空中抛体运动轨迹的解析构造
Analytical construction of the projectile motion trajectory in midair
摘要：
研究了一个经典的抛体运动问题。考虑了空气阻力。阻力采用二次定律。分析方法适用于调查。抛体运动方程可在任意长的时间内解析求解。所构造的解析解具有普适性。作为运动的一种极限情况，得到了垂直渐近线公式。垂直渐近线的值直接从运动的初始条件计算。没有必要用数字来研究这个问题。所发现的解析解在很宽的参数范围内具有很高的精度。以棒球、网球和羽毛球的运动为例进行了仿真。
英文摘要：
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.
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