本文選題：二體軌道　切入點：三體軌道　出處：《中國地質(zhì)大學（北京）》2010年博士論文　論文類型：學位論文

【摘要】： 本文討論了基于理想模型三體軌道運動規(guī)律問題,并給出了一個完整的三體問題的數(shù)值解決方案;另外還研究了與引力有關的基于剛體模型的天體表面引力收斂問題。首先總結了經(jīng)典的二體軌道運動方程和經(jīng)典積分及其結論,在此基礎之上利用二體質(zhì)心系為參考系和新的參數(shù)給出了二體的運動方程和解析解。研究了軌道運動方程的數(shù)值計算方法——龍格-庫塔算法,通過二體微分運動方程的數(shù)值解和解析解結果進行對比來檢驗數(shù)值方法的可靠性。深入研究了基于質(zhì)點系理想動力學理論的三體問題的力學特點及三體運動方程的常用表達方式,分析了幾種三體運動方程的表示方法和特點。選擇了以絕對坐標為參考系的三體運動方程作為數(shù)值計算依據(jù),重點給出了三體系統(tǒng)完整的數(shù)值解決方法,利用解一階微分方程組的數(shù)值方法來解三體軌道微分運動方程,并分析了數(shù)值方法的結果及其運用方法。分析了數(shù)值計算過程中必須注意的若干問題。 另外本文基于理想、天體規(guī)模的剛體數(shù)學模型,利用剛體轉(zhuǎn)動力學理論和引潮力力學理論,對天體表面的重力收斂問題進行了研究。即研究天體表面物質(zhì)所受到的重力指向天體中心點的集合所形成的形狀。深入討論了幾種不同性質(zhì)的力學方式如天體自轉(zhuǎn)、引潮力、進動及章動等,所對應的重力收斂特性、。給出了由各種性質(zhì)的力共同作用形成的一般天體的重力收斂規(guī)律,及標準重力收斂。給出一些典型天體的重心離散度數(shù)值,并指出重力收斂的研究方向和存在的問題。
[Abstract]:In this paper, we discuss the law of three-body orbit motion based on ideal model, and give a complete numerical solution to the three-body problem. In addition, the problem of gravitational convergence of celestial bodies based on rigid body model is studied. Firstly, the classical equations of motion of two-body orbits, classical integrals and their conclusions are summarized. On this basis, the equations of motion and analytical solutions of the two-body are given by using the two-body center system as the reference system and the new parameters. The Runge-Kutta algorithm, a numerical calculation method for the orbital equation of motion, is studied. The reliability of the numerical method is tested by comparing the results of the numerical solution and the analytical solution of the two-body differential equation of motion. The mechanical characteristics of the three-body problem based on the ideal dynamics theory of the particle system and the three-body equation of motion are studied in depth. In general, In this paper, the representation methods and characteristics of several three-body motion equations are analyzed. The three-body motion equations with absolute coordinates as the reference system are selected as the basis of numerical calculation, and the complete numerical solution of the three-body system is given. The differential motion equation of three-body orbit is solved by using the numerical method of solving the first order differential equation system. The results of the numerical method and its application are analyzed, and some problems that must be paid attention to in the process of numerical calculation are analyzed. In addition, based on the ideal, astronomical scale rigid body mathematical model, the theory of rigid body rotation dynamics and the theory of tidal force mechanics are used in this paper. In this paper, the problem of gravity convergence on the surface of celestial bodies is studied. That is to say, the shape formed by gravity pointing to the central points of celestial bodies by gravity on the surface of celestial bodies is studied. Several mechanical methods with different properties, such as rotation of celestial bodies, tidal force, are discussed in depth. The gravity convergence characteristics corresponding to precession and nutation are given. The law of gravity convergence of general celestial bodies formed by the interaction of forces of various properties and the standard gravity convergence are given. The numerical values of gravity center dispersion of some typical celestial bodies are given. The research direction and problems of gravity convergence are pointed out.
【學位授予單位】：中國地質(zhì)大學（北京）
【學位級別】：博士
【學位授予年份】：2010
【分類號】：P135

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本文編號：1644248