Solving Shapes of Hydrostatic Surface in Rectangular and Revolving Symmetrical Tanks Under Microgravity Using Shooting Method

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. Last but 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.