The author studies the stability and bifurcation behavior of a rotating closed loop of homogeneous inextensible and elastic strings under the absence of body forces. Especially the stability and bifurcation of the axial motion, that is a motion where the string flows through a fixed spatial shape where each point is moving in tangential direction, on a circle is considered making use of minimizers of the total energy subject to certain constraints. The existence of such minimizers, which implies orbital Liapunov stability, could be proved both for the inextensional and for stiff elastic strings independent of the amount of a control parameter which is the angular velocity of the circle. For soft elastic strings, however, a critical value for the angular velocity is obtained beyond which a symmetry breaking bifurcation occurs.
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