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Related papers: On the spatial collinear restricted four-body prob…

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We apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four body problem with masses 1, m, m, 1, and also in a…

Dynamical Systems · Mathematics 2015-05-13 Lennard F. Bakker , Tiancheng Ouyang , Skyler Simmons , Duokui Yan , Gareth E. Roberts

We have examined the stability of triangular equilibrium points in Robes's generalised restricted three body problem. The problem is generalised in the sense that more massive primary has been taken as an oblate spheroid. We have found the…

Dynamical Systems · Mathematics 2007-05-23 K. T. Singh , B. S. Kushvah , B. Ishwar

This paper considers two point boundary value problems for conservative systems defined in multiple coordinate systems, and develops a flexible a-posteriori framework for computer assisted existence proofs. Our framework is applied to the…

Dynamical Systems · Mathematics 2023-03-23 Maciej J. Capinski , Shane Kepley , Jason D. Mireles James

The equilibrium points and their linear stability has been discussed in the generalized photogravitational Chermnykh's problem. The bigger primary is being considered as a source of radiation and small primary as an oblate spheroid. The…

Dynamical Systems · Mathematics 2009-02-08 Badam Singh Kushvah

In this paper we consider the circular restricted three body problem which models the motion of a masless body under the influence of the Newtionan gravitational force caused by two other bodies, the primaries, which move along cicular…

Dynamical Systems · Mathematics 2012-10-08 Marcel Guardia , Pau Martin , Tere M. Seara

The present paper deals with the periodic orbits generated by Lagrangian solutions of the restricted three-body problem when both the primaries are oblate bodies. We have illustrated the periodic orbits for different values of $\mu,…

Chaotic Dynamics · Physics 2020-05-25 Amit Mittal , Md Sanam Suraj , Rajiv Aggarwal

We consider the special case of the restricted circular three-body problem, when the two primaries are of equal mass, while the third body of negligible mass performs oscillations along a straight line perpendicular to the plane of the…

Earth and Planetary Astrophysics · Physics 2011-02-17 Vladislav Sidorenko

In hierarchical triple systems, the inner binary is slowly perturbed by a distant companion, giving rise to large-scale oscillations in eccentricity and inclination, known as von-Zeipel-Lidov-Kozai (ZLK) oscillations. Stable systems with a…

Earth and Planetary Astrophysics · Physics 2024-12-19 Evgeni Grishin

The rectilinear elliptic restricted Three Body Problem (TBP) is the limiting case of the elliptic restricted TBP when the motion of the primaries is described by a Keplerian ellipse with eccentricity $e'=1$, but the collision of the…

Earth and Planetary Astrophysics · Physics 2018-01-10 George Voyatzis , Kleomenis Tsiganis , Michalis Gaitanas

Solutions to the collinear three-body problem which do not end in triple collision pass through an infinite number of binary collisions. Given three masses, we show that four geometric quantities generate a finite description of itineraries…

Dynamical Systems · Mathematics 2007-05-23 Samuel R. Kaplan

This paper explores the dynamic properties of the planar system of an ellipsoidal satellite in an equatorial orbit about an oblate primary. In particular, we investigate the conditions for which the satellite is bound in librational motion…

Earth and Planetary Astrophysics · Physics 2015-06-05 Jay W. McMahon , Daniel J. Scheeres

The case of the planar circular restricted three-body problem where one of the two primaries is an oblate spheroid is investigated. We conduct a thorough numerical analysis on the phase space mixing by classifying initial conditions of…

Space Physics · Physics 2017-09-28 Euaggelos E. Zotos

We study orbits near collision in a non-autonomous restricted planar four-body problem. This restricted problem consists of a massless particle moving under the gravitational influence due to three bodies following the figure-eight…

Dynamical Systems · Mathematics 2024-04-03 Abimael Bengochea , Jaime Burgos-García , Ernesto Pérez-Chavela

We consider the planar restricted $N$-body problem where the $N-1$ primaries are assumed to be in a central configuration whereas the infinitesimal particle escapes to infinity in a parabolic orbit. We prove the existence of transversal…

Dynamical Systems · Mathematics 2019-05-14 M. Alvarez-Ramírez , A. García , J. F. Palacián , P. Yanguas

In this paper,we have found the equations of motion of Generalized Photogravitational restricted three body problem with Poynting-Robertson drag. The problem is generalized in the sense that smaller primary is supposed to be an oblate…

Dynamical Systems · Mathematics 2007-05-23 B. S. Kushvah , B. Ishwar

We consider the modified restricted three body problem with power-law density profile of disk, which rotates around the center of mass of the system with perturbed mean motion. Using analytical and numerical methods we have found…

Dynamical Systems · Mathematics 2015-05-28 Badam Singh Kushvah , Ram Kishor , Uday Dolas

The Restricted 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies called the primaries. If one assumes that the primaries perform circular motions and that all three bodies…

Dynamical Systems · Mathematics 2021-07-22 Inmaculada Baldomá , Mar Giralt , Marcel Guardia

The dynamics of the planar circular restricted three-body problem with Kerr-like primaries in the context of a beyond-Newtonian approximation is studied. The beyond-Newtonian potential is developed by using the Fodor-Hoenselaers-Perj\'es…

General Relativity and Quantum Cosmology · Physics 2020-12-09 Shounak De , Suparna Roychowdhury , Roopkatha Banerjee

We present a computer assisted proof or diffusion in the Planar Elliptic Restricted Three Body Problem. We treat the elliptic problem as a perturbation of the circular problem, where the perturbation parameter is the eccentricity of the…

Dynamical Systems · Mathematics 2022-04-20 Maciej J. Capiński , Natalia Wodka

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