The ring spinning machine is used in the textile industry to simultaneously twist staple fibres into yarn and then wind it onto a bobbin for storage. The yarn loop rotating rapidly about a fixed axis generates a surface referred to as a balloon.
Mathematical treatment of the yarn gives rise to time dependent, nonlinear equations of motion. Solutions corresponding to the yarn's tension and spatial coordinates produce dynamical similarities to experimental and actual ring spinning scenarios.
Steady state solutions taken from a rotating frame of reference show that the balloon profiles can be of a single, double or multi- loop nature. Small velocity perturbations give rise to: limit cycles (balloon configurations oscillating about a particular steady state), transitions between different steady states, and much, much more interesting behavior.