相关论文: A Simple Analytical Formulation for Periodic Orbit…

Because the distant retrograde orbits dynamics inherently depends on special functions, approximate analytical solutions in the literature are commonly constrained to providing rough approximations of the qualitative behavior. We rely on…

Gravitational scattering of small bodies (planetesimals) by a planet remains a fundamental problem in celestial mechanics. It is traditionally modeled within the circular restricted three-body problem (CR3BP), where individual particle…

We investigate the qualitative characteristics of a test particle attracted to an irregular elongated body, modeled as a non-homogeneous straight segment with a variable linear density. By deriving the potential function in closed form, we…

We propose a method of determining solutions to the constraint equations of General Relativity approximately describing binary black holes in quasi-stationary circular orbits. Black holes with arbitrary linear momenta are constructed in the…

In this paper decomposition of periodic orbits in bifurcation diagrams are derived in unidimensional dynamics system $x_{n+1}=f(x_{n};r)$, being $f$ an unimodal function. We proof a theorem which states the necessary and sufficient…

For an analytic differential system in $\mathbb R^n$ with a periodic orbit, we will prove that if the system is analytically integrable around the periodic orbit, i.e. it has $n-1$ functionally independent analytic first integrals defined…

The gradual evolution of the restricted hierarchical three body problem is analyzed analytically, focusing on conditions of Kozai-Lidov Cycles that may lead to orbital flips from prograde to retrograde motion due to the octupole (third…

This work develops a functional analytic framework for making computer assisted arguments involving transverse heteroclinic connecting orbits between hyperbolic periodic solutions of ordinary differential equations. We exploit a…

In this work we introduce a planar restricted four-body problem where a massless particle moves under the gravitational influence due to three bodies following the eight figure choreography, and we explore some symmetric periodic orbits of…

It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…

We derive the analytical solutions of the bound timelike geodesic orbits in Kerr spacetime. The analytical solutions are expressed in terms of the elliptic integrals using Mino time $\lambda$ as the independent variable. Mino time decouples…

We report our rederivation of the equations of motion for relativistic compact binaries through the third-and-a-half post-Newtonian (3.5 PN) order approximation to general relativity using the strong field point particle limit to describe…

We propose a survey of Michel H\'enon works devoted to studying periodic solutions of the well-known celestial mechanics problem -- restricted three-body problem. The description of the main results obtained by H\'enon is given in…

In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…

We will address the problem of determining the existence and asymptotic stability of a non-trivial periodic orbit in dynamical systems described by polynomial vector fields. To this end, we will lean upon the celebrated results of Borg,…

Simplified solutions to determine binary elements by astrometry were obtained in terms of elementary functions (Asada et al. 2004), and therefore require neither iterative nor numerical methods. In the framework of the simplified solution,…

A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…

The periodic standing-wave method for binary inspiral computes the exact numerical solution for periodic binary motion with standing gravitational waves, and uses it as an approximation to slow binary inspiral with outgoing waves. Important…

The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be…

Since the discovery of the figure-8 orbit for the three-body problem [Moore 1993] a large number of periodic orbits of the n-body problem with equal masses and beautiful symmetries have been discovered. However, most of those that have…