Related papers: Elementary Solution of Kepler Problem (and a few o…
We derive new solutions of the Schr\"odinger equation which describe the motion of particles in the Penning trap. These solutions are direct counterparts of classical orbits. They are obtained by injection of classical trajectories into the…
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…
The Pavlov equation is one of the simplest integrable systems of vector fields arising from various problems of mathematical physics and differential geometry which are intensively studied in recent literature. In this report, solving a…
The Christoffel problem is equivalent to the existence of convex solutions to the Laplace equation on the unit sphere $S^n$. Necessary and sufficient conditions have been found by Firey and Berg, using the Green function of the Laplacian on…
The quantum problem of an electron moving in a plane under the field created by two Coulombian centers admits simple analytical solutions for some particular inter-center distances. These elementary eigenfunctions, akin to those found by…
The validity of Kepler Laws for the {\it spherical Kepler problem} -- namely, the problem of the motion of a particle on the unit sphere {in $\mathbb R^3$} undergoing an attraction by another particle in the sphere, tangent to the geodesic…
We present a purely algebraic formulation (i.e. polynomial equations only) of the minimum-cost multi-impulse orbit transfer problem without time constraints, while keeping all the variables with a precise physical meaning. We apply general…
In this paper, we present a new ansatz for solving equations of motion for the trapped orbits of the infinitesimal mass (satellite), which is locked in the space trap to be moving near the planet in case of the elliptic restricted problem…
In this paper, we present the controllability properties of Keplerian motion controlled by low-thrust control systems. The low-thrust control system, compared with high or even impulsive control system, provide a fuel-efficient means to…
We study the motion of a particle in a 3-dimensional lattice in the presence of a Coulomb potential, but we demonstrate semiclassicaly that the trajectories will always remain in a plane which can be taken as a rectangular lattice. The…
The linearized Kepler problem is considered, as obtained from the Kustaanheimo-Stiefel (K-S)transformation, both for negative and positive energies. The symmetry group for the Kepler problem turns out to be SU(2,2). For negative energies,…
We define and analyse a least-squares finite element method for a first-order reformulation of the obstacle problem. Moreover, we derive variational inequalities that are based on similar but non-symmetric bilinear forms. A priori error…
It is shown that the Jacobi problem of geodesics on ellipsoid may be reduced to more simple one, namely to the special case of the Clebsch problem. The last one may be solved directly by using Weber's approach in terms of multi-dimensional…
It is shown that Kepler problem in deformed (quantum) four-dimensional space in non relativistic limit is integrable in quadratures. In non relativistic limit group of motion of quantum space coincide with Galilei one.
In this work we present a semi-classical approach to solve the inverse spectrum problem for one-dimensional wave equations for a specific class of potentials that admits quasi-stationary states. We show how inverse methods for potential…
We establish the existence of multiple solutions for singular quasilinear elliptic problems with a precise sign information: two opposite constant sign solutions and a nodal solution. The approach combines sub-supersolutions method and…
We propose an operational method for the solution of differential equations involving vector products. The technique we propose is based on the use of the evolution operator, defined in such a way that the wealth of techniques developed…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
We describe a simple algorithm for classifying orbits into orbit families. This algorithm works by finding patterns in the sign changes of the principal coordinates. Orbits in the logarithmic potential are studied as an application; we…
An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based in calculations known from classical mechanics, but with the addition of the necessary…