the time doubling bifurcation critical point. We also derive the higher order description of the evolution of the tilted orbit. Hamiltonian.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：P132.2

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