Related papers: Elementary Solution of Kepler Problem (and a few o…
The classical Kepler-Coulomb problem on the single-sheeted hyperboloid $H^{3}_1$ is solved in the framework of the Hamilton--Jacobi equation. We have proven that all the bounded orbits are closed and periodic. The paths are ellipses or…
We present the applications of variation -- wavelet analysis to polynomial/rational approximations for orbital motion in transverse plane for a single particle in a circular magnetic lattice in case when we take into account multipolar…
We revisit in this note the H\'enon's isochrone problem. By using the standard Abel inversion technique for one-dimensional motion, we recover in a simple way the H\'enon's parabolae and get all isochrone central potentials under mild…
An exact, number-conserving solution to the generalized, orbit-dependent pairing problem is derived by introducing an infinite-dimensional algebra. A method for obtaining eigenvalues and eigenvectors of the corresponding Hamiltonian is also…
In this paper, we use variational minimizing method to prove the existence of hyperbolic solution with a prescribed positive energy for N-body type problems with strong forces. Firstly, we get periodic solutions using suitable constraints,…
The hodograph of the Kepler-Coulomb problem, that is, the path traced by its velocity vector, is shown to be a circle and then it is used to investigate other properties of the motion. We obtain the configuration space orbits of the problem…
In this paper, we provide a procedure to solve the eigen solutions of Dirac equation with complicated potential approximately. At first, we solve the eigen solutions of a linear Dirac equation with complete eigen system, which approximately…
Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite…
An approximate method is proposed for the recovery of a compactly supported spherically-symmetric potential from the set of fixed-energy phase-shifts known for all angular momenta. The method reduces the inverse scattering problem to a…
We investigate the Kepler problem using a symplectic structure consistent with the commutation rules of the noncommutative quantum mechanics. We show that a noncommutative parameter of the order of $10^{-58} \text m^2$ gives observable…
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…
In view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic equation of general character, that unifies and extends earlier results.…
We derive an efficient algorithm to find solutions to Euler's concordant form problem and rational points on elliptic curves associated with this problem.
This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…
A simple method has been introduced to furnish the equilibrium solution of the Wigner equation for all order of the quantum correction. This process builds up a recursion relation involving the coefficients of the different power of the…
A discrete and exact algorithm for obtaining planetary systems is derived in a recent article (Eur. Phys. J. Plus 2022, 137:99). Here the algorithm is used to obtain planetary systems with forces different from the Newtonian inverse square…
Given a smooth function $U(t,x)$, $T$-periodic in the first variable and satisfying $U(t,x) = \mathcal{O}(\vert x \vert^{\alpha})$ for some $\alpha \in (0,2)$ as $\vert x \vert \to \infty$, we prove that the forced Kepler problem $$ \ddot x…
In this paper we show, in a systematic way, how to relate the Kepler problem to the isotropic harmonic oscillator. Unlike previous approaches, our constructions are carried over in the Lagrangian formalism dealing with second order vector…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.