Scientifique, 92195 Meudon CEDEX, France
- |
    Observatoire de la Côte d’Azur, Département CERGA, Avenue N. Copernic,\
    06130 Grasse, France
author:
- Thibault Damour
- 'David Vokrouhlický[@byline1]'
date: 'March 21, 1995'
title: |
    Conservation laws for systems of extended bodies\
    in the first post-Newtonian approximation
---

Introduction
============

Recently, Damour, Soffel and Xu [@dam1; @dam2; @dam3; @dam4] (DSX) developed a new, exhaustive approach to the first post-Newtonian dynamics of a system of $N$ extended bodies. This theory is based on the complementary use of some local coordinate systems (attached to each body) and of a global coordinate system used to describe the orbital motion of the $N$ bodies. Detailed analyses of the laws of global translational motion [@dam2] and local rotational motion [@dam3] of the bodies have been given.

In this paper, we address the question of the global conservation laws of an $N$-body system, and their link to the quantities introduced in the DSX framework. We use the word conservation laws to mean the first integrals related to the total four momentum and angular momentum of the system, and to the center-of-mass theorem. The existence, on the first post-Newtonian level, of these ten integrals is guaranteed by the general 