Related papers: Approximate action-angle variables for the figure-…
The dynamics of the pseudo-Newtonian restricted four-body problem has been studied in the present paper, where the primaries have equal masses. The parametric variation of the existence as well as the position of the libration points are…
The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more…
We numerically investigate the case of the planar circular restricted three-body problem where the more massive primary is an oblate spheroid. A thorough numerical analysis takes place in the configuration $(x,y)$ and the $(x,E)$ space in…
The essentially unique reduction of the Euler-Poinsot problem may be performed in different sets of variables. Action-angle variables are usually preferred because of their suitability for approaching perturbed rigid-body motion. But they…
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…
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…
We discuss the localization of wavefunctions along planes containing the shortest periodic orbits in a three-dimensional billiard system with axial symmetry. This model mimicks the self-consistent mean field of a heavy nucleus at…
Recent numerical results seem to suggest that in certain regimes of typical particle velocities the gravitational $N-$body problem (for $3\leq N\lesssim 10^3$) is intrinsically less chaotic when the post-Newtonian (PN) force terms are…
For a particular case of three-body scattering in two dimensions, and matching analytical expressions at a transition point, we obtain accurate solutions for the hyperspherical adiabatic basis and potential. We find analytical expressions…
We study three sub-problems of the N-body problem that have two degrees of freedom, namely the n-pyramidal problem, the planar double-polygon problem, and the spatial double-polygon problem. We prove the existence of several families of…
The dynamics of the four-body problem have attracted increasing attention in recent years. In this paper, we extend the basic equilateral four-body problem by introducing the effect of radiation pressure, Poynting-Robertson drag, and solar…
The planar linear restricted four-body problem is used in order to determine the Newton-Raphson basins of convergence associated with the equilibrium points. The parametric variation of the position as well as of the stability of the…
In the 70s McGehee introduced a compactification of the phase space of the restricted 3-body problem by gluing a manifold of periodic orbits "at infinity". Although from the dynamical point of view these periodic orbits are parabolic (the…
Recent advances in spin-dependent optical lattices [Meng et al., Nature \textbf{615}, 231 (2023)] have enabled the experimental implementation of two superimposed three-dimensional lattices, presenting new opportunities to investigate…
We give a geometric account of the relative motion or the shape dynamics of $N$ point vortices on the sphere exploiting the $\mathsf{SO}(3)$-symmetry of the system. The main idea is to bypass the technical difficulty of the…
In a realistic scenario, the evolution of the rotational dynamics of a celestial or artificial body is subject to dissipative effects. Time-varying non-conservative forces can be due to, for example, a variation of the moments of inertia or…
It is well-known that complex hyperbolic triangle groups $\Delta(3,3,4)$ generated by three complex reflections $I_1,I_2,I_3$ in $\mbox{PU(2,1)}$ has 1-dimensional moduli space. Deforming the representations from the classical…
The one body density matrix, momentum distribution, natural orbits and quasi hole states of 16O and 40Ca are analyzed in the framework of the correlated basis function theory using state dependent correlations with central and tensor…
We study the equal-mass classical three rotor problem, a variant of the three body problem of celestial mechanics. The quantum $N$-rotor problem has been used to model chains of coupled Josephson junctions and also arises via a partial…
We investigate performing classical and quantum metrology and parameter estimation by using interacting trapped bosons, which we theoretically treat by a self-consistent many-body approach of the multiconfigurational Hartree type. Focusing…