Related papers: Identifying Fixed Points in the Three-Body Problem…
A reduced-order model based on Proper Orthogonal Decomposition (POD) is proposed for the bidomain equations of cardiac electrophysiology. Its accuracy is assessed through electrocardiograms in various configurations, including myocardium…
We consider the general spatial three body problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic…
The optimization of low-thrust, multi-revolution orbit transfer trajectories is often regarded as a difficult problem in modern astrodynamics. In this paper, a flexible and computationally efficient approach is presented for the…
This article presents a new algorithm, the Hyperbolic and Elliptic Points Tracking Algorithm (HEPTA), designed for automated tracking of elliptic and hyperbolic stationary points in two-dimensional non-stationary velocity fields defined on…
An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp.~6172--6175], which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.~4733--4736]…
This paper presents an efficient algorithm, naming Centralized Searching and Decentralized Optimization (CSDO), to find feasible solution for large-scale Multi-Vehicle Trajectory Planning (MVTP) problem. Due to the intractable growth of…
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…
The main purpose of this article is to study box dimension of orbits near hyperbolic and nonhyperbolic fixed points of discrete dynamical systems in higher dimensions. We generalize the known results for one-dimensional systems, that is,…
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…
Autonomous agents are limited in their ability to observe the world state. Partially observable Markov decision processes (POMDPs) formally model the problem of planning under world state uncertainty, but POMDPs with continuous actions and…
Trajectory optimization of low-thrust perturbed orbit rendezvous is a crucial technology for space missions in low Earth orbits, which is difficult to solve due to its initial value sensitivity, especially when the transfer trajectory has…
The Hilda group is a set of asteroids whose mean motion is in a 3:2 orbital resonance with Jupiter. In this paper we use the planar Circular Restricted Three-Body Problem (CRTBP) as a dynamical model and we show that there exists a family…
The famous three-body problem can be traced back to Newton in 1687, but quite few families of periodic orbits were found in 300 years thereafter. In this paper, we propose an effective approach and roadmap to numerically gain planar…
We investigate the natural families of periodic orbits associated with the equilibrium configurations of the the planar restricted $1+n$ body problem for the case $2\leq n \leq 4$ equal mass satellites. Such periodic orbits can be used to…
The restricted (equilateral) four-body problem consists of three bodies of masses m1, m2 and m3 (called primaries) lying in a Lagrangian configuration of the three-body problem i.e., they remain fixed at the apices of an equilateral…
In this work, we develop a new method to design energy minimum low-thrust missions (L2-minimization). In the Circular Restricted Three Body Problem, the knowledge of invariant manifolds helps us initialize an indirect method solving a…
In this work, we introduce a method based on piecewise polynomial interpolation to enclose rigorously solutions of nonlinear ODEs. Using a technique which we call a priori bootstrap, we transform the problem of solving the ODE into one of…
To date a dozen transiting "Tatooines" or circumbinary planets (CBPs) have been discovered, by eye, in the data from the Kepler mission; by contrast, thousands of confirmed circumstellar planets orbiting around single stars have been…
A topological approach and understanding to the detection of unstable periodic orbits based on a recently proposed method (PRL 78, 4733 (1997)) is developed. This approach provides a classification of the set of transformations necessary…
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…