Related papers: Separation of Potentials in the Two-Body Problem
We present an alternative organizational scheme for developing effective theories of 2- and 3-body systems that is systematic, accurate, and efficient with controlled errors. To illustrate our approach we consider the bound state and…
The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a…
Inspired by string theory ideas, we probe quantum entanglement from the gravitational potential energy. Concretely, we reconsider the study of quantum corrections to the Newtonian potential energy by treating a massive two-particle system…
We consider a two-dimensional, incompressible fluid body, together with self-induced interactions. The body is perturbed by an external particle with small mass. The whole configuration rotates uniformly around the common center of mass. We…
A new approach to the two-body problem based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one is developed. The wave equation with various forms of including the interaction for the system of the spin-1/2 and spin-0 particles is…
A theory of self-propelled particles is developed in two dimensions assuming that the particles can be deformed from a circular shape when the propagating velocity is increased. A coupled set of equations in terms of the velocity and a…
We evaluate the {\em three-dimensional}, {\em non-axis-symmetric}, {\em time-dependent} Newton potential generated by a pair of mutually orbiting objects such as pairs of ordinary or neutron stars and, in some approximations, black holes,…
We derive the equations of motion of test bodies for a theory with nonminimal coupling by means of a multipole method. The propagation equations for pole-dipole particles are worked out for a gravity theory with a very general coupling…
Although rare, collisions of two or more bodies in the N-body problem are apparent obstacles at which Newton's Law of Gravity ceases to make sense. Without understanding the nature of collisions, a complete understanding of the N-body…
We show that two different notions of solutions to the obstacle problem for the porous medium equation, a potential theoretic notion and a notion based on a variational inequality, coincide for regular enough compactly supported obstacles.
One of the outstanding problems of classical celestial mechanics was the restricted 3-body prob- lem, in which a planetoid of small mass is subject to the Newtonian attraction of two celestial bodies of large mass, as it occurs, for…
The study of the dynamics of a two-body system in modified gravity constitutes a more complex problem than in Newtonian gravity. Numerical methods are typically needed to solve the equations of geodesics. Despite the complexity of the…
As shown by Johannes Kepler in 1609, in the two-body problem, the shape of the orbit, a given ellipse, and a given non-vanishing constant angular momentum determines the motion of the planet completely. Even in the three-body problem, in…
The usual equation for both motions of a single planet around the sun and electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena…
A kinematics of the motion of a car is reformulated in terms of the theory of gauge potentials (connection on principal bundle). E(2)-connection originates in the no-slipping contact of the car with a road.
Equations of motion are derived for (visco)elastic, self-gravitating, and variably-rotating planets. The equations are written using a decomposition of the elastic motion that separates the body's elastic deformation from its net…
We revisit the Keplerian-like parametrization of the two-body problem in Yukawa gravity studied in the literature. Some inconsistencies, which spoil Bertrand's theorem, observed in the $\eta$ parametrization of the true anomaly $\theta$ and…
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the…
This paper presents a general formulation of equations of motion of a pendulum with n point mass by use of two different methods. The first one is obtained by using Lagrange Mechanics and mathematical induction(inspection), and the second…
We study here the behaviour of solutions for conjugated (antipodal) points in the $2$-body problem on the two-dimensional sphere $\mathbb{M}^2_R$. We use a slight modification of the classical potential used commonly in \cite{Borisov},…