Related papers: The three-body problem and the Hannay angle
A simple rearrangement of the torque free motion Hamiltonian shapes it as a perturbation problem for bodies rotating close to the principal axis of maximum inertia, independently of their triaxiality. The complete reduction of the main part…
In most books the Delaunay and Lagrange equations for the orbital elements are derived by the Hamilton-Jacobi method: one begins with the 2-body Hamilton equations, performs a canonical transformation to the orbital elements, and obtains…
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…
Adiabatic elimination is a standard tool in quantum optics, which produces an effective Hamiltonian for a relevant subspace of states, incorporating effects of its coupling to states with much higher unperturbed energy. It shares with…
The regularization of a new problem, namely the three-body problem, using 'similar' coordinate system is proposed. For this purpose we use the relation of 'similarity', which has been introduced as an equivalence relation in a previous…
In this paper we consider the planar circular restricted three body problem (PCRTBP), which models the motion of a massless body under the attraction of other two bodies, the primaries, which describe circular orbits around their common…
We explore the near adiabatic dynamics in a non-Hermitian quantum many-body system by investigating a finite-time ramp of the imaginary vector potential in the interacting Hatano-Nelson model. The excess energy, the Loschmidt echo, and the…
The circular restricted three body problem, which considers the dynamics of an infinitesimal particle in the presence of the gravitational interaction with two massive bodies moving on circular orbits about their common center of mass, is a…
Recent work in the literature has studied the restricted three-body problem within the framework of effective-field-theory models of gravity. This paper extends such a program by considering the full three-body problem, when the Newtonian…
The full three-body problem, on the motion of three celestial bodies under their mutual gravitational attraction, is one of the oldest unsolved problems in classical mechanics. The main difficulty comes from the presence of unstable and…
The aim of the present work is to reduce the secular solution around the triangular equilibrium points to periodic solution in the frame work of the generalized restricted thee-body problem. This model is generalized in sense that both the…
The restricted four body problem studies the dynamics of a massless particle under the gravitational force produced by three masses (primaries) in an equilateral configuration. One primary, say m3, is considered too small compared with the…
Several N-body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (``acceleration equal force;'' in most cases, the forces are velocity-dependent) and are amenable to exact…
We investigate the hierarchical gravitational three-body problem, in which a binary is perturbed by a distant object that orbits on a Keplerian ellipse around the binary itself. This phenomenon, known as Kozai-Lidov mechanism in the…
We explore the three-body problem in two dimensions using the adiabatic hyperspherical representation. We develop the main equations in terms of democratic hyperangular coordinates and determine several symmetry properties and boundary…
We consider the planar circular restricted three-body problem (PCRTBP), as a model for the motion of a spacecraft relative to the Earth-Moon system. We focus on the Lagrange equilibrium points $L_1$ and $L_2$. There are families of Lyapunov…
We consider statistics of the disruption and Lyapunov times in an hierarchical restricted three-body problem. We show that at the edge of disruption the orbital periods and the size of the orbit of the escaping body exhibit L\'evy flights.…
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…
We use the planar circular restricted three-body problem in order to numerically investigate the orbital dynamics of orbits of a spacecraft, or a comet, or an asteroid in the Saturn-Titan system in a scattering region around the Titan. The…
Gravitational and electromagnetic interactions are Hamiltonian systems with forces between pairs of particles. We propose an alternative: Hamiltonian dynamics with triplet interactions between point particles. Our system has a potential…