论文标题
空中弹丸运动轨迹的分析结构
Analytical construction of the projectile motion trajectory in midair
论文作者
论文摘要
研究了弹丸以与地平线角度倾斜的弹丸运动的经典问题。考虑空气阻力力。使用二次阻力法。一种分析方法适用于研究。弹丸运动的方程在任意的时间内进行分析求解。构造的分析解决方案是通用的。作为运动的极限情况，获得了垂直渐近线公式。垂直渐近线的值是直接根据运动的初始条件计算的。无需数字研究问题。在广泛的参数中，发现的分析解决方案非常准确。列出了棒球，网球和羽毛球的运动作为例子。
A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account. The quadratic law for the resistance force is used. An analytic approach applies for the investigation. Equations of the projectile motion are solved analytically for an arbitrarily large period of time. The constructed analytical solutions are universal. As a limit case of motion, the vertical asymptote formula is obtained. The value of the vertical asymptote is calculated directly from the initial conditions of motion. There is no need to study the problem numerically. The found analytical solutions are highly accurate over a wide range of parameters. The motion of a baseball, a tennis ball and shuttlecock of badminton are presented as examples.
