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Related papers: Symbolic Dynamics of the Collinear Three-Body Prob…

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The goal of this paper is to obtain an approximate solution of the restricted three-body problem in the case of small perturbations in the vicinity of, but not in exact resonance. In this paper, we study the restricted threebody problem…

Earth and Planetary Astrophysics · Physics 2025-11-11 Alexey Rosaev , Eva Plavalova , Pavel Nesterov

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…

Solar and Stellar Astrophysics · Physics 2016-09-02 A. Odrzywolek

We consider the elliptic three body problem as a perturbation of the circular problem. We show that for sufficiently small eccentricities of the elliptic problem, and for energies sufficiently close to the energy of the libration point L2,…

Dynamical Systems · Mathematics 2015-03-13 Maciej J. Capinski , Piotr Zgliczynski

A unified analytical solution is presented for constructing the phase space near collinear libration points in the Circular Restricted Three-body Problem (CRTBP), encompassing Lissajous orbits and quasihalo orbits, their invariant…

Mathematical Physics · Physics 2024-03-28 Mingpei Lin , Tong Luo , Hayato Chiba

We study a class of piecewise linear solutions to the inviscid Burgers equation driven by a linear forcing term. Inspired by the analogy with peakons, we think of these solutions as being made up of solitons situated at the breakpoints. We…

Exactly Solvable and Integrable Systems · Physics 2009-03-18 Hans Lundmark , Jacek Szmigielski

(abbreviated) We use a semi-numerical approach to study the secular behavior of a system composed of a central star and two massive planets in eccentric co-planar orbits. We show that the secular dynamics of this system can be described…

Astrophysics · Physics 2009-11-10 T. A. Michtchenko , R. Malhotra

Continuing work initiated in earlier publications [Yamada, Asada, Phys. Rev. D 82, 104019 (2010), 83, 024040 (2011)], we investigate the post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem. For…

General Relativity and Quantum Cosmology · Physics 2011-05-05 Takumi Ichita , Kei Yamada , Hideki Asada

The principal angles between binary collision subspaces in an $N$-billiard system in $d$-dimensional Euclidean space are computed. These angles are computed for equal masses and arbitrary masses. We then provide a bound on the number of…

Dynamical Systems · Mathematics 2020-11-24 Sean Gasiorek

The configuration space of the planar three-body problem when collisions are excluded has a rich topology which supports a large set of free homotopy classes. Most classes survive modding out by rotations. Those that survive are called the…

Dynamical Systems · Mathematics 2014-12-09 Richard Moeckel , Richard Montgomery

The case of the planar circular restricted three-body problem where one of the two primaries has a stronger gravitational field with respect to the classical Newtonian field is investigated. We consider the case where two primaries have the…

Chaotic Dynamics · Physics 2017-09-28 Euaggelos E. Zotos

The class of solvable many-body problems "of goldfish type" is extended by including (the additional presence of) three-body forces. The solvable $N$-body problems thereby identified are characterized by Newtonian equations of motion…

Exactly Solvable and Integrable Systems · Physics 2013-10-10 Oksana Bihun , Francesco Calogero

We give a non-iterative solution to a particular case of the four-point three-views pose problem when three camera centers are collinear. Using the well-known Cayley representation of orthogonal matrices, we derive from the epipolar…

Computer Vision and Pattern Recognition · Computer Science 2011-09-15 Evgeniy Martyushev

In this paper, for the spatial Newtonian $2n$-body problem with equal masses, by proving the minimizers of the action functional under certain symmetric, topological and monotone constraints are collision-free, we found a family of spatial…

Dynamical Systems · Mathematics 2018-01-15 Guowei Yu

Various astrophysical processes are known, where the fly-by of a massive object affects matter initially supported against gravity by rotation. Examples are perturbations of galaxies, protoplanetary discs or planetary systems. We…

Earth and Planetary Astrophysics · Physics 2017-11-06 Andreas Breslau , Kirsten Vincke , Susanne Pfalzner

To explain both the dynamics of a globular cluster and its production of gravitational waves from coalescing binary black holes, it is necessary to understand its population of dynamically-formed (or, `three-body') binaries. We provide a…

Astrophysics of Galaxies · Physics 2023-12-06 Daniel Marín Pina , Mark Gieles

We perform an analytical study of the bifurcation of the halo orbits around the collinear points $L_1$, $L_2$, $L_3$ for the circular, spatial, restricted three--body problem. Following a standard procedure, we reduce to the center manifold…

Mathematical Physics · Physics 2016-01-20 Marta Ceccaroni , Alessandra Celletti , Giuseppe Pucacco

We consider the Earth-Moon planar circular restricted three body problem and present a proof of the existence orbits, which approach arbitrarily close to one of the primary masses, and at the same time after each approach they move away…

Dynamical Systems · Mathematics 2024-01-24 Maciej J. Capiński , Aleksander Pasiut

This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…

Analysis of PDEs · Mathematics 2020-05-21 Martin Fencl , Julián López-Gómez

We investigate the motion of a massless body interacting with the Maxwell relative equilibrium, which consists of n bodies of equal mass at the vertices of a regular polygon that rotates around a central mass. The massless body has three…

Dynamical Systems · Mathematics 2018-01-11 Renato Calleja , Eusebius Doedel , Carlos García-Azpeitia

This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…

Classical Analysis and ODEs · Mathematics 2025-06-11 Shalmali Bandyopadhyay , Svetlin G. Georgiev