Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new set of variables in the three-body problem   We propose a set of variables of the general three-body problem both for
two-dimensional and three-dimensional cases. Variables are
$(\lambda,\theta,\Lambda, \Theta,k,\omega)$ or equivalently
$(\lambda,\theta,L,\dot{I},k,\omega)$ for the two-dimensional problem, and
$(\lambda,\theta,L,\dot{I},k,\omega,\phi,\psi)$ for the three-dimensional
problem. Here $(\lambda,\theta)$ and $(\Lambda,\Theta)$ specifies the positions
in the shape spheres in the configuration and momentum spaces, $k$ is the
virial ratio, $L$ is the total angular momentum, $\dot{I}$ is the time
derivative of the moment of inertia, and $\omega,\phi$, and $\psi$ are the
Euler angles to bring the momentum triangle from the nominal position to a
given position. This set of variables defines a {\it shape space} of the
three-body problem. This is also used as an initial condition space. The
initial condition of the so-called free-fall three-body problem is
$(\lambda,\theta,k=0,L=0,\dot{I}=0,\omega=0)$. We show that the hyper-surface
$\dot{I} = 0$ is a global surface of section.

29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
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
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio