航天技术中的若干数学问题及其解法

<正>一、前言大家知道要决定一次很好的航天飞行,须要:1)选择最优飞行轨道,2)制定最优推力规划;3)决定最优设计方案。这就有赖于运用适当的数学方法及“三C”技术的密切配合(“三C”技术是计算机Computer、通讯Communication、与控制Control技术。航天技术中的数学问题很多,笔者试就航天器在高超声速流运动以及湍流的敏感性分析和火箭在发射架上运动的相互干扰等所出现的重要数学问题挑选几个,并提出解决的方案或方法。这些由航天技术中抽象出来的理论性问题的研究、探索,往往对提出新型的设计思想或方案是有促进作用的;反过来又能丰富数学的内涵。

Some Mathematical Problems of Astronautical Technics

To determine once space flight, one should select the optimal space trajectories, discriminate the optimal thrust programme & determine the optimal design of freight rocket (vehicle) , etc. So they must use mathematical methods & "three C" (Computer, Communication, Control) technics. How to solve the mathematical problems of austronautical technics is full of meaning. This paper summarizes briefly the solving methods of some math- ematical problems of astronautical technics.①The singular equations of pressure distribution on a coplanar wing in supersonic flow.②The boundary value problem for wings at large angle of attack in steady & unsteady flow.③How to solve the equations of hypersonic interactions with surface mass transfer?④To solve the problem of viscous flow over cylinders in unsteady motion.⑤To evaluate the validity of turbulence calculations & models.⑥The problem for transverse vibrations of nonisotropic & nonuniform elastic plates.⑦How to solve the equations for the coupled interaction launch behavior of a flexible rocket and flexible launcher.In the last two decades a large number of investigations in different areas of astronautics & aeronautics have been devoted to the study of "astronautical mathematics"), which is an important and rising branch of applied mathematics.