Spin-Yaw Lockin of an Elastic Finned Projectile

摘要

Supersonic finned projectiles carrying very long dense metallic rods have been observed to have significantly large flexing motion. The appropriate Lagrangian for a pitching, yawing, rolling, and flexing missile is derived and the powerful finite element method used to construct differential equations for finite element parameters. These differential equations for constant spin are used to calculate frequencies and damping rates of transient motion and trim response motion to missile-fixed inertia and aerodynamic forcing terms associated with inelastic deformations. The results agree with earlier results based on a much more difficult iterative integration of a complex differential equation with unusual boundary conditions. Only three elements were necessary for reasonable accuracy, although codes for five and seven elements have been prepared and exercised. The finite element ordinary differential equations allowed calculation of the time history of missile motion with varying spin and demonstrated the occurrence of spin-yaw resonance at the aerodynamic frequency and at the lowest elastic frequency.