抛体运动的轨迹长度与所围面积研究

空气阻力对抛体的运动可以产生显著的影响.运用近似的方法处理超越方程,给出了考虑空气阻力时抛体运动轨迹的长度和轨迹所包围的面积的近似解析解.数值计算表明：（1）当kt/m越小时轨迹长度与所围面积的近似解析解与真实值越接近;（2）抛体运动轨迹的长度取最大值时,抛射角随空气阻力系数的增大而减小：（3）抛体运动轨迹所围面积取最大值时,抛射角随空气阻力系数的增大而增加.

The Perimeter of end the area encompassed by the Trajectory of Projectile Motion

Air friction has a notable effect on the motion of projectile.The perimeters of and the areas encompassed by the trajectory with consideration of air friction are obtained by using the approximate method to solve the equations. The numerical results show that the analytical values are consistent with the exact values if,the projectile angles increase following when the perimeters of the trajectory is maximum,and the projectile angles decrease following when the areas encompassed by the trajectory is maximum.