Mathematical Sciences: Applications of Modern Hamiltonian Mechanics to the Attitude Dynamics of Satellites

小行星9505450 建议在人造卫星姿态动力学的确定和控制中出现的实际力学问题的背景下，研究先进理论动力学的最新进展。 该项目将与计算机科学公司（CSC）合作开展。 其根本动机是，博士后助理可以促进和利用技术的双向转让，其中现代分析和数值专业知识，是在大学可用的，是在CSC现有的专业知识，即传统力学方法的广泛知识测试，并在飞行卫星出现的实际问题。 该项目将包括对具体运行卫星的个案研究以及与实际飞行数据的比较。 将被考虑的数学技术包括应用i）Arnol'd的非正则哈密顿公式来预测所谓的重力梯度和对卫星姿态动力学的其他扰动效应，ii）杆模型的现代哈密顿公式来描述天线和吊杆的动力学，辛积分和能量动量积分在高精度数值模拟中的应用。 需要研究的相关物理效应将包括：一）由于卫星尺寸有限，以及内部和外部阻尼，姿态和轨道动力学之间的耦合，二）自旋上升动力学和不稳定共振，特别是三）卫星灵活性的影响。 最终目标是提高对卫星姿态动力学的认识，这将导致可靠、高效和准确的数值模拟。

9505450 MADDOCKS It is proposed to investigate recent progress in advanced theoretical dynamics within the context of the practical mechanics problems that arise in the determination and control of the attitude dynamics of artificial satellites. The project will be carried out in collaboration with Computer Sciences Corporation (CSC). The underlying motivation is that a postdoctoral associate could facilitate and exploit a two-way transfer of technology in which the modern analytical and numerical expertise that is available in the University, is tested in the light of the expertise available at CSC, namely an extensive knowledged of traditional mechanics approaches, and of practical questions that arise in flying satellites. The project will comprise case studies of specific operational satellites and comparison with actual flight data. The mathematical techniques that will be considered include applications of i) the non- canonical Hamiltonian formulation of Arnol'd to predict so-called gravity-gradient and other perturbation effects on the attitude dynamics of satellites, ii) modern Hamiltonian formulations of rod models to describe the dynamics of antennas and booms, and iii) applications of symplectic and energy-momentum integrator in high accuracy numerical simulations. The associated physical effects to be investigated will include i) coupling between attitude and orbit dynamics due to finite satellite size, and internal and external damping, ii) spin-up dynamics and instability resonances, and especially iii) effects of flexibility of satellites. The final objective is improved understanding of the attitude dynamics of satellites that will lead to robust, efficient and accurate numerical simulations.