Dynamics of an unusual spinning re-entry body.

Abstract

Coning motions are analyzed for an unusual spinning re-entry body whose roll moment of inertia is nearly as large as its moment of inertia in pitch or yaw. The analysis treats the rotational motion during re-entry caused by dynamic mass unbalance and by initial angle of attack and angular velocity. Even though some of the motions are complicated, analytical results are presented which are useful in predicting many facets of the motion. Initial angle of attack excites a fairly simple coning motion with the body symmetry axis spiraling in toward the velocity vector at a rate increasing with dynamic pressure. Initial angular velocity leads to a more complex sequence of cycloidal motions. During early re-entry, mass unbalance causes a beat phenomenon peculiar to a body with such moment-of-inertia characteristics. Later in the re-entry period, there is a severe build-up in angle of attack in the region where the natural pitching frequency of the body is nearly equal to its spin rate.Nomenclature total angle-of-attack amplitude complex angle of attack = a + i ft angle-of-attack projection on pitch plane angle-of-attack projection on yaw plane normal force coefficient slope of normal force coefficient = axial force coefficient aerodynamic force vector acceleration due to gravity altitude pitch/yaw moment of inertia roll moment of inertia I -IxO'xyz C) = nonspinning body axes = time derivative applied moment vector mass spin rate stability parameter = dynamic pressure [(n/2) 2 + Q'p" reference area time velocity vector static margin angle-of-attack projection in XZ plane angle-of-attack projection in XY plane pitch flight-path angle pitch flight-path angle at re-entry pitch flight-path angle change =7 -70 mass unbalance angle r -n/2 • r + n/2 yaw flight-path angle air density pitch attitude angle roll attitude angle yaw attitude angle natural frequency of nonspinning vehicle complex angular velocity = co y + earth-fixed axes translating axes (\\OXYZ)