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

9505450马多克建议结合在确定和控制人造卫星姿态动力学方面出现的实际力学问题，研究高级理论动力学方面的最新进展。该项目将与计算机科学公司(CSC)合作实施。其基本动机是，博士后助理可以促进和利用双向技术转让，在这种技术转让中，大学现有的现代分析和数值专门知识将根据CSC现有的专门知识进行测试，即对传统力学方法和飞行卫星中出现的实际问题具有广泛的知识。该项目将包括特定业务卫星的案例研究以及与实际飞行数据的比较。将考虑的数学技术包括：i)Arnol‘d非正则哈密顿公式用于预测所谓的重力梯度和对卫星姿态动力学的其他摄动影响；ii)杆模型的现代哈密顿公式用于描述天线和吊杆的动力学；以及iii)辛和能量-动量积分器在高精度数值模拟中的应用。要研究的相关物理效应将包括：i)由于卫星尺寸有限而引起的姿态和轨道动力学之间的耦合，以及内部和外部阻尼，ii)自旋动力学和不稳定共振，特别是iii)卫星灵活性的影响。最终的目标是改善对卫星姿态动力学的理解，这将导致稳健、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.