Instability of controlled projectiles in ascending or descending flight

Lloyd and Brown have shown that constant horizontal and vertical side forces and moments applied to a spinning projectile can result in dynamic instability. This instability arises from the nonlinear terms in the fixedplane coordinate system spin that appear in the equations of motion. By the use of the fixed-plane system (rather than Lloyd and Brown's nonrolling system) simpler relations can be developed, the full effects of gravity, drag and roll damping obtained, and the limitation to large gyroscopic stability factors removed. Very simple stability bounds are given for spinning finned missiles with spin rates well above resonance as well as for a gyroscopically stable shell. Exact solutions are given for finned missiles with zero spin but the motion of slowly spinning missiles should be numerically computed.