Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connecting planar linear chains in the spatial $N$-body problem   The family of planar linear chains are found as collision-free action
minimizers of the spatial $N$-body problem with equal masses under $D_N$ or
$D_N \times \zz_2$-symmetry constraint and different types of topological
constraints. This generalizes a previous result by the author in \cite{Y15c}
for the planar $N$-body problem. In particular, the monotone constraints
required in \cite{Y15c} are proven to be unnecessary, as it will be implied by
the action minimization property.
  For each type of topological constraints, by considering the corresponding
action minimization problem in a coordinate frame rotating around the vertical
axis at a constant angular velocity $\om$, we find an entire family of simple
choreographies (seen in the rotating frame), as $\om$ changes from $0$ to $N$.
Such a family starts from one planar linear chain and ends at another (seen in
the original non-rotating frame). The action minimizer is collision-free, when
$\om=0$ or $N$, but may contain collision for $0 < \om < N$. However all
possible collisions must be binary and each collision solution is $C^0$
block-regularizable.
  Moreover for certain types of topological constraints, based on results from
\cite{BT04} and \cite{CF09}, we show that when $\om$ belongs to some
sub-intervals of $[0, N]$, the corresponding minimizer must be a rotating
regular $N$-gon contained in the horizontal plane. As a result, this
generalizes Marchal's $P_{12}$ family of the three body problem to arbitrary $N
\ge 3$.

29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics