Artificial Parameter Perturbation Method and Parameter-Expansion Method Used in Accurate Prediction of the Ring-Spinning Balloon in Zero Air Drag

Numerical solutions of quasi-stationary ring-spinning equations have been extensively investigated after the appearance of computer. However, mathematicians and engineers are more willing to obtain analytical solutions. This paper presents a technique for analytical solution of the dynamics of ring-spinning balloon. Artificial parameter is introduced in order to be used as an expanding parameter. Parameter-expansion method is also used to enlarge the feasible region. Detailed derivation of the analytical solution is presented and the air drag is not considered to simplify the procedure. Some results are performed, from which this method seems to be very efficient and reliable in the prediction of ring-spinning process.