Related papers: Oscillatory motions for the restricted planar circ…
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 character of motion for the three-dimensional circular restricted three-body problem with oblate primaries is investigated. The orbits of the test particle are classified into four types: non-escaping regular orbits around the…
In the present work a systematic study has been presented in the context of the existence of libration points, their linear stability, the regions of motion where the third particle can orbit and the domain of basins of convergence linked…
Solutions to the collinear three-body problem which do not end in triple collision pass through an infinite number of binary collisions. Given three masses, we show that four geometric quantities generate a finite description of itineraries…
This paper concerns the classical dynamics of three coupled rotors: equal masses moving on a circle subject to attractive cosine inter-particle potentials. It is a simpler variant of the gravitational three-body problem and also arises as…
In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…
We present a diffusion mechanism for time-dependent perturbations of autonomous Hamiltonian systems introduced in [25]. This mechanism is based on shadowing of pseudo-orbits generated by two dynamics: an `outer dynamics', given by…
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…
We propose a new treatment for the quantum three-body problem. It is based on an expansion of the wave function on harmonic oscillator functions with different sizes in the Jacobi coordinates. The matrix elements of the Hamiltonian can be…
We present a numerical study on the stability of the 1/2, 2/1 and 1/1 retrograde mean motion resonances in the 3-body problem composed of a solar mass star, a Jupiter mass planet and an additional body with zero mass (elliptic restricted…
The theory of the post-Newtonian (PN) planar circular restricted three-body problem is used for numerically investigating the orbital dynamics of a test particle (e.g., a comet, asteroid, meteor or spacecraft) in the planar Sun-Jupiter…
We develop a framework based on energy kicks for the evolution of high-eccentricity long-period orbits with Jacobi constant close to 3 in the restricted circular planar three-body problem where the secondary and primary masses have mass…
This thesis studies instabilities and singularities in a geometrical approach to the planar 3-body problem as well as instabilities, chaos and ergodicity in the 3-rotor problem. Trajectories of the planar 3-body problem are expressed as…
We investigate the dynamical origin and kinematic signatures of spiral structure in an N-body simulation of an isolated barred galaxy, assessing whether invariant manifold theory provides a consistent dynamical framework to disentangle the…
We discuss the influence of the cosmological constant on the gravitational equations of motion of bodies with arbitrary masses and eventually solve the two-body problem. Observational constraints are derived from measurements of the…
I calculate the classical effects induced by an isotropic mass loss of a body on the orbital motion of a test particle around it; the present analysis is also valid for a variation of the Newtonian constant of gravitation. I perturbatively…
The prospect of unprecedented high-quality data of gravitational waves in the upcoming decades demands a theoretical effort to optimally study and analyze the signals that next generation detectors will provide. Here we study the…
For the Newtonian 4-body problem in space we prove that any zero angular momentum bounded solution suffers infinitely many coplanar instants, that is, times at which all 4 bodies lie in the same plane. This result generalizes a known result…
The so-called Lidov-Kozai oscillation is very well known and applied to various problems in solar system dynamics. This mechanism makes the orbital inclination and eccentricity of the perturbed body in the circular restricted three-body…
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…