Question

6.14(a) Prove that the brachistochrone curve (6.26) is indeed a cycloid, that is, the curve traced by a point on the circumference of a wheel of radius a rolling along the underside of the x axis. (b) Although the cycloid repeats itself indefinitely in a succession of loops, only one loop is relevant to the brachistochrone problem. Sketch a single loop for three different values of a (all with the same starting point 1) and convince yourself that for any point 2 (with positive coordinates x2, y2) there is exactly one value of a for which the loop goes through the point 2. (c) To find the value of a for a given point x2, y2 usually requires solution of a transcendental equation. Here are two cases where you can do it more simply: For X2 = πb, уг = 2b and again for x2 2π b. У2-0 find the value of a for which the cycloid goes through the point 2 and find the corresponding minimum times.

Answer 1

the curve followed by a point on the perimeter of a wheel of range " a " along x - axis.