In Question 11 (Exercises 8.2.8) the equation of the path of P was found to be such that

Use the substitution x = a sech u to integrate this differential equation and show that

This curve is called a tractrix.

Data from Question 11

A small weight is dragged across a horizontal plane by a string PQ of length a, the end P being attached to the weight while the end Q is made to move steadily along a fixed line perpendicular to the original position of PQ. Choosing the coordinate axes so that Oy is that fixed line and Ox passes through the initial position of P, as shown in Figure 8.14, show that the curve y = y(x) described by P is such that

The resulting curve is called a tractrix.

Transcribed Image Text:

dy (a-x) dx X with y = 0 at x = a