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Earth's Rotation: A Challenging Problem in Mathematics and Physics

机译：地球自转：数学和物理学中一个具有挑战性的问题

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摘要

A suitable knowledge of the orientation and motion of the Earth in space is a common need in various fields. That knowledge has been ever necessary to carry out astronomical observations, but with the advent of the space age, it became essential for making observations of satellites and predicting and determining their orbits, and for observing the Earth from space as well. Given the relevant role it plays in Space Geodesy, Earth rotation is considered as one of the three pillars of Geodesy, the other two being geometry and gravity. Besides, research on Earth rotation has fostered advances in many fields, such as Mathematics, Astronomy and Geophysics, for centuries. One remarkable feature of the problem is in the extreme requirements of accuracy that must be fulfilled in the near future, about a millimetre on the tangent plane to the planet surface, roughly speaking. That challenges all of the theories that have been devised and used to-date; the paper makes a short review of some of the most relevant methods, which can be envisaged as milestones in Earth rotation research, emphasizing the Hamiltonian approach developed by the authors. Some contemporary problems are presented, as well as the main lines of future research prospected by the International Astronomical Union/International Association of Geodesy Joint Working Group on Theory of Earth Rotation, created in 2013.
机译：在各个领域中普遍需要适当了解地球在太空中的方向和运动。进行天文观测一直以来都需要这种知识，但是随着太空时代的到来，它对于进行卫星观测，预测和确定其轨道以及从太空观测地球也变得至关重要。考虑到地球在大地测量学中的相关作用，地球自转被认为是大地测量学的三个支柱之一，另外两个是几何和重力。此外，几个世纪以来，关于地球自转的研究促进了许多领域的发展，例如数学，天文学和地球物理学。该问题的一个显着特征是对精度的极端要求，必须在不久的将来满足这一要求，粗略地说，在与行星表面相切的平面上大约为1毫米。这挑战了迄今为止已经设计和使用的所有理论;本文简要回顾了一些最相关的方法，这些方法可以看作是地球自转研究的里程碑，强调作者开发的哈密顿方法。报告提出了一些当代问题，以及国际天文学联合会/国际大地测量学协会地球自转理论联合工作组（于2013年成立）所展望的未来研究的重点。

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