Relaxation of viscoelastic tumblers with application to 1I/2017 U1 ('Oumuamua) and 4179 Toutatis
Relaxation of viscoelastic tumblers with application to 1I/2017 U1 ('Oumuamua) and 4179 Toutatis
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粘弹性滚筒的松弛适用于 1I/2017 U1 (Oumuamua) 和 4179 Toutatis
DOI：
10.1093/mnras/staa1933
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发表时间：
2020
影响因子：
4.8
通讯作者：
J. A.
中科院分区：
文献类型：
--
作者：
Kwiecinski;J. A.
在观测到彗星和小行星以非主轴(NPA)态旋转的激励下，我们研究了自由进动的三轴椭球旋转体向其最低能量自旋态的驰豫。进动的松弛是由自重产生的内部耗散应力和自旋产生的惯性力引起的。我们发展了一个一般的理论来确定在任何线性流变学下，长轴(LAM)和短轴(SAM)模式下转子的粘弹性应力。利用连续介质力学的方法，计算了应力场和粘弹性材料应变所耗散的能量，从而确定了进动衰减的时间尺度。为了说明该理论是如何使用的，我们将我们的框架应用于Maxwell制度下的三轴1I/2017(‘Oumuamua)和4179 Toutatis。对于前者，使用非常冷的整体式小行星的典型粘弹性参数，使衰减时间尺度延长1010倍，并高于依赖因子方法的工作中发现的时间尺度，而后者由于考虑了自引力，产生的时间尺度短107。我们进一步将我们的三轴理论简化为扁平几何的物体，并导出了一族相对简单的解析近似，确定了麦克斯韦旋转子的NPA衰减时间，以及确定自引力在驰豫过程中是否可以忽略的判据。与数值积分相比，对于接近非耗散的物体和中等到高能量耗散的旋转体，我们的近似显示出不大于的相对误差。
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 time-scale 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 time-scale longer by a factor of 1010and higher than the time-scales found in the works relying on the-factor approach, while the latter yields a time-scale shorter by 107as 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, when compared to numerical integration, for close to non-dissipative bodies andfor moderately to highly energy dissipating rotators.