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Related papers: A Circular Restricted n-body Problem

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We describe a framework that can integrate prior physical information, e.g., the presence of kinematic constraints, to support data-driven simulation in multi-body dynamics. Unlike other approaches, e.g., Fully-connected Neural Network…

Computational Engineering, Finance, and Science · Computer Science 2024-07-12 Jingquan Wang , Shu Wang , Huzaifa Mustafa Unjhawala , Jinlong Wu , Dan Negrut

Many exoplanetary systems are multiplanet configurations whose long-term dynamics are governed by N-body gravitational interactions. Consequently, their detection signatures cannot be adequately described by Keplerian orbits. Accurately…

Earth and Planetary Astrophysics · Physics 2026-04-13 Hong-Fei Jia , Sheng Jin , Dong-Hong Wu , Shang-Fei Liu

The case of the planar circular restricted three-body problem is used as a test field in order to determine the character of the orbits of a small body which moves under the gravitational influence of the two heavy primary bodies. We…

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

In this paper, novel approaches are developed to explore the dynamics of motion in periodic orbits near libration points in cislunar space using the Differential Algebra (DA) framework. The Circular Restricted Three-Body Problem (CR3BP)…

Dynamical Systems · Mathematics 2024-09-06 Mohammed Atallah , Simone Servadio

As low-thrust space missions increase in prevalence, it is becoming increasingly important to design robust trajectories against unforeseen thruster outages or missed thrust events. Accounting for such events is particularly important in…

Optimization and Control · Mathematics 2025-06-18 Amlan Sinha , Ryne Beeson

The restricted planar four body problem describes the motion of a massless body under the Newtonian gravitational force of other three bodies (the primaries), of which the motion gives us general solutions of the three body problem. A…

Dynamical Systems · Mathematics 2020-12-02 Tere Seara , Jianlu Zhang

In this paper, we present a new ansatz for solving equations of motion for the trapped orbits of the infinitesimal mass (satellite), which is locked in the space trap to be moving near the planet in case of the elliptic restricted problem…

General Physics · Physics 2021-04-19 Sergey Ershkov , Alla Rachinskaya

This work introduces a novel path-following control strategy inspired by the famous two-body problem, aiming to stabilize any Keplerian orbit. Utilizing insights from the mathematical structure of the two-body problem, we derive a robust…

Systems and Control · Electrical Eng. & Systems 2024-11-18 Rodolfo Batista Negri , Antônio Fernando Bertachini de Almeida Prado

The design of transfers to periodic orbits in the Earth-Moon system has regained prominence with NASA's Artemis and CNSA's Chang'e programs. This work addresses the problem of linking ballistic capture trajectories - exploiting multi-body…

Earth and Planetary Astrophysics · Physics 2026-01-09 Lorenzo Anoè , Roberto Armellin , Jack Yarndley , Thomas Caleb , Stéphanie Lizy-Destrez

We develop the foundations of an effective-one-body (EOB) model for eccentric binary coalescences that includes the conservative dynamics, radiation reaction, and gravitational waveform modes from the inspiral and the merger-ringdown…

General Relativity and Quantum Cosmology · Physics 2018-01-08 Tanja Hinderer , Stanislav Babak

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

Many unstable periodic orbits of the planar circular restricted 3-body problem (PCRTBP) persist as invariant tori when a periodic forcing is added to the equations of motion. In this study, we compute tori corresponding to exterior…

Dynamical Systems · Mathematics 2021-10-01 Bhanu Kumar , Rodney L. Anderson , Rafael de la Llave , Brian Gunter

We present a new C++ code for collisional N-body simulations of star clusters. The code uses the Hermite fourth-order scheme with block time steps, for advancing the particles in time, while the forces and neighboring particles are computed…

Instrumentation and Methods for Astrophysics · Physics 2010-11-08 Simos Konstantinidis , Kostas D. Kokkotas

The planar circular restricted three body problem (PCRTBP) is symmetric with respect to the line of masses and there is a corresponding anti-symplectic involution on the cotangent bundle of the 2-sphere in the regularized PCRTBP. Recently…

Symplectic Geometry · Mathematics 2014-10-16 Jungsoo Kang

(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 three body problem is a special case of the n body problem where one takes the initial positions and velocities of three point masses and attempts to predict their motion over time according to Newtonian laws of motion and universal…

Machine Learning · Computer Science 2021-01-22 Pratyush Kumar , Aishwarya Das , Debayan Gupta

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.

Mathematical Physics · Physics 2012-08-06 Donglun Wu , Shiqing Zhang

In the last decades a peculiar family of solutions of the Circular Restricted Three Body Problem has been used to explain the temporary captures of small bodies and spacecrafts by a planet of the Solar System. These solutions, which transit…

Earth and Planetary Astrophysics · Physics 2021-09-01 Rocío Isabel Páez , Massimiliano Guzzo

We propose a Constraint Molecular Dynamics model for Fermionic system. In this approach the equations of motion of wave packets for the nuclear many-body problem are solved by imposing that the one-body occupation probability…

Nuclear Theory · Physics 2009-11-06 M. Papa , T. Maruyama , A. Bonasera

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