三体轨道数值模拟及理想天体重力收敛范围研究

发布时间：2018-03-21 14:25

本文选题：二体轨道　切入点：三体轨道　出处：《中国地质大学（北京）》2010年博士论文　论文类型：学位论文

【摘要】： 本文讨论了基于理想模型三体轨道运动规律问题,并给出了一个完整的三体问题的数值解决方案;另外还研究了与引力有关的基于刚体模型的天体表面引力收敛问题。首先总结了经典的二体轨道运动方程和经典积分及其结论,在此基础之上利用二体质心系为参考系和新的参数给出了二体的运动方程和解析解。研究了轨道运动方程的数值计算方法——龙格-库塔算法,通过二体微分运动方程的数值解和解析解结果进行对比来检验数值方法的可靠性。深入研究了基于质点系理想动力学理论的三体问题的力学特点及三体运动方程的常用表达方式,分析了几种三体运动方程的表示方法和特点。选择了以绝对坐标为参考系的三体运动方程作为数值计算依据,重点给出了三体系统完整的数值解决方法,利用解一阶微分方程组的数值方法来解三体轨道微分运动方程,并分析了数值方法的结果及其运用方法。分析了数值计算过程中必须注意的若干问题。另外本文基于理想、天体规模的刚体数学模型,利用刚体转动力学理论和引潮力力学理论,对天体表面的重力收敛问题进行了研究。即研究天体表面物质所受到的重力指向天体中心点的集合所形成的形状。深入讨论了几种不同性质的力学方式如天体自转、引潮力、进动及章动等,所对应的重力收敛特性、。给出了由各种性质的力共同作用形成的一般天体的重力收敛规律,及标准重力收敛。给出一些典型天体的重心离散度数值,并指出重力收敛的研究方向和存在的问题。
[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.
【学位授予单位】：中国地质大学（北京）
【学位级别】：博士
【学位授予年份】：2010
【分类号】：P135

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