Radiodrome

The term is derived from the Latin word radius (Eng.

ray; spoke) and the Greek word dromos (Eng.

Introduce a coordinate system with origin at the position of the dog at time zero and with y-axis in the direction the hare is running with the constant speed Vt.

The position of the hare at time zero is (Ax, Ay) with Ax > 0 and at time t it is The dog runs with the constant speed Vd towards the instantaneous position of the hare.

and taking the derivative with respect to x, using that one gets or From this relation, it follows that where B is the constant of integration determined by the initial value of y' at time zero, y' (0)= sinh(B − (Vt /Vd) lnAx), i.e.,

Graph of a radiodrome, also known as a dog curve
The path of a dog chasing a hare running along a vertical straight line at a constant speed. The dog runs towards the momentary position of the hare, and will be changing his heading continuously.