Angular motion of a re-entering symmetric missile

Abstract

For the case of cubic static-moment constant air density and no damping, the exact solution for the combined pitching and yawing motion of a symmetric missile can be expressed in terms of elliptic functions. A perturbation method that makes use of this exact solution is then developed to determine the effect of air-density variations and nonlinear aerodynamic Magnus and damping moments when the static moment is strongly nonlinear. Stability boundaries for initial conditions are computed, and the conditions for circular limit motions are derived. These circular limit motions have been experimentally observed and conditions for a possible nonlinear moment expansion have already been derived for a slightly nonlinear static moment by a quasilinear analysis. The various predictions of the approximate theory have been verified by numerical integration of the exact differential equations of motion. The great value of the methods developed lies in their ability to yield quickly the effect of various parameters and initial conditions on missile motion, thereby releasing the designer from the necessity of performing a large number of numerical integrations. The results of the theory, however, are limited to altitudes for which the density variations over a cycle of the motion is small (i.e., less than 10%).