Throughout the history of sounding rockets, there has been a steady flow of analytical studies trying to explain and predict the, often untoward, dynamic phenomena attendant on upward flight. This article offers a summing-up of these contributions, and of the main results so far achieved. Following a brief review of the specific conditions incident to ascent, and of the mathematical model generally adopted to represent the sounding rocket, the general equations of motion are set up, then simplified so as to enable each phenomenon to be studied on its own merits. Under standard flight conditions, the linear theory provides analytical expressions for the variation of the angle of attack, thus revealing the respectively convergent or divergent modes of oscillation at incidence. More particularly, it helps to make the stability criteria explicit, with due allowance for the variation in air density, the gyroscopic effect and the Magnus effect. The phenomenon of resonance, provoked by the disturbances peculiar to rockets set in rolling motion, is also explored. Dynamic processes not explicable in terms of linear theory must be grappled with by suitable analyses making use of some simplifying assumptions. This provides the means of explicitly expressing the conditions under which such phenomena as roll lock-in, catastrophic yaw and persistent resonance occur as a result either of rocket unbalance or a rolling moment induced at an oblique angle of attack, complicated by the presence of an aerodynamic side moment. A further study is made of wide-amplitude limit cycles and their stability. Lastly, there is an analysis of the sensitivity of sounding-rocket trajectories to external disturbances, such as the impact of stage separation and the wind.
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