Related papers: Oscillatory motions, parabolic orbits and collisio…
Previously, we have considered the equations of motion of the three-body problem in a Lagrange form (which means a consideration of relative motions of 3-bodies in regard to each other). Analyzing such a system of equations, we considered…
In the framework of the planar restricted three body problem we study a considerable number of resonances associated to the Kuiper Belt dynamics and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic…
The two-body problem is extensively studied in open systems and asymptotically flat spacetimes. However, there are many systems where radiation is trapped: they range from radiating charges in cavities to low-energy excitations of massive…
We consider the Newtonian planar three-body problem, defining a syzygy (velocity syzygy) as a configuration where the positions (velocities) of the three bodies become collinear. We demonstrate that if the total energy is negative, every…
Our aim is to identify and classify mean-motion resonances (MMRs) for the coplanar circular restricted three-body problem (CR3BP) for mass ratios between 0.10 and 0.50. Our methods include the maximum Lyapunov exponent, which is used as an…
The circular restricted three body problem is investigated in the context of accretion and scattering processes. In our model a large number of identical non-interacting mass-less planetesimals are considered in planar case orbiting a…
Chaplygin's equations describing the planar motion of a rigid body in an unbounded volume of an ideal fluid involved in a circular flow around the body are considered. Hamiltonian structures, new integrable cases, and partial solutions are…
The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.
Goal of the presented research is to construct simplified model of the core-halo structures in binary systems. Examples are provided by Thorne-Zytkov objects, hot Jupiters, protoplanets with large moons, red supergiants in binaries and…
Hamiltonian normal forms allow for the analytical approximation of center manifold trajectories and their invariant manifolds through the separation of the saddle and center subspaces that make up the dynamics at the collinear libration…
Periodic orbits (POs) play a central role in the circular restricted three-body problem (CRTBP). This paper introduces a method to search for POs by identifying single- and multiple-revolution fixed points in chosen Poincare maps that…
The Hannay angle has been previously studied for a celestial circular restricted three-body system by means of an adiabatic approach. In the present work, three main results are obtained. Firstly, a formal connection between perturbation…
We discuss some examples of equations of the three-body problem with the oscillating asymptotics at large momentum: (i) the fixed-center approximation, (ii) the unitarized equation in the fixed-center approximation, (iii)…
We introduce a -- somewhat holographic -- dictionary between gravitational observables for scattering processes (measured at the "boundary") and adiabatic invariants for bound orbits (in the "bulk"), to all orders in the Post-Minkowskian…
The dynamics of the four-body problem have attracted increasing attention in recent years. In this paper, we extend the basic equilateral four-body problem by introducing the effect of radiation pressure, Poynting-Robertson drag, and solar…
We introduce a restricted four body problem in a 2+2 configuration extending the classical Sitnikov problem to the Double Sitnikov problem. The secondary bodies are moving on the same perpendicular line to the planewhere the primaries…
The restricted four body problem studies the dynamics of a massless particle under the gravitational force produced by three masses (primaries) in an equilateral configuration. One primary, say m3, is considered too small compared with the…
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…
We review the orbital stability of the planar circular restricted three-body problem, in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill…
Natural orbital theory is a computationally useful approach to the few and many-body quantum problem. While natural orbitals are known and applied since many years in electronic structure applications, their potential for time-dependent…