Abstract
One end of a thread is attached to a steadily rotating arm and at the other end a mass is supported after the thread has passed through an eyelet on the axis of rotation (the arm rotating in a vertical plane, so that the axis of rotation is horizoutal, and the part of the thread beyond the eyelet hangs vertically with the mass at its end).
The effect of air resistance has been neglected.
A complete solution of the equations of motion of a steadily rotating thread has been obtained in terms of elliptic functions.
The equations thus obtained have an nfinity of solutions, and the actual form assumed by the thread is determined by consideration of energy.
Of all the possible configurations, the thread will tend to take up that for which V has the least possible value. In this report, in order to compare the values of V in the different configurations, we shall regard η as given and discuss ζ and V as functions of the parameter q. It will be found that the possible equilibrium configurations group themselves in pairs, of which one is then presumably stable and the other unstable. Each such pair is possible only up to a certain value of ζ, so that for this value of ζ an abrupt change in form must occur.
