Large amplitude whirling of an elastic string -- a nonlinear eigenvalue problem

The whirling of a string is a problem of some antiquity, the linearized solutions to a number of such problems having been derived by D. Bernoulli (1700-1782) and L. Euler (1707-1783). The nonlinear theory of whirling of inextensible strings has been discussed by Kolodner [1] and Caughey [2], [3]. Carrier [4], [5] has discussed the theory of nonlinear vibration of an elastic string using perturbation methods. In the present paper exact solutions will be presented for the whirling of an elastic string with fixed ends, and it will be shown that the modes of free whirling are orbitally stable.