Flight Motion of a Continuously Elastic Finned Missile

The motion of elastic finned projectiles has been analyzed by various approximate theories. The correct equations of small-amplitude motion are derived for a symmetric missile. The aerodynamic and elastic symmetries are used to allow the use of complex variables to describe the lateral motion in a nonrotating coordinate system. Although the resulting equations are both ordinary and partial differential equations, frequencies and damping rates of free oscillations are obtained from an ordinary differential equation with boundary conditions. The induced drag coefficients for each mode are computed as functions of the missile’s elasticity. Equations for a permanently deformed bent missile are derived, and an ordinary differential equation for the forced motion of a bent missile is obtained. Sample calculations for a finned projectile with fineness ratio of 20 show resonant motion at the aerodynamic frequency, as well as at each elastic frequency. The nonlinear roll moment associated with a bent missile is computed and the location of possible spin–yaw lock-in is determined.