Related papers: Oscillatory motions, parabolic orbits and collisio…
We study the motion of neutral test particles in the gravitational field of two charged black holes described by the extreme Reissner-Nordstr{\o}m dihole metric where the masses and charges of the black holes are chosen such that the…
Gravitational and electromagnetic interactions are Hamiltonian systems with forces between pairs of particles. We propose an alternative: Hamiltonian dynamics with triplet interactions between point particles. Our system has a potential…
The discovery of interstellar interlopers such as 1I/`Oumuamua, 2I/Borisov, and 3I/ATLAS have highlighted the necessity of understanding the dynamical pathways that eject small bodies from planetary systems into hyperbolic trajectories. In…
Using the canonical Arnowitt-Deser-Misner Hamiltonian formalism, a "first law of mechanics" is established for binary systems of point masses moving along generic stable bound (eccentric) orbits. This relationship is checked to hold within…
We present numerical simulations of the gravitational three-body problem, in which three particles lie at rest close to the vertices of an equilateral triangle. In the unperturbed problem, the three particles fall towards the center of mass…
This paper concerns the classical dynamics of three coupled rotors: equal masses moving on a circle subject to attractive cosine inter-particle potentials. It is a simpler variant of the gravitational three-body problem and also arises as…
We extract all the invariants (i.e. all the functions which do not depend on the choice of phase-space coordinates) of the dynamics of two point-masses, at the third post-Newtonian (3PN) approximation of general relativity. We start by…
We map the general relativistic two-body problem onto that of a test particle moving in an effective external metric. This effective-one-body approach defines, in a non-perturbative manner, the late dynamical evolution of a coalescing…
This paper investigates the motion of a rotating test body in the Schwarzschild space-time. After reduction, this problem reduces to an analysis of a three-degree-of-freedom. Hamiltonian system whose desired trajectories lie on the…
As shown by Johannes Kepler in 1609, in the two-body problem, the shape of the orbit, a given ellipse, and a given non-vanishing constant angular momentum determines the motion of the planet completely. Even in the three-body problem, in…
This paper investigates the motion of a small particle moving near the triangular points of the Earth-Moon system. The dynamics are modeled in the Hill restricted 4-body problem (HR4BP), which includes the effect of the Earth and Moon as in…
We prove the existence of chaotic motions in a planar restricted four body problem, establishing that the system is not integrable. The idea of the proof is to verify the hypotheses of a topological forcing theorem. The forcing theorem…
We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the Brutus N-body code to include Post-Newtonian pairwise terms…
In the present paper, using the first-order approximation of the $n$-body Lagrangian (derived on the basis of the post-Newtonian gravitational theory of Einstein, Infeld, and Hoffman), we explicitly write down the equations of motion for…
We consider the problem of three body motion for a relativistic one-dimensional self-gravitating system. After describing the canonical decomposition of the action, we find an exact expression for the 3-body Hamiltonian, implicitly…
In the $n$-body problem, when bodies tend to a total collision, then its normalized shape curve converges to the set of normalized central configurations, which has $SO(3)$ symmetry in the planar case. This leaves a possibility that the…
We discuss the motion of electrically and magnetically charged particles in the electromagnetic swirling universe. We show that the equations of motion can be decoupled in the Hamilton-Jacobi formalism, revealing the existence of a fourth…
We show that the planar circular restricted three body problem is of restricted contact type for all energies below the first critical value (action of the first Lagrange point) and for energies slightly above it. This opens up the…
We study the Robe's restricted three-body problem. Such a motion was firstly studied by A. G. Robe in \cite{Robe}, which is used to model small oscillations of the earth's inner core taking into account the moon attraction. For the linear…
This paper investigates the secular motion of a massless asteroid within the framework of the double-averaged elliptic restricted three-body problem. By employing Poincar\'e variables, we analyze the stability properties of asteroid orbits…