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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…
A Hamiltonian that approaches the study of the three-body problem in general relativity is obtained. We use it to study the relativistic version of the circular restricted three-body problem in which the first body is the heaviest and the…
We show that, for the scalar field cosmology with exponential potential, the set of values of the coupling parameter for which the solutions undergo a transient period of acceleration is much larger than the set discussed in the literature.…
The scattering of small bodies by planets is an important dynamical process in planetary systems. We present an analytical model to describe this process using the simplifying assumption that each particle's dynamics is dominated by a…
Attaining the ultimate precision remains a central objective in the engineering of nanoscale systems and the investigation of nonequilibrium processes. While thermodynamic and kinetic uncertainty relations establish fundamental precision…
Some novel TWO-body effects analogous to the well-known THREE-body Efimov effect are predicted. In the systems considered, particle A is constrained on a TRUNCATED or BENT one-dimensional line or two-dimensional plane, or on one side of a…
Fractons are exotic quasiparticles whose mobility in space is restricted by symmetries. In potential real-world realisations, fractons are likely lodged to a physical material rather than absolute space. Motivated by this, we propose and…
We consider a restricted four-body problem with a precise hierarchy between the bodies: two point-mass bigger bodies, a smaller one with oblate shape, and an infinitesimal body in the neighborhood of the oblate body. The three heavy bodies…
We consider the motion of a rigid body immersed in an incompressible perfect fluid which occupies a three-dimensional bounded domain. For such a system the Cauchy problem is well-posed locally in time if the initial velocity of the fluid is…
We consider either 3 spinless bosons or 3 equal mass spin-1/2 fermions, interacting via a short range potential of infinite scattering length and trapped in an isotropic harmonic potential. For a zero-range model, we obtain analytically the…
Decoherence is ubiquitous in quantum physics, from the conceptual foundations to quantum information processing or quantum technologies, where it is a threat that must be countered. While decoherence has been extensively studied for simple,…
The size distribution and orbital architecture of dust, grains, boulders, asteroids, and major planets during the giant branch phases of evolution dictate the preponderance and observability of the eventual debris, which have been found to…
For the zero-range interaction providing a given mass M_2 of the two-body bound state, the mass M_3 of the relativistic three-boson state is calculated. We have found that the three-body system exists only when M_2 is greater than a…
We study the long term evolution of the distance between two Keplerian confocal trajectories in the framework of the averaged restricted 3-body problem. The bodies may represent the Sun, a solar system planet and an asteroid. The secular…
We treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this setting the main result of [4] is applicable. This guarantees…
Confined to small regions, quantum systems exhibit electronic and structural properties different from their free space behavior. In Coulomb 3-body problems, configurations of close proximity of identically charged particles are classically…
More than 10% of extra-solar planets (EPs) orbit in a binary or multiple stellar system. We investigated the motion of planets revolving in binary systems in the frame of the particular case of the three body problem. We carried out an…
Paradoxes in the impact dynamics of rigid bodies are known to arise in the presence of friction. We show here that, on specificc occasions, in the absence of friction, the conservation laws of classical mechanics are also incompatible with…
In the Newtonian limit of $f(R)$ gravity, for an isolated self-gravitating system consisting of $N$ extended fluid bodies, the inter-body dynamics are studied by applying the symmetric and trace-free formalism in terms of irreducible…
The gravitational $N$-body problem is a nearly universal problem in astrophysics which, despite its deceptive simplicity, still presents a significant computational challenge. For collisional systems such as dense star clusters, the need to…