论文标题
$ 2 $ -DIM滚动的可控性结果。违反$ 3 $ -DIM。里曼尼亚人的歧管
Controllability results for the rolling of $2$-dim. against $3$-dim. Riemannian Manifolds
论文作者
论文摘要
在本文中，我们考虑了两个尺寸的$（m，g）$（m，g）$（m，g）$（m，g）$（m，g）$（m，g）$（\ hat {m}，\ hat {g}）$ 2 $ 2 $和$ 3 $的滚动（或开发），并具有无跨度和无刺的约束。目前的工作是\ cite {mortadakokkonenchitour}的延续，该作品建模了两种riemannian连接的歧管的滚动的一般设置，这些歧管与纤维上的空间$ q $上的无漂流控制仿期系统相关联，重点是理解滚动孔的局部结构，即$ quess $。在本文中，状态空间$ q $具有八个尺寸，我们表明非开放滚动轨道的可能尺寸属于集合$ \ {2,5,6,7 \} $。我们描述了尺寸$ 2 $的轨道的结构，尺寸$ 5 $的滚动轨道的本地结构和某些尺寸$ 7 $。
In this article, we consider the rolling (or development) of two Riemannian connected manifolds $(M,g)$ and $(\hat{M},\hat{g})$ of dimensions $2$ and $3$ respectively, with the constraints of no-spinning and no-slipping. The present work is a continuation of \cite{MortadaKokkonenChitour}, which modelled the general setting of the rolling of two Riemannian connected manifolds with different dimensions as a driftless control affine system on a fibered space $Q$, with an emphasis on understanding the local structure of the rolling orbits, i.e., the reachable sets in $Q$. In this paper, the state space $Q$ has dimension eight and we show that the possible dimensions of non open rolling orbits belong to the set $\{2,5,6,7\}$. We describe the structures of orbits of dimension $2$, the possible local structures of rolling orbits of dimension $5$ and some of dimension $7$.
