Abstract
This paper deals with the differential equations which describe curves of pursuit, in which the pursuer's velocity vector always points directly towards the pursued. We use the Laplace Transform method to solve the classic problem of four mice pursuit.
Highlights
A curve of pursuit is the path an object takes when chasing another object
The problem of pursuit probably originated with Leonardo da Vinci
He was the first one to study this problem when the pursued moved along a straight line
Summary
The problem of pursuit probably originated with Leonardo da Vinci He was the first one to study this problem when the pursued moved along a straight line. It is to find the curve by which a pirate ship moves while pursuing a merchant vessel, supposing that the speeds of the two vessels are always in the same ratio When the speed ratio k is larger than 1, the pursuer travels faster than the pursued. This would usually be the case in a physical situation, it is not a necessary assumption for the mathematical analysis of the problem. We specialize to the case when the curve of the pursued is a straight line
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