The Maximum Reachable Domain for a Rocket Flying Over a Rotating Spherical Earth

• Main Authors: Shen-Tai Lu, 盧申泰
• Other Authors: D. L. Sheu
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/95300863919544711638

碩士 === 國立成功大學 === 航空太空工程學系碩博士班 === 93 === 　　In this thesis, the maximum reachable domain for a rocket flying over a spherical earth surface is analyzed by using the optimal control theory. The rocket is assumed to be a point mass. The direction of rocket is controlled by the angle between the thrust, which is assumed to be constant, and the velocity. The angle between the thrust and the velocity can be defined by two angles in three-dimensional space. Each angle is assumed to be a linear function of the time and therefore there are totally four control parameters in the system. In this study, the necessary conditions for optimality are derived by using a parametric optimization method. These necessary conditions plus the boundary conditions are found to be a set of nonlinear simultaneous algebraic equations of the control parameters and the final time. The problem is solved by first guessing a set of control parameters and the final time and then using the Newton-Raphson method to refine them iteratively. In each iterative process, the state variables at the final time in the necessary conditions and the boundary conditions are determined by integrating the system equations from the initial to the final time, and therefore, when the parameters and the final time are convergent, the optimal trajectory is also obtained. In order to understand the effects of Coriolis force on flight trajectories, two approaches are conducted in this study. One is to fix the latitude of the launch point but variate the heading direction and the other is to fix the heading direction but variate the latitude of the launch point. It is found that the trajectories on the north hemisphere have a potential to turn right while the trajectories on the south hemisphere have a potential to turn left. Also, due to the rotation of the Earth, the range to the east is larger than that to the west.