发表机构
Mohamed bin Zayed University of Artificial Intelligence; University of Delaware; The George Washington University（穆罕默德·本·扎耶德人工智能大学; 特拉华大学; 乔治华盛顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了保留末端姿态和角速度积分的有限维李群概要，证明其精确复合且满射，并用欠驱动卫星示例关联几何相位。
AI 中文摘要
我们构造了基于旋转路径的有限维李群概要，这些概要保留了精确的末端姿态和选定的迭代角速度积分。这些概要称为旋转轨迹概要，在路径拼接下精确复合。基于Magnus和Chen的经典工作，我们在每个有限阶上建立了保留末端的体、空间和混合概要群，并给出了求值Magnus层级的一致矩阵实现。我们从三阶起将该层级与完整的Chen签名区分开来，并证明精确末端独立于体、空间或组合角速度签名的任何有限截断：概要映射在每个有限阶上都是满射的。一个欠驱动卫星示例将保留的坐标与航天器姿态动力学中的几何相位联系起来。
英文摘要
We construct finite-dimensional Lie-group summaries of based rotational paths that retain the exact terminal attitude and selected iterated angular-velocity integrals. These summaries, called rotational trajectory synopses, compose exactly under path concatenation. Building on the classical works of Magnus and Chen, we establish endpoint-retaining body, spatial, and hybrid synopsis groups at every finite order and give a uniform matrix realization for the evaluated Magnus hierarchy. We distinguish this hierarchy from the full Chen signature from order three onward and prove \chg{that the exact endpoint is independent of every finite truncation of the body, spatial, or combined angular-velocity signature: the synopsis maps are surjective at every finite order}. An underactuated satellite example connects the retained coordinates to geometric phase in spacecraft attitude dynamics.
