Dynamic analysis of a non-rolling ballistic missile rapidly ascending throught the atmosphere

Abstract

An analysis of the dynamic behaviour of a ballistic non-rolling missile rapidly ascending through the atmosphere has been performed. Both the boosting and coasting phase have been considered in plane motion. It has been shown that the three original governing equations under certain, yet realistic, conditions can be reduced to a single second order differential equation in angle of incidence describing the dynamics of the missile. An explicit solution to this equation, which has varying coefficients, is available. Criteria giving conditions for divergence, damped oscillations and tumbling have been derived. A numerical method for solving the complete equations has been developed. A comparison of the explicit and the numerical solution for a particular case was made and showed good agreement.