The influence of roll orientation-dependent aerodynamics on the stability of cruciform missile configurations

The angular motion of a symmetric, cruciform missile, having roll orientation-dependent aerodynamics, is studied. An aerodynamic moment expansion, consistent with rotational and reflectional symmetry arguments, is incorporated into the equations of missile angular motion. A generalized version of the method of multiple scales is incorporated to generate approximate solutions to the equations of angular motion for three specific cases: free-flight angular motion at constant roll rate, induced rolling motion with a priori yawing motion, and finally the combined problem of coupled yawing and rolling motion. Critical roll rates are identified and solutions valid in the vicinity of these singular conditions are generated. Approximate solutions used to derive stability criteria are compared with numerical solutions of exact, nonlinear equations of motion. Results of the perturbation solutions show good agreement with the exact calculations for moderate angles of attack.