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Related papers: A Circular Restricted n-body Problem

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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

The Hill Restricted 4-Body Problem (HR4BP) is a coherent time-periodic model that can be used to represent motion in the Sun-Earth-Moon (SEM) system. Periodic orbits were computed in this model to better understand the periodic orbit family…

Dynamical Systems · Mathematics 2025-02-03 Gavin M. Brown , Luke T. Peterson , Damennick B. Henry , Daniel J. Scheeres

To better understand the orbital dynamics of exoplanets around close binary stars, i.e., circumbinary planets (CBPs), we applied techniques from dynamical systems theory to a physically motivated set of solutions in the Circular Restricted…

Earth and Planetary Astrophysics · Physics 2023-03-08 Andrew Langford , Lauren M. Weiss

The Circular Restricted Three-Body Problem (CR3BP) models the motion of a massless body under the gravitational influence of two primaries. We present a method for approximating a given family of periodic orbits by low-degree implicit…

Algebraic Geometry · Mathematics 2026-04-30 Ruiqi Huang , Anton Leykin

We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable manifolds in systems of ordinary differential equations. Specifically, we consider the…

Dynamical Systems · Mathematics 2017-06-01 Renato C. Calleja , Eusebius J. Doedel , Antony R. Humphries , Alexandra Lemus , Bart E. Oldeman

Consider the Restricted Planar Circular Three Body Problem (RPC3BP), which models the motion of a massless particle (Asteroid) under the gravitational influence of two massive bodies (the primaries) moving on circular orbits. By considering…

Mathematical Physics · Physics 2025-12-24 Marcel Guardia , José Lamas , Tere M-Seara

Dynamical structures in the circular restricted three-body problem (CR3BP) are fundamental for designing low-energy transfers, as they aid in analyzing phase space transport and designing desirable trajectories. One of these dynamical…

Chaotic Dynamics · Physics 2026-05-14 Naoki Hiraiwa , Mai Bando , Yuzuru Sato , Shinji Hokamoto

Trajectory design in cislunar space under a High-Fidelity Ephemeris Model (HFEM) is pursued through a nonlinear optimization perspective anchored on the transition of solutions from lower fidelity models, namely the Circular Restricted…

Optimization and Control · Mathematics 2026-03-27 António Nunes , Sérgio Brás , Pedro Batista , João Xavier

This paper presents a Nonlinear Model Predictive Control (NMPC) scheme for maintaining a spacecraft within a specified family of periodic orbits near the libration points in cislunar space. Unlike traditional approaches that track a…

Systems and Control · Electrical Eng. & Systems 2025-07-29 Mohammed Atallah , Simone Servadio

In this paper we consider the planar circular restricted three body problem (PCRTBP), which models the motion of a massless body under the attraction of other two bodies, the primaries, which describe circular orbits around their common…

Dynamical Systems · Mathematics 2024-07-25 Marcel Guardia , José Lamas , Tere M. Seara

Isolating block and isolating neighborhood methods have previously been implemented to find transit trajectories and orbits around libration points in the autonomous circular restricted three-body problem. For some applications, the direct…

Dynamical Systems · Mathematics 2023-08-15 Rodney L. Anderson , Robert W. Easton , Martin W. Lo

The goal of this paper it to prove existence theorems for one parameter families (branches) of ejection-collision orbits in the planar circular restricted three body problem (CRTBP), and to study some of their bifurcations. The orbits…

Dynamical Systems · Mathematics 2025-01-14 Gianni Arioli , James D. Mireles James

The restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of…

Dynamical Systems · Mathematics 2018-08-07 Amadeu Delshams , Vadim Kaloshin , Abraham de la Rosa , Tere M. Seara

The circular restricted three-body problem (CR3BP) with solar radiation pressure (SRP) has often been analyzed with assumptions made on a spacecraft's attitude, such that the problem remains Hamiltonian. These assumptions are…

Dynamical Systems · Mathematics 2024-02-13 Hailee Hettrick , David W. Miller , Begum Cannataro

We herein utilize the general three-body problem (GTBP) as a model, in order to simulate resonant systems consisting of a star and two planets, where at least one of them is highly eccentric. We study them in terms of their long-term…

Earth and Planetary Astrophysics · Physics 2015-09-10 K. I. Antoniadou , G. Voyatzis

In this work, we investigate trajectories that require thrust to maintain periodic structure in the circular restricted three-body problem (CR3BP). We produce bounds in position and velocity space for the energy-constrained reachable set of…

Dynamical Systems · Mathematics 2024-11-19 Colby C. Merrill , Jackson Kulik , Dmitry Savransky

Gravitational scattering of small bodies (planetesimals) by a planet remains a fundamental problem in celestial mechanics. It is traditionally modeled within the circular restricted three-body problem (CR3BP), where individual particle…

Earth and Planetary Astrophysics · Physics 2026-02-11 Yukun Huang , Brett Gladman , Eiichiro Kokubo

This study addresses optimal impulsive trajectory design within the Circular Restricted Three-Body Problem (CR3BP), presenting a global optimization-based approach to identify minimum $\Delta V$ transfers between periodic orbits, including…

Space Physics · Physics 2024-05-30 Flavio Tagliaferri , Emmanuel Blazquez , Giacomo Acciarini , Dario Izzo

Mounting discoveries of debris discs orbiting newly-formed stars and white dwarfs (WDs) showcase the importance of modeling the long-term evolution of small bodies in exosystems. WD debris discs are in particular thought to form from very…

Earth and Planetary Astrophysics · Physics 2017-02-10 Kyriaki I. Antoniadou , Dimitri Veras

Near-Earth Objects (NEOs) are attractive exploration targets due to their accessibility, scientific value, and resources. Although trajectory design has revealed efficient pathways to these bodies, systematic strategies for Earth-NEO…

Earth and Planetary Astrophysics · Physics 2026-03-31 Alessandro Beolchi , Mauro Pontani , Kathleen Howell , Chiara Pozzi , Sean Swei , Elena Fantino
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