物体中的潮汐围绕自旋轨道共振振动。达尔文-考拉理论的推广
Tides in a body librating about a spin-orbit resonance. Generalisation of the Darwin-Kaula theory
摘要：
达尔文-考拉的天体潮汐理论是针对没有天平动的自转天体的。我们证明，这个理论，在其习惯的形式，是不适用于一个librating机构。具体来说，在经度上存在天平动的情况下，傅立叶潮汐模式的实际频谱不同于达尔文-考拉理论为非天平动天体提供的传统频谱。这就需要推导出适用于天平动的潮汐力矩和潮汐加热率的公式。我们推导出潮汐频谱纵向强迫天平动与一个和两个主要频率，概括到更多的主要频率是直接的。(By我们理解的主要频率是由于振动体的三轴性而出现的频率。）单独地，我们考虑在一个频率的自由天平动的情况（再次，推广到更多的频率是直接的）。我们还计算了潮汐扭矩。该扭矩提供对三轴度引起的物理天平动的校正。我们的理论不是自洽的：我们假设潮汐力矩比永久三轴性引起的力矩小得多，因此潮汐引起的附加天平动比永久三轴性引起的主天平动弱得多。最后，我们计算了经历主模式强迫振动、一个频率的自由振动或叠加强迫振动和自由振动的物体的潮汐耗散率。
英文摘要：
The Darwin-Kaula theory of bodily tides is intended for celestial bodies rotating without libration. We demonstrate that this theory, in its customary form, is inapplicable to a librating body. Specifically, in the presence of libration in longitude, the actual spectrum of Fourier tidal modes differs from the conventional spectrum rendered by the Darwin-Kaula theory for a non-librating celestial object. This necessitates derivation of formulae for the tidal torque and the tidal heating rate, that are applicable under libration. We derive the tidal spectrum for longitudinal forced libration with one and two main frequencies, generalisation to more main frequencies being straightforward. (By main frequencies we understand those emerging due to the triaxiality of the librating body.) Separately, we consider a case of free libration at one frequency (once again, generalisation to more frequencies being straightforward). We also calculate the tidal torque. This torque provides correction to the triaxiality-caused physical libration. Our theory is not self-consistent: we assume that the tidal torque is much smaller than the permanent-triaxiality-caused torque; so the additional libration due to tides is much weaker than the main libration due to the permanent triaxiality. Finally, we calculate the tidal dissipation rate in a body experiencing forced libration at the main mode, or free libration at one frequency, or superimposed forced and free librations.
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