In 1799, Laplace derived the system of differential equations (now called Liouville-Euler) that fully describes the motions of the rotation axis of any celestial body. Laplace showed that only the gravitational forces and kinetic moments from other celestial bodies influence the rotation of any one of them. The equations involve three Euler angles that specify the motions of a body's rotation axis; they can be reduced to a system of two equations for the inclination and time derivative of the declination of the rotation axis. Laplace showed the existence of a forced annual oscillation and the so-called free Chandler wobble. Most current theories retain only two Euler angles and invoke an elastic Earth to match observations. We analyze the much longer time series of polar motion (coordinates m₁ and m₂ of the rotation pole at the Earth's surface) now available, in order to further explore phenomena that Laplace could not investigate, given the dearth of data in his time. We use singular spectral analysis (SSA) to extract components of the time series. The first three components (trend or Markowitz drift, forced annual oscillation and free Chandler oscillation) account for 73% of the variance of polar motion. Under the current theory, their modulation is thought to be a response to reorganization of oceanic and atmospheric masses. However, the periods of the first six SSA components of polar motion have been encountered in previous studies of sunspots and in the ephemerids of Jovian planets. We also analyze the derivatives of the envelopes of the three SSA components of polar motion. Again, most of these components have periods and modulations that correspond to the ephemeris (periods and combinations of commensurable periods) of Jovian planets. Examples include 171.5 yr (the Jose cycle linked to Neptune), 90 yr (the Gleissberg cycle linked to Uranus), 40 yr (a commensurable period linked to the Jovian planets), 22 yr, 11 yr (Jupiter, Sun), 60 yr, 30 yr (Saturn). Fig. 3 can be considered as the central result of the paper. It shows that the sum of forces of the four Jovian planets matches in a striking way the polar motion reconstructed with SSA components (the Markowitz trend removed). All our results argue that significant parts of Earth's polar motion are a consequence (rather than a cause) of the evolution of planetary ephemerids. The Sun's activity and many geophysical indices show the same signatures, including many climate indices. Two different mechanisms (causal chains) are likely at work: a direct one from the Jovian Planets to Earth, another from planetary motions to the solar dynamo; variations in solar activity would in turn influence meteorological and climatic phenomena. Given the remarkable coincidence between the quasi-periods of many of these phenomena, it is reasonable to assume that both causal chains are simultaneously at work. In that sense, it is not surprising to find the signatures of the Schwabe, Hale and Gleissberg cycles in many terrestrial phenomena, reflecting the characteristic periods of the combined motions of the Jovian planets.

1799年，拉普拉斯（Laplace）推导了微分方程组（现称为Liouville-Euler），该系统完全描述了任何天体旋转轴的运动。拉普拉斯（Laplace）表明，只有来自其他天体的重力和动力矩会影响其中任何一个的旋转。这些方程式涉及三个欧拉角，这些欧拉角指定了物体旋转轴的运动。可以将它们简化为由两个方程组成的系统，用于计算旋转轴的倾斜度和时间导数。拉普拉斯（Laplace）显示了强迫性年度振荡的存在，以及所谓的自由钱德勒（Chandler）摇摆。当前大多数理论仅保留两个欧拉角，并调用弹性地球来匹配观测值。我们分析了更长的极运动时间序列（坐标m ₁和m ₂鉴于地球上缺乏数据，为了进一步探索拉普拉斯无法调查的现象，现在可以使用它在地球表面的旋转极）。我们使用奇异频谱分析（SSA）提取时间序列的成分。前三个分量（趋势或Markowitz漂移，强迫年振荡和自由钱德勒振荡）占极运动方差的73％。根据当前的理论，它们的调制被认为是对海洋和大气质量重组的一种反应。但是，在先前对太阳黑子和木星行星的星历中的研究中已经遇到了极运动的前六个SSA分量的周期。我们还分析了极运动的三个SSA分量的包络的导数。再次，这些成分中的大多数都具有对应于木星行星的星历（周期和相应周期的组合）的周期和调制。例子包括171.5年（与海王星有关的何塞周期），90年（与天王星有关的格里斯贝格周期），40年（与木星相关的相当时期），22年，11年（木星，太阳），60年，30年（土星）。如图。3可以认为是本文的主要结果。它显示出四个木星行星的力之和以惊人的方式与使用SSA分量重建的极运动相匹配（已消除了Markowitz趋势）。我们所有的结果都表明，地球极地运动的重要部分是行星星历表演变的结果（而不是原因）。太阳的活动和许多地球物理指数显示出相同的特征，包括许多气候指数。可能有两种不同的机制（因果链）起作用：一种是从木星行星到地球的直接机制，另一种是从行星运动到太阳发电机的机制；另一种是从行星运动到太阳发电机的机制。太阳活动的变化反过来会影响气象和气候现象。鉴于许多这类现象的准周期之间有惊人的巧合，有理由假设两个因果链同时起作用。从这个意义上讲，在许多地球现象中找到Schwabe，Hale和Gleissberg周期的标志并不奇怪，这反映了木星行星组合运动的特征时期。