粘弹性扁转子的进动松弛
Precession Relaxation of Viscoelastic Oblate Rotators
摘要：
各种扰动都会破坏小天体旋转的稳定性，使其处于非主自旋状态。在这种状态下，物体经受由惯性力产生的交变应力。这产生章动松弛，即，自旋朝着围绕最大惯性轴的主旋转的演变。在小天体动力学研究中，衰减章动所需的时间尺度是至关重要的。在迄今为止的文献中，章动弛豫总是借助于引入的经验品质因数$\,Q\,$来描述能量耗散率。这种方法的缺点之一是不能描述弛豫速率对当前章动角的依赖性。这是因为我们对品质因数对强迫频率的依赖性缺乏了解。在这篇文章中，我们直接从材料所服从的流变定律导出章动阻尼的描述。这使我们章动阻尼率作为当前章动角的函数，以及物体的形状和流变参数。与基于经验$\,Q\,$ -因子的方法相比，我们的开发在球形极限中给出了零阻尼率。我们的方法是通用的，适用于任何形状和任何线性流变法。然而，为了简化的发展，在这里，我们考虑一个动态扁圆转子与麦克斯韦流变。
英文摘要：
Perturbations of all sorts destabilise the rotation of a small body and leave it in a non-principal spin state. In such a state, the body experiences alternating stresses generated by the inertial forces. This yields nutation relaxation, i.e., evolution of the spin towards the principal rotation about the maximal-inertia axis. Knowledge of the timescales needed to damp the nutation is crucial in studies of small bodies' dynamics. In the literature hitherto, nutation relaxation has always been described with aid of an empirical quality factor $\,Q\,$ introduced to parameterise the energy dissipation rate. Among the drawbacks of this approach was its inability to describe the dependence of the relaxation rate upon the current nutation angle. This inability stemmed from our lack of knowledge of the quality factor's dependence on the forcing frequency. In this article, we derive our description of nutation damping directly from the rheological law obeyed by the material. This renders us the nutation damping rate as a function of the current nutation angle, as well as of the shape and the rheological parameters of the body. In contradistinction from the approach based on an empirical $\,Q\,$-factor, our development gives a zero damping rate in the spherical-shape limit. Our method is generic and applicable to any shape and to any linear rheological law. However, to simplify the developments, here we consider a dynamically oblate rotator with a Maxwell rheology.
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