Equilibria of the circular elastica under a uniform central force field

Abstract

A mathematical model for the problem of an inextensible circular elastica under a uniform centrally directed force field is derived and studied. It is shown analytically that stable large amplitude solutions exist at forces P > P 1 P > {P_1} , the first eigenpressure for the linearized model, and it is shown numerically that these solutions have only one axis of symmetry. These results agree with experiment. In addition, numerical solutions are calculated for states with more than one axis of symmetry which resemble those found in the literature on elastic rings under hydrostatic pressure.