一、问题的提出在火箭设计中,有一类问题是寻求在最小推进剂消耗下,使给定的有效载荷达到给定的高度。阻碍火箭上升的主要因素有两个:一是重力(地球引力),另一是空气阻力。它们都随着高度的增加而减小。然而,减小这两种影响因素的方法是相互矛盾的。因为重力造成的损失与飞行时间成正比,而空气阻力造成损失与速度某次方成正比,因此,为了减小重力所造成的损失,必须缩短飞行时间,即要求尽可能大的速度飞行;为了减小空气阻力所造成的损 I. PROBLEM PROBLEMS In rocket design, there is a problem of seeking to achieve a given height of a given payload with minimum propellant consumption. There are two main factors hindering the rise of rockets: one is gravity (Earth’s gravity) and the other is air resistance. They all decrease with height. However, there are conflicting approaches to reducing these two influencing factors. Since the loss due to gravity is proportional to the time of flight and the loss due to air resistance is proportional to the square of the speed, in order to reduce the losses caused by gravity, the flight time must be shortened to require as fast a flight as possible; Reduce the air resistance caused by damage