THE CUSP CATASTROPHE AND THE STABILITY PROBLEM OF HELICOPTER GROUND RESONANCE

Catastrophe theory is used to derive closed form expressions for the critical speeds of helicopters in ground resonance. The results are obtained for an adaptation of Coleman's model of helicopters with soft, in-plane hingeless rotors. It is shown that the characteristic polynomial of the rotorcraft system is diffeomorphic to a versal unfolding of the cusp catastrophe germ. Expressions are computed for the equilibrium manifold and the bifurcation set. The expression for the bifurcation set is then used to obtain a frequency equation for finding the exact critical speeds.