Some special cases of spin-yaw lock-in

Abstract

Abstract : A slightly asymmetric missile is a basically symmetric missile with a nonzero pitch moment at zero angle of attack. In flight this moment causes a trim angle that rotates with the missile and has a maximum when the spin is near resonance with the missile's natural pitch frequency. This report considers a roll moment that can be induced by this trim angle and can cause resonant lock- in spin. Simple expressions for this induced rolled moment are given and the existence and stability conditions for equilibrium spin are derived. The special case of the induced roll moment caused by a radial center of mass offset is considered and a number of different types of possible equilibrium spin combinations are shown. The possibility of resonant lock-in spin in the opposite sense to the expected steady-state spin is indicated. It is further shown that there are induced roll moments for which the design steady-state spin will not occur under any launch conditions. If several stable equilibrium spins are possible, the one that occurs in flight can be determined by the orientation of the initial pitch angular velocity. Finally the form of an induced pitch moment is given and its possible effect on the angular motion is discussed.