用打靶法求解微重力下矩形和旋转对称贮箱内静液面形状

摘要

The application of Shooting Method in solving nonlinear second order differential equations with unknown parameters is briefly introduced. Moreover, shapes of hydrostatic surface in rectangular and revolving symmetrical tanks under microgravity are controlled by nonlinear second order differential equations with unknown parameters, hence can be solved by Shooting Method. This paper solves the shapes of hydrostatic surface in rectangular and revolving symmetrical tanks under microgravity using Shooting Method. There is one unknown parameter in the Shooting Method solving the shapes in rectangular tanks under microgravity. There are two unknown parameters in the Shooting Method solving the shapes in columnar tanks under microgravity. And there are both three unknown parameters in the Shooting Method solving the shapes in spheroidal tanks and Cassini tanks under microgravity. When the initial values of these unknown parameters are set aptly, Shooting Method is indicated to be fast and effective through large amount of calculations. Lastbut not the least, Shooting Method is compared with Runge-Kutta method in other literatures for solving shapes of rectangular and revolving symmetrical tanks under microgravity, and the advantage and disadvantage of these two methods are analyzed respectively. The conclusion is that Shooting Method is always a better choice.%简要介绍了打靶法用于求解带未知参数的非线性二阶常微分方程组问题．由于微重力环境下矩形和旋转对称贮箱内的静液面形状能够用一个带参数的二阶常微分方程组表示，因此可用打靶法求解．利用打靶法求解了微重力下矩形、圆柱形、旋转椭球形以及Cassini贮箱内的静液面形状，通过大量数值计算可知，当未知参数初值选取恰当时，这种方法是快速有效的．将打靶求解法与其他文献所用的龙格库塔求解法进行比较，结果表明，绝大多数情况下采用打靶法效果更好．