相关论文: Hierarchical Three-Body Problem at High Eccentrici…

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…

In recent years, the long-term effects of non-linear perturbations were found to be important for the evolution of the hierarchical triple system, which, for the central third body of a larger mass, can significantly suppress the…

We develop a technique for estimating the inner eccentricity in hierarchical triple systems with well separated components. We investigate systems with initially circular and coplanar orbits and comparable masses. The technique is based on…

Consider the spatial three-body problem, in the regime where one body revolves far away around the other two, in space, the masses of the bodies being arbitrary but fixed; in this regime, there are no resonances in mean motions. The…

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…

We consider the planar three-body problem perturbed by a celestial body modeled as a time-dependent perturbation that decays in time. We assume that the motion of the celestial body is given and is unbounded with a non-zero asymptotic…

The very long-term evolution of the hierarchical restricted three-body problem with a slightly aligned precessing quadrupole potential is studied analytically. This problem describes the evolution of a star and a planet which are perturbed…

The Sitnikov problem is a special case of the three-body problem. The system is known to be chaotic and has been studied by symbolic dynamics (J. Moser, Stable and random motions in dynamical systems, Princeton University Press, 1973). We…

Context: The Circular Restricted Three-Body Problem provides a fundamental framework for understanding resonant dynamics in binary star systems. Aims: We develop a unified Hamiltonian formulation for mean-motion resonances that encompasses…

We demonstrate that both kinds of the Hamiltonian intermittency exert an influence on the disruption statistics in the equal mass three-body problem. Studying initially-resting triple systems we found a narrow region in the vicinity of the…

(abbreviated) We use a semi-numerical approach to study the secular behavior of a system composed of a central star and two massive planets in eccentric co-planar orbits. We show that the secular dynamics of this system can be described…

The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…

Extrasolar planetary systems commonly exhibit planets on eccentric orbits, with many systems located near or within mean-motion resonances, showcasing a wide diversity of orbital architectures. Such complex systems challenge traditional…

In 1900, Macfarlane proposed a hyperbolic variation on Hamilton's quaternions that closely resembles Minkowski spacetime. Viewing this in a modern context, we expand upon Macfarlane's idea and develop a model for real hyperbolic 3-space in…

We explore the stability of gravitational triple systems comprising a central massive body and a tight binary of less massive pairs. In the present paper, we focus on improving the Hill-type stability criterion for the binary in those…

We consider a class of autonomous Hamiltonian systems subject to small, time-periodic perturbations. When the perturbation parameter is set to zero, the energy of the system is preserved. This is no longer the case when the perturbation…

We describe a new kind of resonance occuring in relativistic three-body hierarchical systems: the precession resonance, occuring when the relativistic precession timescale of a binary equals the period of a distant perturber. We find that,…

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…

We investigate the dynamics of small trojan exoplanets in domains of secondary resonances within the tadpole domain of motion. We consider the limit of a massless trojan companion of a giant planet. Without other planets, this is a case of…

In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…