本文選題：小天體 + 平衡點��； 參考：《清華大學》2014年博士論文

【摘要】：小天體引力場中的軌道動力學是現(xiàn)代天體力學的一個重要研究方向，其中包含著豐富的物理現(xiàn)象和深刻的數(shù)學內(nèi)涵。隨著一系列小行星實地探測任務的深入開展，理解小天體附近的軌道運動規(guī)律也成為航天領域所面對的眾多挑戰(zhàn)之一。本文作為一項應用基礎研究，嘗試在近似真實的動力學模型下，討論具有代表性和普遍意義的軌道動力學問題，考察了小天體引力場中的四類軌道運動：平衡點、周期軌道、赤道面附近的共振軌道和表面附近的自由運動軌道。對這四類軌道的研究，都以真實小天體為對象，基于多面體法發(fā)展新的數(shù)值計算方法，包括搜索小天體附近大范圍周期軌道的分層網(wǎng)格算法、用于模擬小天體表面附近自由運動的全過程仿真算法等，并開發(fā)了相應的FORTRAN程序包。 在平衡點和周期軌道的研究中，本文關注系統(tǒng)的定性性質，特別是這兩類運動附近的一般軌道性態(tài)。通過對小行星216Kleopatra系統(tǒng)零速度面三維幾何結構的分析，確定了4個平衡點的穩(wěn)定性和特征結構；引入局部流形上的運動分析方法，得到了平衡點附近的6族局部周期軌道，并確定了各平衡點附近軌道運動的一般形式。發(fā)現(xiàn)了Kleopatra附近的29個周期軌道族，應用Poincaré映射方法研究各族軌道的穩(wěn)定性和拓撲結構，并研究各族軌道拓撲類型的轉換規(guī)律。通過對線性化映射的特征結構的分析，給出了29族周期軌道附近的5類基本運動形式，根據(jù)運動分解的觀點，確定了周期軌道附近的一般軌道性態(tài)。 在共振軌道和自由運動軌道的研究中，本文強調(diào)數(shù)值試驗方法對特定的小天體系統(tǒng)研究的作用。從能量角度說明了赤道面附近的1:1共振的動力學本質，，通過參數(shù)空間上的網(wǎng)格搜索，分析該類共振發(fā)生的參數(shù)條件，說明了1:1共振是形成拋射軌道的主要原因；進一步給出了拋射軌道在參數(shù)平面上的分布情況，確定了形成拋射軌道的臨界條件，說明Kleopatra附近存在共振導致的危險區(qū)域。在對小行星1620Geographos表面附近自由運動的研究中，分析了平衡區(qū)域與表面坡度的相互聯(lián)系，并說明起飛速度對局部地形曲率的依賴性。通過Monte Carlo仿真，分析了貼近Geographos表面的自由運動軌道的一般形式，確定了影響小天體表面附近自由運動的幾種主要動力學機制。 需要說明的是，雖然本文的各項研究都是基于特定的小天體模型開展的，但文中所討論的是所有小天體系統(tǒng)的共性問題，并且研究思路和方法對一類小天體對象是通用的，因而具有比較廣泛的借鑒意義和參考價值。
[Abstract]:Orbital dynamics in the gravitational field of small celestial bodies is an important research direction in modern celestial mechanics, which contains rich physical phenomena and profound mathematical connotations. With the development of a series of asteroid field exploration missions, understanding the orbital motion near small objects has become one of the challenges in the space field. In this paper, as an applied basic research, we try to discuss the orbital dynamics problems with representative and universal significance under the approximate real dynamic model, and investigate the four orbital motions in the gravitational field of small celestial bodies: equilibrium point, periodic orbit, and so on. Resonance orbits near the equator and free motion orbits near the surface. Based on the polyhedron method, a new numerical calculation method is developed, including the hierarchical grid algorithm for searching large periodic orbits near small objects. The whole process simulation algorithm is used to simulate the free motion near the surface of small objects, and the corresponding FORTRAN package is developed. In the study of equilibrium points and periodic orbits, this paper focuses on the qualitative properties of the system, especially the general orbital behavior near these two kinds of motions. The stability and characteristic structure of the four equilibrium points are determined by analyzing the three-dimensional geometric structure of the zero velocity plane of the asteroid 216Kleopatra system, and the six families of local periodic orbits near the equilibrium point are obtained by introducing the motion analysis method on the local manifold. The general form of orbital motion near each equilibrium point is determined. In this paper, 29 periodic orbital families near Kleopatra are found. Poincar 茅 mapping method is used to study the stability and topological structure of the orbits, and the transformation laws of the topological types of the orbits are studied. Based on the analysis of the characteristic structure of the linear mapping, five kinds of basic motion forms near 29 periodic orbits are given. According to the viewpoint of motion decomposition, the general orbital behavior near periodic orbits is determined. In the study of resonant orbits and free motion orbits, this paper emphasizes the role of numerical test methods in the study of specific small celestial bodies. The dynamic essence of 1:1 resonance near the equatorial plane is explained from the energy angle. The parametric conditions of the resonance are analyzed by grid search in the parameter space. It is shown that 1:1 resonance is the main reason for the formation of the ejection orbit. Furthermore, the distribution of projectile orbits on the parametric plane is given. The critical conditions for the formation of projectile orbits are determined. It is shown that there is a dangerous region in the vicinity of Kleopatra due to resonance. In the study of the free motion near the surface of the asteroid 1620 Geographos, the relationship between the equilibrium region and the slope of the surface is analyzed, and the dependence of the take-off velocity on the local topographic curvature is explained. Through Monte Carlo simulation, the general form of free motion orbit close to Geographos surface is analyzed, and several main dynamic mechanisms affecting the free motion near the surface of small objects are determined. It should be noted that although all the studies in this paper are based on specific small object models, what is discussed in this paper is the common problems of all small celestial systems, and the research ideas and methods are common to a class of small celestial objects. Therefore, it has more extensive reference significance and reference value.
【學位授予單位】：清華大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：P173;V412.41

【共引文獻】

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