The Bountiful Intersection of Differential Geometry, Mechanics, and Control Theory
The Bountiful Intersection of Differential Geometry, Mechanics, and Control Theory
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微分几何、力学和控制理论的丰富交叉
DOI：
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发表时间：
2018
期刊：
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通讯作者：
A. D. Lewis
中科院分区：
文献类型：
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作者：
A. D. Lewis
力学和控制理论领域与微分几何这一广泛的数学学科有着丰富而富有成效的相互作用历史。本文概述了黎曼微分几何和仿射微分几何以及矢量分布几何中这些类型的相互作用。它强调微分几何方法在解决不使用这些方法难以解决的问题方面发挥关键作用的领域。它还强调方法的简洁和优雅的呈现，而不是详细和具体的呈现。结果概述，虽然形成一个连贯和优雅的工作主体，在范围上是有限的。审查结束时讨论了为什么这种方法是有限的，并简要审议了必须解决的问题，然后才能扩展这里提出的类型的结果。
The areas of mechanics and control theory have a rich and productive history of interaction with the broad mathematical subject of differential geometry. This article provides an overview of these sorts of interplay in the areas of Riemannian and affine differential geometry and the geometry of vector distributions. It emphasizes areas where differential geometric methods have played a crucial role in solving problems whose solutions are difficult to achieve without access to these methods. It also emphasizes a concise and elegant presentation of the approach, rather than a detailed and concrete presentation. The results overviewed, while forming a coherent and elegant body of work, are limited in scope. The review closes with a discussion of why the approach is limited and a brief consideration of issues that must be resolved before the results of the type presented here can be extended.