Steady state response and stability of ballooning strings in air

This paper theoretically and experimentally investigates the steady state response and stability of ballooning strings under the influence of air drag. The equations of motion are derived using Hamilton's principle. Numerical solution of the non-linear steady state equations reveals the dependence of the three-dimensional balloon shapes and eyelet tension on the string length and air drag coefficient. Linearization and approximation using Galerkin's method allows stability analysis of the steady state solutions. The theoretically predicted balloon shapes, eyelet tension, and stability are experimentally verified.