Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A sphere moving down the surface of a static sphere and a simple phase
  diagram   A small sphere placed on the top of a big static frictionless sphere, slips
until it leaves the surface at an angle $\theta_{l}=\cos^{-1}{2/3}$. On the
other extreme, if the surface of the big sphere has coefficient of static
friction, $\mu_s\to\infty$, the small sphere starts rolling and continues to do
so until it leaves the surface at an angle $\theta_{l} =\cos^{-1}{10/17}$. In
the case where, $0\leq\mu_s<\infty$, we get a simple phase diagram. The three
phases are pure rolling, rolling with slipping and detached state. One phase
line separates pure rolling from rolling with slipping. This diagram is
obtained when stopping angles for pure rolling are plotted against static
friction coefficients $\mu_s$. Study in this article is restricted to the case
when the mobile sphere starts at the top of the static sphere with
infinitesimal kinetic energy.

27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs