标枪比赛中标枪运动规律的数学建模.doc

摘 要

本文主要研究对于标枪最终投掷距离的初始的条件的影响，例如出手的角度、

出手的速度等。而空气动力学的研究表明，单纯增加标枪投掷的初始速度，获得

的成效并不能令人满意。这时，就引入了初始攻角这个概念。同时，还要考虑到

在标枪的飞行过程中所受到的空气阻力。对这些回产生影响的因素之间的关系进

行简化，使用这些参数建立起标枪的飞行轨迹模型。最后，对于这些影响最终投

掷距离的参数的相对重要性进行合理的总结和分析。最终得出，标枪初始的速度

和出手的角度两种参数的影响较大，其中在出手角度为 41°时达到最大值，而

初始攻角的影响相对较小，在 18°时达到最大值。其他的参数造成的影响几乎

javelin throwing is not as effective. At this point, the concept of the initial angle of

attack is introduced. At virtually the same moment, during the flight of the Javelin, the

air resistance must be taken into account. Between these factors, the relationship is

simplified, and the flight trajectory model of Javelin is established by using those

variable. Finally, the relative importance of these parameters which influence the final

throw distance is reasonably summarized and analyzed. The final results lay out that

the initial velocity and the angle of the Javelin throw have a great influence on the

javelin throw, and the maximum value is reached when the angle of the javelin throw

is 41, while the effect of the initial angle of attack is relatively small, reaching the

maximum value at 18. The impact of the other parameters is almost negligible.

2.模型假设 ...........................................................................................................................1

3.符号说明 ...........................................................................................................................2

4.问题分析 ...........................................................................................................................3

4.1 受力分析 ................................................................................................................3

4.2 标枪的几何参数 ..................................................................................................4

4.3 问题分析 ................................................................................................................5

5.模型的建立与求解 .........................................................................................................5

5.1 问题一模型建立与求解.....................................................................................5

5.2 问题二模型建立与求解.....................................................................................6

5.3 问题三模型建立与求解.....................................................................................8

引言