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On the bases of the Papapetrou equations with various supplementary conditions and other approaches a comparative analysis of the equations of motion of rotating bodies in general relativity is made. The motion of a body with vertical spin…

General Relativity and Quantum Cosmology · Physics 2007-05-23 O. B. Karpov

Reliable predictions of general relativity theory are extracted using approximation methods. Among these, the powerful post-Newtonian approximation provides us with our best insights into the problems of motion and gravitational radiation…

General Relativity and Quantum Cosmology · Physics 2010-03-12 Luc Blanchet

We describe a post-Minkowskii approximation of general relativity as a power series expansion in G, Newton's gravitational constant. Material sources are hidden behind boundaries, and only the vacuum Einstein equations are considered. An…

General Relativity and Quantum Cosmology · Physics 2010-05-12 Steven Detweiler , Lee H. Brown

We try to lay down the foundations of a Newtonian theory where inertia and gravitational fields appear in a unified way aiming to reach a better understanding of the general relativistic theory. We also formulate a kind of equivalence…

General Relativity and Quantum Cosmology · Physics 2015-06-11 Xavier Jaén , Alfred Molina

Relativistic modelling of rotational motion of extended bodies represents one of the most complicated problems of Applied Relativity. The relativistic reference systems of IAU (2000) give a suitable theoretical framework for such a…

Earth and Planetary Astrophysics · Physics 2015-05-14 S. A. Klioner , E. Gerlach , M. H. Soffel

We discuss the dynamics of extended test bodies for a large class of scalar-tensor theories of gravitation. A covariant multipolar Mathisson-Papapetrou-Dixon type of approach is used to derive the equations of motion in a systematic way for…

General Relativity and Quantum Cosmology · Physics 2014-11-27 Yuri N. Obukhov , Dirk Puetzfeld

The worldlines (in harmonic coordinates) of two gravitationally interacting massive bodies at the second post-Minkowskian order are described in explicit form. Both the conservative case and the radiation-reacted case are considered. We use…

General Relativity and Quantum Cosmology · Physics 2024-09-02 Donato Bini , Thibault Damour , Andrea Geralico

We describe "small bodies" in a non-metric gravity theory previously studied by this author. The main dynamical field of the theory is a certain triple of two-forms rather than the metric, with only the spacetime conformal structure, not…

General Relativity and Quantum Cosmology · Physics 2009-11-13 Kirill Krasnov

Although rare, collisions of two or more bodies in the N-body problem are apparent obstacles at which Newton's Law of Gravity ceases to make sense. Without understanding the nature of collisions, a complete understanding of the N-body…

Dynamical Systems · Mathematics 2012-09-03 Lenanrd F. Bakker

The present paper derives the post-Newtonian Lagrangian of translational motion of N arbitrary-structured bodies with all mass and spin multipoles in a scalar-tensor theory of gravity. The multipoles depend on time and evolve in accordance…

General Relativity and Quantum Cosmology · Physics 2020-07-21 Sergei M. Kopeikin

The dynamics of the Restricted 3 Body Problem in the Post Newtonian context have been, and continue to be, studied extensively and a number of characteristics such as ejections of bodies from the system, precession of orbits, chaotic…

General Relativity and Quantum Cosmology · Physics 2023-11-07 Patric de Gentile-Williams

General properties of the three-body problem in a model of modified dynamics are investigated. It is shown that the three-body problem in this model shares some characters with the similar problem in Newtonian dynamics. Moreover, the planar…

Astrophysics of Galaxies · Physics 2023-04-14 Hossein Shenavar

The two full body problem concerns the dynamics of two spatially extended rigid bodies (e.g. rocky asteroids) subject to mutual gravitational interaction. In this note we deduce the Euler-Poincare and Hamiltonian equations of motion using…

Classical Physics · Physics 2019-01-04 Tanya Schmah , Cristina Stoica

We investigate the gravitational field of an extended spherically symmetric body within the framework of Extended Relativity (ER), a Lorentz-covariant formulation of relativistic gravity on a Minkowski background. Using a relativistic…

General Relativity and Quantum Cosmology · Physics 2026-05-22 Y. Friedman , S. I. Klimovsky

In the cosmos, any two bodies share a gravitational attraction. When in proximity to one another in empty space, their motions can be modeled by Newtonian gravity. Newton found their orbits when the two bodies are infinitely small, the…

Classical Analysis and ODEs · Mathematics 2023-07-06 Jodin Morey

We summarize a recent work done on the title's subject. First, we present the asymptotic scheme of post-Newtonian (PN) approximation for general relativity in the harmonic gauge. Then, we discuss the definition of the mass centers and the…

General Relativity and Quantum Cosmology · Physics 2007-11-19 Mayeul Arminjon

We formulate new general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids. They have been used to re-derive, in the first post-Newtonian approximation, the well known geometric dragging of frames. We…

General Relativity and Quantum Cosmology · Physics 2015-06-24 Patryk Mach , Edward Malec

We derive the equations of motion for binary systems of compact bodies in the post-Newtonian (PN) approximation to general relativity. Results are given through 2PN order (order (v/c)^4 beyond Newtonian theory), and for gravitational…

General Relativity and Quantum Cosmology · Physics 2009-11-07 Michael E. Pati , Clifford M. Will

The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the…

General Relativity and Quantum Cosmology · Physics 2019-03-26 Amar Maheshwari , Emil Nissimov , Ivan Todorov

A novel approach to the Effective One-Body description of gravitationally interacting two-body systems is introduced. This approach is based on the post-Minkowskian approximation scheme (perturbation theory in G, without assuming small…

General Relativity and Quantum Cosmology · Physics 2016-11-15 Thibault Damour