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Cited by 275

The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.

General-relativistic celestial mechanics II. Translational equations of motion

Damour, Thibault, Soffel, Michael, Xu, Chongming·1992·Physical Review D
DOI 10.1103/physrevd.45.1017
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Abstract

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 ${(\frac{v}{c})}^{4}$ 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 the post-Newtonian multipole moments of the other bodies.

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Metadata

Authors
Damour, T., Soffel, M., & Xu, C.
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
1992-02-15
Volume
45
Issue
4
Pages
1017-1044
ISSN
0556-2821 (ISSN-L)
DOI
10.1103/physrevd.45.1017
OpenAlex
W1978510652
Cited by
275
References
25
FWCI
9.18
Type
journal article
Language
en
Open access
closed

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CoChat. (2026). Citation check: General-relativistic celestial mechanics II. Translational equations of motion. https://app.cochat.ai/papers/10.1103/physrevd.45.1017
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Damour, T., Soffel, M., & Xu, C. (1992). General-relativistic celestial mechanics II. Translational equations of motion. Physical Review D. https://doi.org/10.1103/physrevd.45.1017

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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

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