Curve of pursuit
A curve representing a solution of the "pursuit" problem, which is posed as follows: Let a point $M$ be moved uniformly along a given curve. The trajectory has to be found of the uniform movement of a point $N$, such that the tangent drawn towards the trajectory at any moment of the movement would pass through the position of $M$ corresponding to that moment in time.
In a plane, the system of equations which the curve of pursuit must satisfy takes the form
where $dy/dx$ is the slope of the curve of pursuit, and $F(\xi,\eta)=0$ is the equation of the given curve.
The "pursuit" problem was posed by Leonardo da Vinci and solved by P. Bouguer (1732). For a generalization of it see the last Chapter of .
|||A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)|
|||J.E. Littlewood, "A mathematician's miscellany" , Methuen (1953)|
Curve of pursuit. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Curve_of_pursuit&oldid=32278