Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Third post-Newtonian dynamics of compact binaries: Equations of motion
  in the center-of-mass frame   The equations of motion of compact binary systems and their associated
Lagrangian formulation have been derived in previous works at the third
post-Newtonian (3PN) approximation of general relativity in harmonic
coordinates. In the present work we investigate the binary's relative dynamics
in the center-of-mass frame (center of mass located at the origin of the
coordinates). We obtain the 3PN-accurate expressions of the center-of-mass
positions and equations of the relative binary motion. We show that the
equations derive from a Lagrangian (neglecting the radiation reaction), from
which we deduce the conserved center-of-mass energy and angular momentum at the
3PN order. The harmonic-coordinates center-of-mass Lagrangian is equivalent,
{\it via} a contact transformation of the particles' variables, to the
center-of-mass Hamiltonian in ADM coordinates that is known from the
post-Newtonian ADM-Hamiltonian formalism. As an application we investigate the
dynamical stability of circular binary orbits at the 3PN order.

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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: chem-ph