Related papers: A new perturbative solution to the motion around t…
In this paper, we use the central configuration coordinate decomposition to study the linearized Hamiltonian system near the elliptic Euler solutions. Then using the Maslov-type \omega-index theory of symplectic paths and the theory of…
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…
This monograph describes a Riemannian geometric reduction approach to the three-body problem. The fundamental theorems are presented in the introductory part, whereas their proofs are provided in later chapters where specific topics are…
In the spatial circular restricted three-body problem librational motion around the Lagrangian points $L_4$ and $L_5$ exists up to high inclinations of the massless object. We report the results of numerical investigations on the stability…
The motion of a rigid body in a quadratic potential is an important example of an integrable Hamiltonian system on a dual to a semidirect product Lie algebra so(n) x Symm(n). We give a Lagrangian derivation of the corresponding equations of…
Employing techniques from scattering amplitudes and effective field theory, we model the dynamics of hierarchical triples, which are three-body systems composed of two bodies separated by a distance $r$ and a third body a distance $\rho$…
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 provide an analytical approximation of a periodic solution of the three body problem in celestial mechanics, the so-called figure eight solution, discovered 1993 by C. Moore. This approximation has the form of a Fourier series whose…
We develop an approach in solving exactly the problem of three-body oscillators including general quadratic interactions in the coordinates for arbitrary masses and couplings. We introduce a unitary transformation of three independent…
We consider the two-body problem in post-Newtonian approximations of general relativity. We report the recent results concerning the equations of motion, and the associated Lagrangian formulation, of compact binary systems, at the third…
Continuing work initiated in an earlier publication [Yamada, Tsuchiya, and Asada, Phys. Rev. D 91, 124016 (2015)], we reexamine the linear stability of the triangular solution in the relativistic three-body problem for general masses by the…
We study orbits near collision in a non-autonomous restricted planar four-body problem. This restricted problem consists of a massless particle moving under the gravitational influence due to three bodies following the figure-eight…
The non-integrability of the Hill problem makes that its global dynamics must be necessarily approached numerically. However, the analytical approach is feasible in the computation of relevant solutions. In particular, the nonlinear…
The case of the planar circular restricted three-body problem where one of the two primaries is an oblate spheroid is investigated. We conduct a thorough numerical analysis on the phase space mixing by classifying initial conditions of…
The three-body problem is a fundamental long-standing open problem, with applications in all branches of physics, including astrophysics, nuclear physics and particle physics. In general, conserved quantities allow to reduce the formulation…
Various astrophysical processes are known, where the fly-by of a massive object affects matter initially supported against gravity by rotation. Examples are perturbations of galaxies, protoplanetary discs or planetary systems. We…
In this paper we develop an $hp$-adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbation. Our approach combines both adaptive Newton schemes and…
The Eckart frame is used to separate out the collective rotations in the quantum three-body problem. Explicit expressions for the corresponding rotational and vibro-rotational (i.e. Coriolis) Hamiltonians are derived. Special attention is…
In this article we consider the affinely-rigid body moving in the three-dimensional physical space and subject to the Kirchhoff-Love constraints, i.e., while it deforms homogeneously in the two-dimensional central plane of the body it…
In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the…