Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An intrinsic formulation of the rolling manifolds problem   We present an intrinsic formulation of the kinematic problem of two
$n-$dimensional manifolds rolling one on another without twisting or slipping.
We determine the configuration space of the system, which is an
$\frac{n(n+3)}2-$dimensional manifold. The conditions of no-twisting and
no-slipping are decoded by means of a distribution of rank $n$. We compare the
intrinsic point of view versus the extrinsic one. We also show that the
kinematic system of rolling the $n$-dimensional sphere over $\mathbb R^n$ is
controllable. In contrast with this, we show that in the case of $SE(3)$
rolling over $\mathfrak{se}(3)$ the system is not controllable, since the
configuration space of dimension 27 is foliated by submanifolds of dimension
12.

22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th