应用于1 I/2017（`Oumuamua）和4179 Toutatis的粘弹性滚筒的松弛
Relaxation of Viscoelastic Tumblers with Application to 1I/2017 (`Oumuamua) and 4179 Toutatis
摘要：
基于对彗星和小行星在非主轴（NPA）状态下旋转的观测，我们研究了自由旋进三轴椭球旋转体向其最低能量自旋态的弛豫。旋进的弛豫是由自引力和自旋产生的惯性力产生的内部耗散应力引起的。我们开发了一个通用的理论，以确定在转子的粘弹性应力，在任何线性流变学，为长轴（LAM）和短轴（SAM）模式。通过连续介质力学的方法，我们计算了由应力场和粘弹性材料应变所消耗的功率，从而使我们能够确定进动阻尼的时间尺度。为了说明如何使用该理论，我们将我们的框架应用于麦克斯韦制度下的三轴1 I/2017（'Oumuamua）和4179 Toutatis。对于前者，采用典型的非常冷的单片小行星的粘弹性参数呈现阻尼时标更长的一个因素的$10^{10}$和更高的时间尺度在依赖于$\,Q$ -因素的方法的作品中发现，而后者产生一个显着较短的时间尺度，包括自引力的结果。我们进一步减少我们的三轴理论的扁圆形的几何形状的机构，并得出一个家庭的相对简单的解析近似确定的NPA阻尼时间麦克斯韦转子，以及一个标准，确定是否自引力是可以忽略不计的松弛过程。我们的近似表现出不大于$0.2\%$的相对误差，当与数值积分相比，接近非耗散机构和$0.002\%$的高耗能转子。
英文摘要：
Motivated by the observation of comets and asteroids rotating in non-principal axis (NPA) states, we investigate the relaxation of a freely precessing triaxial ellipsoidal rotator towards its lowest-energy spin state. Relaxation of the precession arises from internal dissipative stresses generated by self-gravitation and inertial forces from spin. We develop a general theory to determine the viscoelastic stresses in the rotator, under any linear rheology, for both long-axis (LAM) and short-axis (SAM) modes. By the methods of continuum mechanics, we calculate the power dissipated by the stress field and the viscoelastic material strain which enables us to determine the timescale of the precession dampening. To illustrate how the theory is used, we apply our framework to a triaxial 1I/2017 (`Oumuamua) and 4179 Toutatis under the Maxwell regime. For the former, employing viscoelastic parameters typical of very cold monolithic asteroids renders a dampening timescale longer by a factor of $10^{10}$ and higher than the timescales found in the works relying on the $\,Q$-factor approach, whilst the latter yields a significantly shorter timescale as a consequence of including self-gravitation. We further reduce our triaxial theory to bodies of an oblate geometry and derive a family of relatively simple analytic approximations determining the NPA dampening times for Maxwell rotators, as well as a criterion determining whether self-gravitation is negligible in the relaxation process. Our approximations exhibit a relative error no larger than $0.2\%$, when compared to numerical integration, for close to non-dissipative bodies and $0.002\%$ for highly energy dissipating rotators.
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