质点追踪对策问题研究

A Study on the Pursuit Game of Two Particles

本文研究了以平面内两个可以自由行动的质点为局中人的追踪对策问题1和2:问题1规定,当追逃双方之间的距离等于零时,才认为追者追到了逃者;问题2规定,当追逃双方之间的距离不大于定长时,便认为追者追到了逃者。文中利用初等几何方法,就这两个问题分别给出了(追者速度大于逃者速度时)追者的一个必胜策略(定理1.4和定理2.6)。并确定了追者采取该策略追到逃者需耗费的时间的最大值(定理1.6和定理2.9)。从某种意义上说,该策略是追者的最优策略。

This paper studies the problems of. an interesting game played try two particles moving freely on a plane, with one of them escaping and the other pursuing.To determine that the escaper is said to have been caught up by the pursuer, the aathor suggests two possible solution: 1, when the distance between the two gets to be zero; 2, when the distance from each other becomes less than a given length.The best strategy of ensuring the pursuer success in the two possibilities is given according to some elementary geometric methods.