一个追逐问题的数学模型和matlab仿真

Mathematical Model of a Chasing Problem and Its Matlab Simulation

就两人绕正三角形的追逐问题建立起了两个数学模型:一个充分应用运动的周期性首先给出了两人共边的充要条件,然后直接给出在一个周期内两人共边的次数及起止时刻;另一个则利用初等数论的方法给出了两人共边的另一个充要条件.利用matlab长于计算和强大的绘图功能,分别给出了求解两个模型的matlab程序,通过动画仿真演示两个绕正三角形的追逐模型,并给出了二者同边的时间起止点和同边的次数.

Pursuit problem is a familiar problem in true-life. In this note a problem of one running after another anticlockwise along a regular triangle is discussed and two mathematcial model are given： （ i ） it is derived from running＇s periodicity that the sufficient and necessry condition for these two men＇s running in the same edge is given and the number of their running in the same edge in a periodicity and the start time and end time they run in the same edge are all showed precisely; （ ii ） by elementary number theory another sufficient and necessry condition for their running in the same edge are obtained. For its powerful computation and plot functions two matlab program are designed to solve the mathematical models described as above; moreover the second one displays the running course by motion.