Related papers: Numerical integration of a relativistic two-body p…
The Newtonian n-Body Problem is modified assuming positive inertial masses but different sign for the interacting force which is assumed with the possibility of two different signs for the gravitational masses, according to the prescription…
A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid…
The hypothesis of the scale invariance of the macroscopic empty space, which intervenes through the cosmological constant, has led to new cosmological models. They show an accelerated cosmic expansion and satisfy several major cosmological…
We present the Euler--Langrage equations for a many-body system of coupled planar pendulums. Hence, imposing initial condition data, the equations of motion are linearized and later developed in an idealized model for the pseudo-periodicity…
One of the outstanding problems of classical celestial mechanics was the restricted 3-body prob- lem, in which a planetoid of small mass is subject to the Newtonian attraction of two celestial bodies of large mass, as it occurs, for…
I give a short non-technical review of the results obtained in recent work on "Doubly Special Relativity", the relativistic theories in which the rotation/boost transformations between inertial observers are characterized by two…
Dixon's multipoles for a system of N relativistic positive-energy scalar particles are evaluated in the rest-frame instant form of dynamics. The Wigner hyperplanes (intrinsic rest frame of the isolated system) turn out to be the natural…
It is shown that the phenomenon of irreversibility in many-body and few-body systems can be explained and described within the framework of the concept of direct (not instantaneous) interaction of particles without using probabilistic…
We use variational minimizing methods to study spatial restricted N+1-body problems with a zero mass moving on the vertical axis of the moving plane for N equal masses. We prove that the minimizer of the Lagrangian action on the anti-T/2 or…
We calculate the motion of binary mass systems in gravity up to the fourth post--Newtonian order. We use momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates by applying…
We perform a statistical analysis of the binary black hole problem in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal…
The paper deals with the study of a satellite attracted by n primary bodies, which form a relative equilibrium. We use orthogonal degree to prove global bifurcation of planar and spatial periodic solutions from the equilibria of the…
This paper investigates the coplanar and circular three-body problem in the parametrized post-Newtonian (PPN) formalism, for which we focus on a class of fully conservative theories characterized by the Eddington-Robertson parameters…
The hypothesis that the Lorentz transformations may be modified at Planck scale energies is further explored. We present a general formalism for theories which preserve the relativity of inertial frames with a non-linear action of the…
We develop a formalism for General Relativistic N-body simulations in the weak field regime, suitable for cosmological applications. The problem is kept tractable by retaining the metric perturbations to first order, the first derivatives…
The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent…
A constant homogeneous magnetic field is applied to a composite system made of two scalar particles with opposite charges. Motion is described by a pair of coupled Klein-Gordon equations that are written in closed form with help of a…
Based on the kinetic energy theorem, as one of the fundamental theorems from the classical mechanics, throughout the first part of the article an attempt has been made to derive the mathematical model of a material point motion in the…
We present a framework for general relativistic N-body simulations in the regime of weak gravitational fields. In this approach, Einstein's equations are expanded in terms of metric perturbations about a Friedmann-Lema\^itre background,…
The paper presents equations determining the particle spin evolution in the post-Newtonian approximation in the problem of motion of two mass and spin possessing particles. The equations are derived with the Einstein-Infeld-Hoffmann method…