Related papers: Creating deterministic collisions between two orbi…
A collision of a rubber rod to a hard floor is regarded as a simple example of obstacle problems for elastic material. In this article we have proposed a new mathematical model for the collision phenomenon by applying beam equations with…
This paper deals with the theory of collisions between two ultracold particles with a special focus on molecules. It describes the general features of the scattering theory of two particles with internal structure, using a time-independent…
The circular orbits and elliptical orbits of moving objects in a gravitational field are essential information in astronomy. There have been many methods developed in the literature and textbooks to describe these orbits. In this report, I…
The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.
We study collisions of many point-like particles in three-dimensional anti-de Sitter space, generalizing the known result with two particles. We show how to construct exact solutions corresponding to the formation of either a black hole or…
The mean angular momentum associated with the collision of two celestial objects moving in almost circular heliocentric orbits was studied. The results of these studies were used to develop models of the formation of binaries at the stage…
We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained…
A fast algorithm to study one-dimensional self-gravitating systems, and, more generally, systems that are Lagrangian integrable between collisions, is presented. The algorithm is event-driven, and uses a heap-ordered set of predicted future…
In this paper we study two electrons on a line on the same side of the nucleus which interact with each other by their mean value. We prove that there exists a unique periodic orbit and examine for which charges the two orbits of the…
Recently Usov's mechanism of pair creation on the surface of compact astrophysical objects has been revisited [1] with a conclusion that the pair creation rate was previously underestimated in the literature by nearly two orders of…
We study the orbits of two interacting particles described by a fully relativistic classical mechanical Hamiltonian. We use two sets of initial conditions. In the first set (dynamics 1) the system's center of mass is at rest. In the second…
The dynamics of planetesimals plays an important role in planet formation, because their velocity distribution sets the growth rate to larger bodies. When planetesimals form in protoplanetary discs, their orbits are nearly circular and…
We show that short-term perturbations among massive planets in multiple planet systems can result in radial velocity variations of the central star which differ substantially from velocity variations derived assuming the planets are…
We describe aspects of particle creation in strong fields using a quantum kinetic equation with a relaxation-time approximation to the collision term. The strong electric background field is determined by solving Maxwell's equation in…
We propose a new approach to the Casimir effect based on classical ray optics. We define and compute the contribution of classical optical paths to the Casimir force between rigid bodies. We reproduce the standard result for parallel plates…
We present a new method for computing orbits in the perturbed two-body problem: the position and velocity vectors of the propagated object in Cartesian coordinates are replaced by eight orbital elements, i.e., constants of the unperturbed…
A massive, charged, spherical central body can be neutralized by attracting particles of opposite charge. We calculate the time it takes to neutralize these central bodies using classical mechanics, special relativistic mechanics, and…
In recent works, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential, and examined the proposed mechanics of turbulence formation in a simple model of two particles for a variety…
In this paper, we consider a time-periodically forced Kepler problem in any dimensions, with an external force which we only assume to be regular in a neighborhood of the attractive center. We prove that there exist infinitely many periodic…
We study the circumstances under which first collisions occur in young and dense star clusters. The initial conditions for our direct $N$-body simulations are chosen such that the clusters experience core collapse within a few million…