抛体运动的Runge—Kutta解

Runge-Kutta Solutions of the Projectile Motion

研究抛体运动的基本方法有略去空气阻力的作用，亦不考虑地球自转的影响，在惯性参考系中分析抛体运动的抛物线理论，以及将物体与地球视为二体运动的椭圆理论．本文既考虑空气阻力的作用，又考虑到地球自转的影响，给出了抛体运动的Ｒｕｎｇｅ—Ｋｕｔｔａ数值解．得到了抛体运动过程中的速度，位置及轨迹，揭示了空气阻力及地球自转对抛体运动影响的规律，数值结果与解析比较表明，方法不但精度高而且简便，亦可应用其数值分析更为复杂的抛体问题．

in the study of projectile motions,there are usually two fundmental methods,oneis the parabolic theory in the inertical system with the functions of air resistance and rotationof the earth neglected; another is the elliptic theory in which the projectile objects and theearth are regarded as two body movement.In this paper,Runge-Kutta numerical solution isgiven with the regard of air resistance and rotation of the earth,and the velocity,position andthe orbit of the projectile motion are obtained,thus bringing to light the regularity of effectsof air resistance and rotation of earth on the projectile motion. Numerical results and analyticcomparison shows that this method is not only of the advantages of computational convienceand superior accuracy,but also is suitable to be used in more complex projectile motions.