Related papers: Linearized averaged resonant equations and their s…
This paper investigates the secular motion of a massless asteroid within the framework of the double-averaged elliptic restricted three-body problem. By employing Poincar\'e variables, we analyze the stability properties of asteroid orbits…
Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…
In this work we classify all radial non-radiative solutions to the 5D nonlinear wave equations with a wide range of energy critical nonlinearity. We show that such a solution always comes with two characteristic numbers. These…
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…
Exact solutions of several nonstationary problems of quantum mechanics are obtained. It is shown that if the initial conditions of the problem correspond to the localized-in-space particle, then it moves exactly along the classical…
We consider the general case of an accelerating, expanding and shearing model of a radiating relativistic star using Lie symmetries. We obtain the Lie symmetry generators that leave the equation for the junction condition invariant, and…
An elliptic relative equilibrium (ERE) is a special solution of the planar $N$-body problem generated by a central configuration. Its linear stability depends on the eccentricity $e$ and the masses of the bodies. However, for $e>0$, the…
The regularization of a new problem, namely the three-body problem, using 'similar' coordinate system is proposed. For this purpose we use the relation of 'similarity', which has been introduced as an equivalence relation in a previous…
The paper is devoted to the motion of a body in a fluid under the influence of gravity and drag. Depending on the regime considered, the drag force can exhibit a linear, quadratic or even more general dependence on the velocity of the body…
In 1993, a proof was published, within ``Classical and Quantum Gravity,'' that there are no regular solutions to the {\it linearized} version of the twisting, type-N, vacuum solutions of the Einstein field equations. While this proof is…
For the study of nonlinear stability of a dynamical system, normalized Hamiltonian of the system is very important to discuss the dynamics in the vicinity of invariant objects. In general, it represents a nonlinear approximation to the…
The linearization of a type of $f(R)$ gravity is studied directly in the higher-order frame for an arbitrary five-dimensional warped space-time background. The quadratic actions of the normal modes of the scalar, vector, and tensor…
Ill-posed inverse problems are common in astronomy, and their solutions are unstable with respect to noise in the data. Solutions of such problems are typically found using two classes of methods: parametrization and fitting the data…
We study the thermalization of the classical Klein-Gordon equation under a u^4 interaction. We numerically show that even in the presence of strong nonlinearities, the local thermodynamic equilibrium state exhibits a weakly nonlinear…
Let a number, N, of particles interact classically through Newton's Laws of Motion and Newton's inverse square Law of Gravitation. The resulting equations of motion provide an approximate mathematical model with numerous applications in…
We apply the open systems concept and the influence functional formalism introduced in Paper I to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the…
The dynamics of quantum systems can be approximated by the time propagation of Gaussian wave packets. Applying a time dependent variational principle, the time evolution of the parameters of the coupled Gaussian wave packets can be…
Pulsars are believed to loose their rotational kinetic energy primarily by a large amplitude low frequency electromagnetic wave which is eventually converted into particle creation, acceleration and followed by a broad band radiation…
The restricted (equilateral) four-body problem consists of three bodies of masses m1, m2 and m3 (called primaries) lying in a Lagrangian config- uration of the three-body problem, i,e,. they remain fixed at the apices of an equilateral…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…