Flight Mechanics of an Elastic Symmetric Missile

Abstract

Abstract : The free-flight motion of an elastic missile is approximated with three bodies connected by two massless elastic cantilever beams. If the mass distribution of the three bodies is 1-2-1, the frequency of the symmetric oscillation of the outer bodies is within 5% of the classical frequency of the oscillation of a free-free beam. A second combined pitching antisymmetric flexing motion can occur with a frequency that is almost twice that of the symmetric flexing motion. As the beam stiffness is reduced, the symmetric flexing motion frequency approaches the rigid body aerodynamic zero-spin frequency, and the flight zero-spin aerodynamic frequency is considerably reduced. Moderate beam damping can cause dynamic instability for spins greater than the zero-spin aerodynamic frequency. Resonance mode amplification can occur when the spin is equal to the zero-spin aerodynamic frequency, but more importantly it can occur when the spin is equal to the two elastic flexing frequencies. Spin-yaw lock-in occurs at the lower elastic frequency.