Related papers: Elementary Solution of Kepler Problem (and a few o…
We prove existence and multiplicity of periodic motions for the forced 2-body problem under conditions of topological character. In the different cases, the lower bounds obtained for the number of solutions are related to the winding number…
We prove the existence of one or more solutions to a singularly perturbed elliptic problema with two potential functions.
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part, according to variational approach we obtain a…
In this paper, we propose an orbital iteration based parallel approach for electronic structure calculations. This approach is based on our understanding of the single-particle equations of independent particles that move in an effective…
We calculate the precession of Keplerian orbits under the influence of arbitrary central-force perturbations. Our result is in the form of a one-dimensional integral that is straightforward to evaluate numerically. We demonstrate the…
We introduce a method for solving Calder\'on type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider a model for spin-orbital motion: orbital…
The Lambert problem is to determine the gravitational orbit between two points that has a specified time of flight, allowing the second point to be a moving target such as a satellite. After a review of gravitational orbits, a solution of…
In this paper we prove existence of radial solutions for the nonlinear elliptic problem \[ -\mathrm{div}(A(|x|)\nabla u)+V(|x|)u=K(|x|)f(u) \quad \text{in }\mathbb{R}^{N}, \] \noindent with suitable hypotheses on the radial potentials…
We review basic ideas and basic examples of the theory of the inverse spectral problems.
We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using complex numbers. In particular, we derive in a new way exact…
The goal of the paper is to develop a method that will combine the use of variational techniques with regularization methods in order to study existence and multiplicity results for the periodic and the Dirichlet problem associated to the…
Euler's three-body problem is the problem of solving for the motion of a particle moving in a Newtonian potential generated by two point sources fixed in space. This system is integrable in the Liouville sense. We consider the Euler problem…
We propose an alternative solution to a quantum-mechanical four-particle system in one dimension with two- and three-particle interactions. The solution of the eigenvalue equation in center-of-mass and Jacobi coordinates is considerably…
We solve a difficult problem involving velocity and acceleration components along oblique axes, and propose two problems of central force motion to be solved using oblique axes.
We first discuss the use of dimensional arguments (and of the quadrupolar emission hypothesis) in the derivation of the gravitational power radiated on a circular orbit. Then, we show how to simply obtain the instantaneous power radiated on…
The existence of entire solutions to quasilinear elliptic systems exhibiting both singular and convective reaction terms is discussed. An auxiliary problem, obtained by `freezing' the convection terms and `shifting' the singular ones, is…
The non-linearities of the dynamics of Earth artificial satellites are encapsulated by two formal integrals that are customarily computed by perturbation methods. Standard procedures begin with a Hamiltonian simplification that removes…
The incompressible Micropolar system is given by two coupled equations: the first equation gives the evolution of the velocity field u while the second equation gives the evolution of the microrotation field $\omega$. In this article we…
It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…