Related papers: A new method to study relative equilibria on $\mat…
In this paper the non-canonical Hamiltonian dynamics of a gyrostat in the three body problem will be examined. By means of geometric-mechanics methods some relative equilibria of the dynamics of a gyrostat in Newtonian interaction with two…
We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is…
In Einstein's equation we suggest a geometrical object substituting the tensor of energy of impulse and tension. The obtained equation, together with the equation for external field, makes up the complete problem of mathematical equations…
A geometric method, using the Ricci (or mean) curvature of the Lagrangian (configuration) manifold, is used to study the relative instability of evolving $N$-body gravitating systems with massive centres. The performed numerical experiments…
Complex techniques of general relativity are used to determine \emph{all} the states in the two and three dimensional momentum spaces in which the equality holds in the uncertainty relations for the non-commuting basic observables of…
We investigate the stability of motion close to the Lagrangian equilibrium points L4 and L5 in the framework of the spatial, elliptic, restricted three- body problem, subject to the radial component of Poynting-Robertson drag. For this…
This paper is a direct continuation of our old publication where it was found the exact solution of the Einstein-Maxwell equations for two static sources of Reissner-Nordstrom type in the state of the physical equilibrium. Here we present…
In the three-body system with one resonantly interacting pair, we study the behavior of the $S$-matrix pole near the threshold in the fourth quadrant of the unphysical complex energy plane. Our study is essentially based on the unitarity…
Within a scalar model theory of gravity, where the interaction between particles is given by the half-retarded + half-advanced solution of the scalar wave equation, we consider an N-body problem: we investigate configurations of N particles…
The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided…
Einstein's famous equation $E_{\rm rest}=mc^2$ for the rest energy of a system with mass $m$ requires that the internal energy of the system be included in $m$. Pursuing this idea using Lagrangian and Hamiltonian dynamics yields a…
Recently Penrose, Sorkin and Woolgar have developed a new technique for proving the positive mass theorem in general relativity. We extend their result to produce a new inequality relating the mass, electric and scalar charges in theories…
The unexpected dynamic shift of the center of mass for a rotating hemisphere is shown to produce the general relativistic dipole field in the macroscopic scale. This prompts us the question of what might be its cosmological implications.…
We prove for a large class of n-body problems including a subclass of quasihomogeneous n-body problems, the classical n-body problem, the n-body problem in spaces of negative constant Gaussian curvature and a restricted case of the n-body…
Nullification of the Einstein tensor curvature for the elementary material space with active gravitational field (radial source) and passive field distribution of its inertial particle (radial sink) maintains the conceptual equivalence of…
In this paper we consider equations of motion for 2-body problem according to an observer close to one of the gravitational bodies. The influence of the Thomas precession of the observer's frame has an important role. The equations of…
We consider the slowly rotating relativistic stars with a uniform angular velocity in the scalar-tensor gravity, and examine the rotational effect around such compact objects. For this purpose, we derive a 2nd order differential equation…
The harmonic oscillator plays a central role in physics describing the dynamics of a wide range of systems close to stable equilibrium points. The nonrelativistic one-dimensional spring-mass system is considered a prototype representative…
We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical $N$-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using…
The motion of a continuum of matter subject to gravitational interaction is classically described by the Euler-Poisson system. Prescribing the density of matter at initial and final times, we are able to obtain weak solutions for this…