相关论文: High-Order Resonant Orbit Manifold Expansions For …
We construct and justify leading order weakly nonlinear geometric optics expansions for nonlinear hyperbolic initial value problems, including the compressible Euler equations. The technique of simultaneous Picard iteration is employed to…
We study a three-dimensional dynamical system in two slow variables and one fast variable. We analyze the tangency of the unstable manifold of an equilibrium point with "the" repelling slow manifold, in the presence of a stable periodic…
We address the problem of planning robot motions in constrained configuration spaces where the constraints change throughout the motion. The problem is formulated as a fixed sequence of intersecting manifolds, which the robot needs to…
Geometric representation learning has recently shown great promise in several machine learning settings, ranging from relational learning to language processing and generative models. In this work, we consider the problem of performing…
Many extrasolar systems possessing planets in mean-motion resonance or resonant chain have been discovered to date. The transit method coupled with transit timing variation analysis provides an insight into the physical and orbital…
Many different models of the physical world exhibit chaotic dynamics, from fluid flows and chemical reactions to celestial mechanics. The study of the three-body problem (3BP) and its many different families of unstable periodic orbits…
This paper aims to study time periodic solutions for 3D inviscid quasi-geostrophic model. We show the existence of non trivial rotating patches by suitable perturbation of stationary solutions given by generic revolution shapes around the…
Many binary systems of interest for gravitational-wave astronomy are orbited by a third distant body, which can considerably alter their relativistic dynamics. Precision computations are needed to understand the interplay between…
As interest in the Earth-Moon transfers renewed around the world, understanding the solution space of transfer trajectories facilitates the construction of transfers. This paper is devoted to reporting a novel or less-reported phenomenon…
In this paper we use a Modified Newton's method based on the Continuous analog of Newton's method and high precision arithmetic for a general numerical search of periodic orbits for the planar three-body problem. We consider relatively…
In the framework of multi-body dynamics, successive encounters with a third body, even if well outside of its sphere of influence, can noticeably alter the trajectory of a spacecraft. Examples of these effects have already been exploited by…
Since Poincar\'e, periodic orbits have been one of the most important objects in dynamical systems. However, searching them is in general quite difficult. A common way to find them is to construct families of periodic orbits which start at…
The effectiveness of the hyperbolic relaxation method for solving the Einstein constraint equations numerically is studied here on a variety of compact orientable three-manifolds. Convergent numerical solutions are found using this method…
Correspondence is a ubiquitous problem in computer vision and graph matching has been a natural way to formalize correspondence as an optimization problem. Recently, graph matching solvers have included higher-order terms representing…
This work presents a method for constructing online-efficient reduced models of large-scale systems governed by parametrized nonlinear scalar conservation laws. The solution manifolds induced by transport-dominated problems such as…
The proposal of increasingly complex and innovative space endeavours poses growing demands for mission designers. In order to meet the established requirements and constraints while maintaining a low fuel cost, the use of low-energy…
We propose new methods for the numerical continuation of point-to-cycle connecting orbits in 3-dimensional autonomous ODE's using projection boundary conditions. In our approach, the projection boundary conditions near the cycle are…
In the 70s McGehee introduced a compactification of the phase space of the restricted 3-body problem by gluing a manifold of periodic orbits "at infinity". Although from the dynamical point of view these periodic orbits are parabolic (the…
Near-rectilinear halo orbits (NRHOs) around Earth-Moon L2 in the Circular Restricted 3-Body Problem (CR3BP) exhibit a complex dynamical landscape, featuring a band of normally elliptic orbits embedded within regions of strong instability.…
We describe numerical tools for the stability analysis of extrasolar planetary systems. In particular, we consider the relative Poincare variables and symplectic integration of the equations of motion. We apply the tangent map to derive a…