天体运动的三维DDA模拟

3D DDA Simulation of Celestial Motion

不连续变形分析(DDA)方法广泛应用于岩土工程领域,其中三维球颗粒DDA(3D-SDDA)理论能够对球形物体模型的运动进行数值模拟。本研究将不连续变形分析方法应用于太阳系天体运行模拟,将各天体看作球状物体,仅考虑天体间的引力和其自身惯性力,通过建立系统总体平衡方程式,推导载荷矩阵方程,求解总体方程,编写Matlab计算程序,从而得到各天体的运动参数,对天体运动进行数值模拟。结果表明,利用3D-SDDA理论能够模拟日-地二体系统和日-地-月三体系统在宇宙空间中的运行状态,获取任意时刻天体的空间位置和速度信息。分别将日-地二体系统的数值计算结果与开普勒计算方法所得结果对比,日-地-月三体系统的结果与虚拟天文馆软件Stellarium高精度数据对比,结果吻合良好。同时输入月全食发生的限制条件,能够正确预测出月全食发生时刻。

The discontinuous deformation analysis(DDA)method is widely used in the field of geotechnical engineering,among which the three-dimensional spherical particle DDA(3D-SDDA)theory can numerically simulate the motion of spherical object models.The author innovatively applies it to the simulation of the operation of celestial bodies in the solar system,treating each celestial body as a spherical object,only considering the gravitational force between celestial bodies and their own inertial force.By establishing the overall balance equation of the system,deriving the load matrix equation,solving the overall equation,and writing a Matlab calculation program,the motion parameters of each celestial body are obtained,and the numerical simulation of celestial body motion is carried out.The results indicate that the use of 3D-SDDA theory can simulate the operation of the sun-earth system and the sun-earth-moon system in space,and can obtain the spatial position and velocity information of celestial bodies at any time.The numerical calculation results of the sun-earth system were compared with the Kepler calculation method,and the results of the sun-earth-moon system were compared with the high-precision data of the virtual observatory software Stellarium,and the results were in good agreement.Simultaneously inputting the limiting conditions for the occurrence of a total lunar eclipse can accurately predict the timing of the eclipse.