相关论文: High-Order Resonant Orbit Manifold Expansions For …

Numerical continuation techniques are powerful tools that have been extensively used to identify particular solutions of nonlinear dynamical systems and enable trajectory design in chaotic astrodynamics problems such as the Circular…

The Fast Lyapunov Indicators are functions defined on the tangent fiber of the phase-space of a discrete (or continuous) dynamical system, by using a finite number of iterations of the dynamics. In the last decade, they have been largely…

Space missions have discovered a large number of exoplanets evolving in (or close to) mean-motion resonances (MMRs) and resonant chains. Often, the published data exhibit very high uncertainties due to the observational limitations that…

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…

This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…

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…

For enabling efficient, large-scale coordination of unmanned aerial vehicles (UAVs) under the labeled setting, in this work, we develop the first polynomial time algorithm for the reconfiguration of many moving bodies in three-dimensional…

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…

An alternative numerical method is developed to find stable and unstable periodic orbits of nonlinear dynamical systems. The method exploits the high-efficiency of the Levenberg-Marquardt algorithm for medium-sized problems and has the…

For a given a normally hyperbolic invariant manifold, whose stable and unstable manifolds intersect transversally, we consider several tools and techniques to detect trajectories with prescribed itineraries: the scattering map, the…

The Restricted 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies called the primaries. If one assumes that the primaries perform circular motions and that all three bodies…

The study of wave propagation outside bounded obstacles uncovers the existence of resonances for the Laplace operator, which are complex-valued generalized eigenvalues, relevant to estimate the long time asymptotics of the wave. In order to…

We present a method for establishing invariant manifolds for saddle--center fixed points. The method is based on cone conditions, suitably formulated to allow for application in computer assisted proofs, and does not require rigorous…

In Cislunar space, spacecraft are able to exploit naturally periodic orbits, which provide operational reliability. However, these periodic orbits only exist in a limited volume. Enabled by low-thrust propulsion, spacecraft can produce a…

We develop computer assisted arguments for proving the existence of transverse homoclinic connecting orbits, and apply these arguments for a number of non-perturbative parameter and energy values in the spatial equilateral circular…

We present a computer assisted proof or diffusion in the Planar Elliptic Restricted Three Body Problem. We treat the elliptic problem as a perturbation of the circular problem, where the perturbation parameter is the eccentricity of the…

A method to establish regions of phase space through which pass no invariant tori transverse to a given direction field is applied to the planar circular restricted three-body problem. Implications for the location of stable orbits for…

We investigate the heteroclinic connections between stable and unstable manifolds of unstable periodic orbits associated with the most important mean motion resonances (MMRs) in the Sun-Jupiter planar restricted three-body problem. We…

The continuation of resonant periodic orbits from the restricted to the general three body problem is studied in a systematic way. Starting from the Keplerian unperturbed system we obtain the resonant families of the circular restricted…

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…