Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metric cones, N-body collisions, and Marchal's lemma   Marchal's lemma is the basic tool for eliminating collisions when using the
direct method of the calculus of variations to establish existence of
"designer" solutions to the classical N-body problem. Our goal here is to
understand why Marchal's lemma holds, by taking a metric geometry perspective
and employing the Jacobi-Maupertuis [JM] metric reformulation of mechanics.
Using analysis inspired by the conical metric nature of the standard Kepler
problem at zero-energy, we are able to manufacture potentials, or
"counterexamples", for which Marchal's lemma fails. These counterexamples
overlap significantly with results obtained by Barutello et al. A novel feature
in our proof for the counterexample is the use of piecewise constant
potentials, and the resulting piecewise constant metrics.

22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th