An Analysis of Asymmetric Rolling Bodies with Nonlinear Aerodynamics
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A nonlinear analysis is performed for the motion of a rolling re-entry vehicle for the case of constant roll rate and for the case of variable roll rate, dynamic pressure, and stability derivatives. Each of the restoring, damping, lag, Magnus, and induced moments is assumed to be a cubic function of the angle-of-attack with variable coefficients. In the constant roll rate case, the derivative expansion version of the method of multiple scales is used to derive equations that characterize the time variation of the amplitudes and phases of the nutation and precession modes. In the variable roll rate case, the generalized version of the method of multiple scales is used to derive equations for the roll rate and the amplitudes and phases of the oscillatory modes of the angle of attack near and away from roll resonance. The roll degree of freedom is coupled with the pitch and yaw degrees of freedom instead of assuming a priori the variation of the roll rate. The analytical solutions are found to be in good agreement with the numerical solutions of the full problem. 1972 American Institute of Aeronautics and Astronautics, Inc. All rights reserved.