滚动问题：概述和挑战
The rolling problem: overview and challenges
摘要：
在本文中，我们给出了一个历史帐户-从古典到现代的结果-滚动两个黎曼流形的问题，一个在另一个，与限制，他们不能瞬间滑动或自旋一个相对于其他。在路上，我们展示了这个问题如何受益于发展的内在黎曼几何，从几何控制理论和子黎曼几何。我们还提到了其他领域-如机器人和插值理论-如何采用滚动模型。
英文摘要：
In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with respect to the other. On the way we show how this problem has profited from the development of intrinsic Riemannian geometry, from geometric control theory and sub-Riemannian geometry. We also mention how other areas -such as robotics and interpolation theory- have employed the rolling model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
