【作者】 刘昱；

【导师】 杨进；

【作者基本信息】 中国地质大学（北京） ， 地球物理工程， 2010， 博士

【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。更多还原

【Abstract】 A issues about the orbital modeling of three bodies which are based on ideal rigid body. And therefore give rise to a integrate numerical method of three body problem. The gravity convergence of rigid body is studied based on rigid body model too. At first, the approach with classical equation of two-body orbital motion and integral approach as well as its conclusions are summed up, on this basis, an absolute coordinate and the new parameters in which centroid of two body are taken as reference system are used to give the two-body motion equations and analytical solution. After pre-processing method with a two-body motion equation is studied, the numerical solution of differential motion equations for the two-body and results with the classical analytical solution are compared and analyzed. Mass point dynamics is the basic principium of of all the orbit equations. Runge-kutta numerical is used here. The mechanical characteristics for the issues of three-body, the commonly used expression for the equations of motion, analyze the characteristics of several representations are fully studied. In order to facilitate numerical calculation for the three-body motion equation, the absolute coordinate system is selected in the three-body motion equation as the basis for numerical calculation, a complete numerical method is given with focusing on a three-body system, and a numerical method for solving a first-order differential equations which is known as Runge - Kutta method to solve this celestial orbit differential equations of motion, in which some examples are given ,and the results of numerical methods and its application methods are analyzed,as well as it is emphasized in the numerical results to discover and analyze the initial value in numerical calculation and given initial value and the impact of the trend of the calculated results. In the numerical calculation of the analysis process a number of issues are given for which it should pay attention in processing.Another issue in the paper is the study of gravity convergence. Gravity convergence is A set made up of the points where the gravity directions of substances on the surface of the ideal celestial body point to. Several different kinds of mechanical methods such as celestial rotation, tidal force, precession and nutation, etc as well as its corresponding gravity convergence shape and movement characteristics by gravity are discussed. The gravity convergence shape of common ideal celestial body and standard gravity convergence shape which are formed by the nature of the forces from a variety of general objects are given. Gravity dispersion is proposed as well as a limit of amount for the size of the gravity convergence. Some dispersion values of gravity direction for the typical ideal celestial body is given. Some defects and directions which need to be studied go a step further is proposed and discussed in the paper.更多还原