Related papers: Non-Collision singularities in the Planar two-Cent…
In the $n$-body problem, when bodies tend to a total collision, then its normalized shape curve converges to the set of normalized central configurations, which has $SO(3)$ symmetry in the planar case. This leaves a possibility that the…
We study the problem of two Dirac particles interacting through non-relativistic potentials and confined to a two-dimensional sheet, which is the relevant case for graphene layers. The two-body problem cannot be mapped into that of a single…
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…
It is shown that in the planar equal-mass four-body problem, there exist two sets of new action minimizers connecting two planar boundary configurations with fixed symmetry axes and specific order constraints on the four bodies: a double…
The 2-body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in terms of biquaternions and allows us to address questions…
This study presents a solution to the Yakubovsky equations for four-body bound states in momentum space, bypassing the common use of two-body $t-$matrices. Typically, such solutions are dependent on the fully-off-shell two-body…
We consider a symmetric five-body problem with three unequal collinear masses on the axis of symmetry. The remaining two masses are symmetrically placed on both sides of the axis of symmetry. Regions of possible central configurations are…
The geometric approach for Painlev\'e and quasi-Painlev\'e differential equations in the complex plane is applied to non-autonomous Hamiltonian systems, quartic in the dependent variables. By computing their defining manifolds (analogue of…
A new coordinate system on the tangent space to planar configurations is introduced to simplify some calculations on central configurations and relative equilibria in the $N$-body problem with a homogeneous potential, which includes the…
A (globally) neutral two-body system is supposed to obey a pair of coupled Klein-Gordon equations in a constant homogeneous magnetic field. Considering eigenstates of the pseudomomentum four-vector, we reduce these equations to a…
A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order ($G/c^4$ and $G^2/c^4$) in the spin-orbit interaction. We use a novel approach (valid to linear order in the spins),…
We propose and solve exactly the Schr\"odinger equation of a bound quantum system consisting in four particles moving on a real line with both translationally invariant four particles interactions of Wolfes type \cite{Wolf74} and additional…
For the Newtonian (gravitational) $n$-body problem in the Euclidean $d$-dimensional space, $d\ge 2$, the simplest possible periodic solutions are provided by circular relative equilibria, (RE) for short, namely solutions in which each body…
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 consider a system of three identical bosons in $\mathbb{R}^3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$. Using a quadratic form approach we prove that the corresponding Hamiltonian…
In this paper we consider equations of motion for 2-body problem according to an observer close to one of the gravitational bodies. The influence of the Thomas precession of the observer's frame has an important role. The equations of…
A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occur in a pairwise fashion. It is also…
We find an exact solution to the charged 2-body problem in $(1+1)$ dimensional lineal gravity which provides the first example of a relativistic system that generalizes the Majumdar-Papapetrou condition for static balance.
We study the simplest two-body problem in asymptotically anti-de Sitter spacetime: two, infinitely thin, concentric spherical shells of matter. We include only gravitational interaction between the two shells, but we show that the dynamics…
For the gravitational $n$-body problem, the simplest motions are provided by those rigid motions in which each body moves along a Keplerian orbit and the shape of the system is a constant (up to rotations and scalings) configuration…