The Stability of Spinning Balloon and Balloon Collapse

This paper presents the criterion of the existence of a balloon. We find that there exists a limiting value (T₀/mR²ω²)_c which can predict the critical conditions under which a balloon can be built. Furthermore, we also concluded that the criterion to ascertain the existence of a balloon, formed at conventional ring-spinning frame, can be expressed in a more compact form: (M/m)<(M/m)_c. All our results are founded on the rigorous wide amplitude balloon theory. The stability of an actual spinning balloon is also discussed. Both the stable and unstable configurations of a balloon formed under identical mechanical parameters are presented numerically and graphically.