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Related papers: $L^1$-optimality conditions for circular restricte…

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We consider the planar circular restricted three-body problem (PCRTBP), as a model for the motion of a spacecraft relative to the Earth-Moon system. We focus on the Lagrange equilibrium points $L_1$ and $L_2$. There are families of Lyapunov…

Dynamical Systems · Mathematics 2022-01-12 Marian Gidea , Rafael de la Llave , Maxwell Musser

In this note, we show there exist infinitely many trajectories which are bi-normal (i.e. normal at initial and final times) to the xz-plane, in the Spatial Circular Restricted Three-Body Problem, for energies below or slightly above the…

Symplectic Geometry · Mathematics 2025-06-03 Agustin Moreno , Arthur Limoge

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

We consider the Lagrange problem of optimal control with unrestricted controls and address the question: under what conditions we can assure optimal controls are bounded? This question is related to the one of Lipschitzian regularity of…

Optimization and Control · Mathematics 2007-05-23 Delfim F. M. Torres

Optimal control problems are formulated and efficient computational procedures are proposed for combined orbital and rotational maneuvers of a rigid body in three dimensions. The rigid body is assumed to act under the influence of forces…

Optimization and Control · Mathematics 2016-11-15 Taeyoung Lee , N. Harris McClamroch , Melvin Leok

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

This paper presents a novel fuel-optimal guidance and control methodology for spacecraft swarm reconfiguration in Restricted Multi-Body Problems (RMBPs) with a guarantee of passive safety, maintaining miss distance even under abrupt loss of…

Optimization and Control · Mathematics 2025-10-13 Yuji Takubo , Walter Manuel , Ethan Foss , Simone D'Amico

Context: The Circular Restricted Three-Body Problem provides a fundamental framework for understanding resonant dynamics in binary star systems. Aims: We develop a unified Hamiltonian formulation for mean-motion resonances that encompasses…

Earth and Planetary Astrophysics · Physics 2026-05-08 R. Capuzzo-Dolcetta

Our aim is to identify and classify mean-motion resonances (MMRs) for the coplanar circular restricted three-body problem (CR3BP) for mass ratios between 0.10 and 0.50. Our methods include the maximum Lyapunov exponent, which is used as an…

Earth and Planetary Astrophysics · Physics 2015-06-05 Billy Quarles , Zdzislaw Musielak , Manfred Cuntz

We propose a closed-form (i.e. without expansion in the orbital eccentricities) scheme for computations in perturbation theory in the restricted three-body problem (R3BP) when the massless particle is in an orbit exterior to the one of the…

Mathematical Physics · Physics 2023-07-26 Mattia Rossi , Christos Efthymiopoulos

A new approach is presented for the problem of optimal impulsive rendezvous of a spacecraft in an inertial frame near a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a…

Space Physics · Physics 2015-06-12 Thomas Carter , Mayer Humi

A computational approach is developed for the design of continuous low thrust transfers in the planar circular restricted three-body problem. The transfer design method of invariant manifolds is extended with the addition of continuous low…

Optimization and Control · Mathematics 2015-10-12 Shankar Kulumani , Taeyoung Lee

This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems enjoy certain…

Optimization and Control · Mathematics 2007-05-23 M. Chyba , N. E. Leonard , E. D. Sontag

In this paper we give sufficient conditions for a Pontryagin extremal trajectory, consisting of two bang arcs followed by a singular one, to be a strong local minimizer for a Mayer problem. The problem is defined on a manifold $M$ and the…

Optimization and Control · Mathematics 2016-08-09 Laura Poggiolini , Gianna Stefani

In this paper, we study the minimum time planar tilting maneuver of a spacecraft, from the theoretical as well as from the numerical point of view, with a particular focus on the chattering phenomenon. We prove that there exist optimal…

Optimization and Control · Mathematics 2015-04-24 Jiamin Zhu , Emmanuel Trélat , Max Cerf

This work is devoted to generating optimal guidance commands in real time for attitude-constrained solar sailcrafts in coplanar circular-to-circular interplanetary transfers. Firstly, a nonlinear optimal control problem is established, and…

Optimization and Control · Mathematics 2023-11-17 Kun Wang , Fangmin Lu , Zheng Chen , Jun Li

We present a unified study of first and second order necessary and sufficient optimality conditions for minimax and Chebyshev optimisation problems with cone constraints. First order optimality conditions for such problems can be formulated…

Optimization and Control · Mathematics 2021-02-03 M. V. Dolgopolik

This work presents a robust Model Predictive Controller (MPC) to solve the problem of spacecraft rendezvous in the context of the restricted three-body problem (R3BP) as will be required to dock with space stations in cislunar space. The…

Systems and Control · Electrical Eng. & Systems 2025-01-22 Julio C. Sanchez , Francisco Gavilan , Rafael Vazquez

In this work, we study the motions in the region around the equilateral Lagrangian equilibrium points L4 and L5, in the framework of the Circular Planar Restricted Three-Body Problem (hereafter, CPRTBP). We design a semi-analytic approach…

Earth and Planetary Astrophysics · Physics 2015-08-04 Rocio Isabel Paez , Ugo Locatelli

This paper introduces the Circular Restricted n-Body Problem (CRNBP), an extension of the bicircular restricted four-body problem (BCR4BP) designed to describe the dynamics of an n-body system. In the CRNBP, each massive body in the system…

Systems and Control · Electrical Eng. & Systems 2023-07-21 Rodolfo Batista Negri , Antonio Fernando Bertachini de Almeida Prado