Related papers: Melnikov method for non-conservative perturbations…
The Melnikov method is applied to periodically perturbed open systems modeled by an inverse--square--law attraction center plus a quadrupolelike term. A compactification approach that regularizes periodic orbits at infinity is introduced.…
The long-term stability of the evolution of two-planet systems is considered by using the general three body problem (GTBP). Our study is focused on the stability of systems with adjacent orbits when at least one of them is highly…
Consider the spatial restricted three-body problem, as a model for the motion of a spacecraft relative to the Sun-Earth system. We focus on the dynamics near the equilibrium point $L_1$, located between the Sun and the Earth. We show that…
We study the global flow of the anisotropic Manev problem, which describes the planar motion of two bodies under the influence of an anisotropic Newtonian potential with a relativistic correction term. We first find all the heteroclinic…
We study the dynamics of the collinear points in the planar, restricted three-body problem, assuming that the primaries move on an elliptic orbit around a common barycenter. The equations of motion can be conveniently written in a rotating…
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…
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…
In a recent paper by the author (K. Yagasaki, Nonintegrability of the restricted three-body problem, submitted for publication), a technique was developed for determining whether nearly integrable systems are not meromorphically…
We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The centerpiece of our method is…
We present a Melnikov type approach for establishing transversal intersections of stable/unstable manifolds of perturbed normally hyperbolic invariant manifolds. We do not need to know the explicit formulas for the homoclinic orbits prior…
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…
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…
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…
We construct a Nekhoroshev-like result of stability with sharp constants for the planar three body problem, both in the planetary and in the restricted circular case, by using the periodic averaging technique. Our constructions can be…
In this work, we investigate the Earth-Moon system, as modeled by the planar circular restricted three-body problem, and relate its dynamical properties to the underlying structure associated with specific invariant manifolds. We consider a…
In the last decades a peculiar family of solutions of the Circular Restricted Three Body Problem has been used to explain the temporary captures of small bodies and spacecrafts by a planet of the Solar System. These solutions, which transit…
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…
We present a Melnikov method to analyze two-dimensional stable or unstable manifolds associated with a saddle point in three-dimensional non-volume preserving autonomous systems. The time-varying perturbed locations of such manifolds is…
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…
The motion of three bodies can be solved perturbatively when a tightly bound inner binary is orbited by a distant perturber, giving rise for example to the well-known Kozai-Lidov oscillations. We propose to study the relativistic…