Related papers: Corrected Newtonian potentials in the two-body pro…
A general new technique to solve the two-center problem with arbitrarily-orientated deformed realistic potentials is demonstrated, which is based on the powerful potential separable expansion method. As an example, molecular single-particle…
In this treatise the well-known 2-body problem with a rotating central body is systematically reinvestigated on the basis of the Projective Unified Field Theory (PUFT) under the following aspects (including the special case of the Newton…
We consider the impact of a power-law correction to the Newtonian potential, inspired by ungravity or $f(R)$ extensions of the Standard Model, and draw conclusions on the possibility of measuring the relevant parameters through observables…
We consider the Novikov problem, namely, the problem of describing the level lines of quasiperiodic functions on the plane, for a special class of potentials that have important applications in the physics of two-dimensional systems.…
We investigate the qualitative characteristics of a test particle attracted to an irregular elongated body, modeled as a non-homogeneous straight segment with a variable linear density. By deriving the potential function in closed form, we…
Synergies between self-force theory and other approaches to the gravitational two-body problem have traditionally relied on calculations of gauge-invariant observables as functions of orbital frequencies. However, in self-force theory one…
Exact solutions are found for Euler's equations of rigid body motion for general asymmetrical bodies under the influence of torque by using Jacobi elliptic functions. Differential equations are determined for the amplitudes and the…
In this paper, we consider the dual fractional parabolic problem in the right half space. We prove that the positive solutions are strictly increasing in $x_1$ direction without assuming the solutions be bounded. So far as we know, this is…
We develop a series of resonant short-range two-boson potentials reproducing the same two-body low-energy observables and apply them in three- and four-body calculations. We demonstrate that the universal behavior predicted by effective…
We study the resonant dynamics in a simple one degree of freedom, time dependent Hamiltonian model describing spin-orbit interactions. The equations of motion admit periodic solutions associated with resonant motions, the most important…
We consider quantum mechanical effects of the modified Newtonian potential in the presence of extra compactified dimensions. We develop a method to solve the resulting Schroedinger equation and determine the energy shifts caused by the…
This work deals with the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. If the potential has no inversion symmetry and its fluctuations are asymmetric and correlated in time, a net flow can be generated…
The dynamics of extended bodies is a fundamental problem in any gravitational theory. In the case of General Relativity, this problem is under study since the theory was published. Several methods have been developed and different…
An identity that relates multipolar solutions of the Einstein equations to Newtonian potentials of bars with linear densities proportional to Legendre polynomials is used to construct analytical potential-density pairs of infinitesimally…
This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been…
Laboratory experiments on gravitation are usually performed with objects of constant density, so that the analysis of the forces concerns only the geometry of their shape. In an ideal experiment, the shapes of the constituent parts will be…
We find a new solution to calculate the orbital periastron advance of a test body subject to a central gravitational force field, for relativistic theories and models beyond Einstein. This analitycal formula has general validity that…
We study the properties of the Newtonian gravitational potential in a spherical Universe for different topologies. For this, we use the non-Euclidean Newtonian theory developed in Vigneron [2022, Class. & Quantum Gravity, 39, 155006]…
The case of the planar circular restricted three-body problem where one of the two primaries has a stronger gravitational field with respect to the classical Newtonian field is investigated. We consider the case where two primaries have the…
Using a fixed-energy amplitude in Randall-Sundrum single brane scenario, we compute the Newton potential on the brane. It is shown that the correction terms to the Newton potential involve a logarithmic factor. Especially, when the distance…