Research Initiation Award: Analytic Theory of Asymmetric Rigid Bodies Subject to Arbitary Body-Fixed Torques and Forces

本项目的目的是发展轴对称刚体在任意体固定力和力矩作用下的动力学运动的一般解析理论。这个问题在过去得到了经典动态学家的一些关注，最近博德瓦特以一种受限的形式得到了关注。不幸的是，普遍的问题还没有得到解决，而且可能无法用现有的方法解决。此外，博德瓦特的解决方案可能是错误的。重点研究了欧拉运动方程、欧拉角、角动量矢量控制和平移加速度方程四个问题。其中的每一个都被进一步细分为子主题。对于第一种情况，当横向角速率不小时，注意力集中在求解析解上，而在时变体固定扭矩的情况下，注意力集中在求解析解上。欧拉角分析试图简化现有的解，并调整解以考虑时变的物体固定扭矩。角动量研究根据欧拉角的解推导出角动量的解。最后，在加速度方程的研究中，重点推导了刚体的速度和位置表达式。这项研究增强了分析动力学的一般知识库。它在航天器和火箭等旋转和推进物体的知识和控制方面有应用。

The intent of this project is to develop a general analytic theory of the dynamical motion of axisymmetric rigid bodies subject to arbitrary body fixed forces and moments. The problem has received some attention in the past by classical dynamicists and more recently, in a restricted form, by Bodewadt. Unfortunately,the general problem has not been solved and may be unsolvable by current methods. Furthermore, the Bodewadt solution may be in error. The research focuses on four topics including the Euler equations of motion, the Eulerian angles, controlling the angular momentum vector, and the translational acceleration equations. Each of these is further subdivided into sub topics. For the first, attention is directed toward finding an analytical solution when the transverse angular rates are not small, and toward the case of time varying body fixed torques. The Eulerian angles analysis attempts to simplify existing solutions, and to adjust the solutions to account for time varying body fixed torques. The angular momentum study derives solutions for the angular momentum based on solutions for the Eulerian angles. Lastly, the acceleration equations study focuses on deriving expressions for velocity and position of the rigid body. This research enhances the general knowledge base in analytical dynamics. It has applications in the knowledge and control of spinning and thrusting bodies such as spacecraft and rockets.