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Scientific paper
Feb 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phrvd..45.1017d&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 45, Issue 4, 15 February 1992, pp.1017-1044
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103
Celestial Mechanics, Exact Solutions
Scientific paper
The translational laws of motion for gravitationally interacting systems of N arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first post-Newtonian approximation of general relativity. The derivation uses our recently introduced multi-reference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass frame of each body, relativistic inertial effects combine with post-Newtonian self- and externally generated gravitational forces to produce a global equilibrium (relativistic generalization of d'Alembert's principle). Within the first post-Newtonian approximation [i.e., neglecting terms of order (v/c)4 in the equations of motion], our work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies. We first obtain the laws of motion of each body as an infinite series exhibiting the coupling of all the (Blanchet-Damour) post-Newtonian multipole moments of this body to the post-Newtonian tidal moments (recently defined by us) felt by this body. We then give the explicit expression of these tidal moments in terms of post-Newtonian multipole moments of the other bodies.
Damour Thibault
Soffel Michael
Xu Chong-ming
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