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Related papers: A trial symbolic dynamics of the planar three-body…

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We study the change of phase space structure of the rectilinear three-body problem when the mass combination is changed. Generally, periodic orbits bifurcate from the stable Schubart periodic orbit and move radially outward. Among these…

Astrophysics · Physics 2007-11-14 Masaya Masayoshi Saito , Kiyotaka Tanikawa

(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

The elliptic isosceles restricted three body problem (REI3BP) models the motion of a massless body under the influence of the Newtonian gravitational force caused by two other bodies called the primaries. The primaries of masses…

Dynamical Systems · Mathematics 2021-06-01 Marcel Guardia , Jaime Paradela , Tere-M. Seara , Claudio Vidal

In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…

Dynamical Systems · Mathematics 2026-02-24 Joshua Fitzgerald , Shane Ross

We use the planar circular restricted three-body problem in order to numerically investigate the orbital dynamics of orbits of a spacecraft, or a comet, or an asteroid in the Saturn-Titan system in a scattering region around the Titan. The…

Earth and Planetary Astrophysics · Physics 2017-09-28 Euaggelos E. Zotos

The Sitnikov problem is a special case of the three-body problem. The system is known to be chaotic and has been studied by symbolic dynamics (J. Moser, Stable and random motions in dynamical systems, Princeton University Press, 1973). We…

Dynamical Systems · Mathematics 2025-08-12 Yuika Kajihara , Mitsuru Shibayama , Guowei Yu

We formulate the three-body problem in one dimension in terms of the (Faddeev-type) integral equation approach. As an application, we develop a spinless, one-dimensional (1-D) model that mimics three-nucleon dynamics in one dimension. Using…

Quantum Physics · Physics 2009-11-07 T. Melde , L. Canton , J. P Svenne

Three-body systems of scalar bosons are described in the framework of relativistic constraint dynamics. With help of a change of variables followed by a change of wave function, two redundant degrees of freedom get eliminated and the…

High Energy Physics - Theory · Physics 2008-11-26 Ph. Droz-Vincent

The free fall of three particles under Newtonian attraction allows to illustrate some of the complexities of the general three body problem. The total collapse or singularity that occurs when starting from one of the five central…

Dynamical Systems · Mathematics 2011-03-21 Frank Janssens

The theory of the post-Newtonian (PN) planar circular restricted three-body problem is used for numerically investigating the orbital dynamics of a test particle (e.g., a comet, asteroid, meteor or spacecraft) in the planar Sun-Jupiter…

Earth and Planetary Astrophysics · Physics 2018-03-21 Euaggelos E. Zotos , F. L. Dubeibe

Forces in the systems of two opposite sign and three identical charges coupled to the dynamical scalar field of the signum-Gordon model are investigated. Three-body force is present, and the exact formula for it is found. Flipping the sign…

High Energy Physics - Theory · Physics 2015-06-17 H. Arodz , J. Karkowski , Z. Swierczynski

We propose a set of variables of the general three-body problem both for two-dimensional and three-dimensional cases. Variables are $(\lambda,\theta,\Lambda, \Theta,k,\omega)$ or equivalently $(\lambda,\theta,L,\dot{I},k,\omega)$ for the…

Chaotic Dynamics · Physics 2007-05-23 Kenji Hiro Kuwabara , Kiyotaka Tanikawa

In this paper, we present a new task that investigates how people interact with and make judgments about towers of blocks. In Experiment~1, participants in the lab solved a series of problems in which they had to re-configure three blocks…

Artificial Intelligence · Computer Science 2017-07-27 Ilker Yildirim , Tobias Gerstenberg , Basil Saeed , Marc Toussaint , Josh Tenenbaum

We consider the classical three-body problem with an arbitrary pair potential which depends on the inter-body distance. A general three-body configuration is set by three "radial" and three angular variables, which determine the shape and…

Classical Physics · Physics 2019-07-16 Michele Castellana

We introduce a circular restricted charged three-body problem on the plane. In this model, the gravitational and Coulomb forces, due to the primary bodies, act on a test particle; the net force exerted by some primary body on the test…

Dynamical Systems · Mathematics 2015-03-31 Abimael Bengochea , Claudio Vidal

The planar $N$-centre problem describes the motion of a particle moving in the plane under the action of the force fields of $N$ fixed attractive centres: \[ \ddot{x}(t)=\sum_{j=1}^N\nabla V_j(x-c_j). \] In this paper we prove symbolic…

Dynamical Systems · Mathematics 2021-10-27 Vivina Barutello , Gian Marco Canneori , Susanna Terracini

We use Monte Carlo simulation to study the phase diagram of three-dimensional dynamical triangulations with a boundary. Three phases are indentified and characterized. One of these phases is a new, boundary dominated phase; a simple…

High Energy Physics - Lattice · Physics 2009-10-31 Simeon Warner , Simon Catterall , Ray Renken

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 this work, we revisit the planar restricted four-body problem to study the dynamics of an infinitesimal mass under the gravitational force produced by three heavy bodies with unequal masses, forming an equilateral triangle configuration.…

Dynamical Systems · Mathematics 2022-08-31 José Alejandro Zepeda Ramírez , Martha Alvarez-Ramírez

In this paper we carry out a quantitative analysis of the three-body systems and map them as a function of decaying time and intial conguration, look at this problem as an example of a simple deterministic system, and ask to what extent the…

Astrophysics · Physics 2009-11-13 H. J. Lehto , S. Kotiranta , M. J. Valtonen , P. Heinamaki , S. Mikkola , A. D. Chernin