Related papers: Three-body periodic collisionless equal-mass free-…
A family of periodic orbits is proven to exist in the spatial lunar problem that are continuations of a family of consecutive collision orbits, perpendicular to the primary orbit plane. This family emanates from all but two energy values.…
The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more…
Six contact binaries lacking a period analysis have been chosen to search for the presence of a third body. The O-C diagrams of these binaries were analyzed with the least-squares method by using all available times of minima. Ten new…
We investigate the multiple bifurcations in periodic orbit families in the potential field of a highly irregular-shaped celestial body. Topological cases of periodic orbits and four kinds of basic bifurcations in periodic orbit families are…
We consider the 3-body problem in 3-dimensional spaces of nonzero constant Gaussian curvature and study the relationship between the masses of the Lagrangian relative equilibria, which are orbits that form a rigidly rotating equilateral…
Comet-type periodic orbits of the circular restricted three-body problem (CR3BP) are periodic solutions that are generated from very large retrograde and direct circular Keplerian motions around the common center of mass of the primaries.…
In (Fusco et. al., 2011) several periodic orbits of the Newtonian N-body problem have been found as minimizers of the Lagrangian action in suitable sets of T-periodic loops, for a given T>0. Each of them share the symmetry of one Platonic…
In this paper, we study the planar circular restricted three-body problem for energy levels slightly above the first critical value. We first observe that the energy hypersurfaces in the Birkhoff regularization corresponding to these energy…
In the current study, the existence of periodic orbits around a fixed homogeneous cube is investigated, and the results have powerful implications for examining periodic orbits around non-spherical celestial bodies. In the two different…
Space missions have discovered a large number of exoplanets evolving in (or close to) mean-motion resonances (MMRs) and resonant chains. Often, the published data exhibit very high uncertainties due to the observational limitations that…
We consider the 3-body problem in relativistic lineal gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly-bound orbits of higher frequency compared to…
In this work, we perform a first study of basic invariant sets of the spatial Hill's four-body problem, where we have used both analytical and numerical approaches. This system depends on a mass parameter mu in such a way that the classical…
A periodic orbit on a frictionless billiard table is a piecewise linear path of a billiard ball that begins and ends at the same point with the same angle of incidence. The period of a primitive periodic orbit is the number of times the…
We consider a one-dimensional system of four inelastic hard spheres, colliding with a fixed restitution coefficient $r$, and we study the inelastic collapse phenomenon for such a particle system. We study a periodic, asymmetric collision…
In this article we continue the study of the collapse of three inelastic particles in dimension $d \geq 2$, complementing the results we obtained in its companion paper. We focus on the particular case of the nearly-linear inelastic…
Some properties of the periodic solution of the three-body problem where three particles of equal mass follow the same trajectory are discussed. This trajectory has the shape of a figure-8. The three particles have a constant separation in…
We present three improved and five new mutual orbits of transneptunian binary systems (58534) Logos-Zoe, (66652) Borasisi-Pabu, (88611) Teharonhiawako-Sawiskera, (123509) 2000 WK183, (149780) Altjira, 2001 QY297, 2003 QW111, and 2003 QY90…
We review some recent progress on the research of the periodic orbits of the N-body problem,and propose a numerical scheme to determine the spatial doubly-symmetric periodic orbits (SDSPs for short). Both comet- and lunar-type SDSPs in the…
Plane Couette flow at Re=1200 (based on the channel half-height and half the velocity difference between the top and bottom plates) is investigated with a spatial domain designed to retain only two spanwise integral length scales. In this…
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…