Resonant Behavior of a Symmetric Missile Having Roll Orientation-Dependent Aerodynamics

Abstract

The transient response of a symmetric cruciform missle having roll orientation-dependent aerodynamics is studied. Aerodynamic force and moment expansions, cubic in angle of attack and harmonic in missle roll orientation, are incorporated into the equations of angular motion. An approximate resonant solution, generated by the method of averaging, is used to identify the special conditions of zero spin, fundamental resonance, and approximately one-half fundamental resonant spin. The roll orientation-dependent restoring and side moments are shown to have a dramatic influence on missile stability at the fundamental resonance roll rate. This work identifies the inherent tetragonal symmetry of the missile as a potential source of resonant behavior, in contrast to the established mechanism of configuration al asymmetries.