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本报告采用多重尺度法来分析在非线性俯仰、阻尼和马格纳斯力矩作用下滚动再入体的运动。假设这些力矩都是攻角的三次函数。本文考虑了三种情况:(1)滚动速度p接近零和远离零的轴对称体;(2)远离滚动共振(即远离章动频率ω_1)的非对称体和(3)接近滚动共振的稍不对称的物体。本文对上述三种情况都推导出能够表达章动和进动的振幅和相角随时间变化的特征方程。这些方程是取p≈0,p≈ω_1,和p≈3ω_1情况下的特殊形式。本文还研究了力矩参数和不对称程度对运动的影响,找到了导致不稳定性的这些参数的范围。对稳态运动及其稳定性的条件也进行了分析。
This report uses a multiscale method to analyze the motion of rolling reentrant bodies under non-linear pitching, damping, and Magnus moments. It is assumed that these torques are all cubic functions of angle of attack. Three cases are considered in this paper: (1) axisymmetric bodies with rolling speed p near zero and away from zero; (2) asymmetric bodies far away from rolling resonance (ie away from the nutation frequency ω_1); and (3) Asymmetric objects. In this paper, the eigenvalues of the amplitude and phase angle of the nutation and precession with time are deduced for all three cases. These equations are special forms in the case of p≈0, p≈ω_1, and p≈3ω_1. The paper also studies the effect of moment parameters and degree of asymmetry on motion and finds the range of these parameters that lead to instability. The conditions of steady-state motion and its stability are also analyzed.