Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Post-1-Newtonian equations of motion for systems of arbitrarily
  structured bodies   We give a surface integral derivation of post-1-Newtonian translational
equations of motion for a system of arbitrarily structured bodies, including
the coupling to all the bodies' mass and current multipole moments. The
derivation requires only that the post-1-Newtonian vacuum field equations are
satisfied in weak-field regions between the bodies; the bodies' internal
gravity can be arbitrarily strong. The derivation extends previous results of
Damour, Soffel and Xu (DSX) for weakly self-gravitating bodies for which the
post-1-Newtonian field equations are satisfied everywhere. The derivation
consists of a number of steps: (i) The definition of each body's current and
mass multipole moments and center-of-mass worldline in terms of the behavior of
the metric in a weak-field region surrounding the body. (ii) The definition for
each body of a set of gravitoelectric and gravitomagnetic tidal moments, again
in terms of the behavior of the metric in a weak-field region surrounding the
body. For the special case of weakly self-gravitating bodies, our definitions
of these multipole and tidal moments agree with definitions given previously by
DSX. (iii) The derivation of a formula, for any given body, of the second time
derivative of its mass dipole moment in terms of its other multipole and tidal
moments and their time derivatives. This formula was obtained previously by DSX
for weakly self-gravitating bodies. (iv) A derivation of the relation between
the tidal moments acting on each body and the multipole moments and
center-of-mass worldlines of all the other bodies. A formalism to compute this
relation was developed by DSX; we simplify their formalism and compute the
relation explicitly. (v) The deduction from the previous steps of the explicit
translational equations of motion, whose form has not been previously derived.

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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: math
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: eess