Rotational Dynamics: New Problems and Theories

AST 0307845VaradiRotation在行星和卫星的理解中占有核心地位。它会导致变形（扁平化），这是解锁身体内部结构的关键。旋转动力学通过潮汐变形和耗散深刻地影响大气和气候，以及内部动力学。潮汐耦合旋转和轨道运动，导致某些特殊的共振配置（例如，月球的同步旋转），揭示了数十亿年来轨道和自旋状态的演变。多卫星系统，如木星的伽利略卫星，显示出更复杂的相互作用。 Ferenc Varadi博士的这个项目的目标是通过开发新的分析理论来促进对旋转动力学的理解，这些理论将通过与直接数值模拟结果的比较进行广泛的测试。与星历计算的具体理论相反，该项目的目标是使用不针对特定行星或卫星的一般框架来寻找现象的物理解释，该项目还将为推广卡西尼状态的概念提供理论基础，在卡西尼状态中，自由运动因潮汐而完全阻尼。主要的动机来自最近的结果大振幅的物理振动，这是相反的旋转动力学的流行观点。该方法还将使人们有可能确定广义卡西尼状态没有限制性假设的轨道运动。虽然很大一部分的工作是有关同步旋转，物理天平动及其长期影响也将调查快速旋转。新的理论将提供自洽的动力学方程的基础上微扰计算和平均。新的，更精确的方程将被导出的自旋轴的演变。将开发类地行星、小行星和类木行星的应用。该项目的一个重要组成部分将是建立与轨道和旋转动力学相结合的旋转和潮汐变形的微分方程。而不是使用洛夫数形式主义，这需要在时间上的谱分解，以适应粘弹性行为，在时间和空间的身体变形的方程被改写成一个系统的常微分方程的时间。这个系统可以通过微扰理论和平均技术来分析，从而发展出一个自洽的变形体模型，通过这个项目所取得的进展将对行星天文学中的一些问题和项目做出重大贡献。特别是，该项目可能使人们有可能从精确的天体测量中推断出外行星卫星的轨道特性，如日食和掩星时间。此外，该项目预计将为分析正在进行的和计划中的美国空间飞行任务的数据提供理论基础，例如水星信使使命和土星卡西尼使命。

AST 0307845VaradiRotation has a central place in the understanding of planets and satellites. It causes deformation(flattening) which is a key to unlocking the internal structure of a body. Rotational dynamicsprofoundly affects the atmosphere and climate, as well as the internal dynamics through tidaldeformation and dissipation. Tides couple rotational and orbital motions, resulting in certainspecial resonant configurations (e.g., the synchronous rotation of the Moon) that shed light onthe evolution of the orbit and spin state over billions of years. Multiple satellite systems, such asthe Galilean satellites of Jupiter, show even more complex interactions. The goal of this project of Dr. Ferenc Varadi is to advance the understanding of rotational dynamics by developing new analytical theories which will be extensively tested through comparisons with the results of direct numerical simulations. As opposed to specific theories for ephemeris computations, the goal of the project is to find physical explanations for phenomena using a general framework that is not tailored to a specific planet or satellite.The project will also provide the theoretical basis for generalizing the notion of Cassini states in which free motions are completely damped due to tides. The main motivation comes from recent results on large-amplitude physical librations, which are contrary to the prevailing view of rotational dynamics. The approach will also make it possible to determine generalized Cassini states without restrictive assumptions on orbital motions. While a large part of the work is related to synchronous rotation, physical librations and their long-term effects will also be investigated for fast rotators. The new theories will provide self-consistent dynamical equations based on perturbation computations and averaging. New, more accurate equations will be derived for spin axis evolution. Applications for the terrestrial planets, asteroids and the Jovian planets will be developed. An important component of the project will be the development of differential equationsfor the rotational and tidal deformations that are coupled to orbital and rotational dynamics. Rather than using a Love number formalism, which requires a spectral decomposition in time to accommodate viscoelastic behavior, the equations for the deformation of the body in time and space are recast into a system of ordinary differential equations in time. This system can then be analyzed via the same techniques of perturbation theory and averaging to develop a self consistent model for deformable bodies.The advances made through this project will significantly contribute to several problems andprojects in planetary astronomy. In particular, this project may make it possible to infer the interiorproperties of outer planet satellites from precise astrometric measurements, such as eclipseand occultation timings. In addition, the project is expected to provide theoretical basis for theanalysis of data from ongoing and planned US space missions, such as the Messenger mission toMercury and the Cassini mission to Saturn.***