Related papers: Chaotic dynamics for the two body problem on a sph…

We consider a problem of mass points interacting gravitationally whose motion is subjected to certain holonomic constraints. The motion of points is restricted to certain curves and surfaces. We illustrate the complicated behaviour of…

In the present paper, using the first-order approximation of the $n$-body Lagrangian (derived on the basis of the post-Newtonian gravitational theory of Einstein, Infeld, and Hoffman), we explicitly write down the equations of motion for…

We consider the Bohmian trajectories in a 2-d quantum harmonic oscillator with non commensurable frequencies whose wavefunction is of the form $\Psi=a\Psi_{m_1,n_1}(x,y)+b\Psi_{m_2,n_2}(x,y)+c\Psi_{m_3,n_3}(x,y)$. We first find the…

A half century ago, Lorenz found the "butterfly effect" of chaotic dynamic systems and made his famous claim that long-term prediction of chaos is impossible. However, the meaning of the "long-term" in his claim is not very clear. In this…

We investigate regular and chaotic dynamics of Two Bodies Swinging on a Rod, which differs from all the other mechanical analogies: depending on initial conditions, its oscillation could end very quickly and the reason is not a drag force…

We prove that one cannot construct, for arbitrary initial data, global-in-time physical classical solutions to Euler's equations of continuum rigid body mechanics when the constituent rigid bodies are not perfect spheres. By 'physical'…

In the framework of the scale relativity theory, the chaotic behavior in time only of a number of macroscopic systems corresponds to motion in a space with geodesics of fractal dimension 2 and leads to its representation by a…

We prove that for large enough data, the life span of smooth solutions to the Cauchy problem for the following two quasilinear hyperbolic systems is finite: (1) equations of relativistic compressible fluid dynamics, (2) equations of plasma…

The circular restricted three body problem, which considers the dynamics of an infinitesimal particle in the presence of the gravitational interaction with two massive bodies moving on circular orbits about their common center of mass, is a…

In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…

We present numerical simulation results of driven vortex lattices in presence of random disorder at zero temperature. We show that the plastic dynamics is readily understood in the framework of chaos theory. Intermittency "routes to chaos"…

In this paper we first prove the existence and uniqueness of the solution to the stochastic Navier--Stokes equations on the rotating 2-dimensional sphere. Then we show the existence of an asymptotically compact random dynamical system…

An approach is developed to find approximate solutions to the classical Newtonian problem of N bodies. Sets of N gravitating bodies having spherically symmetric mass distributions, small angular velocities (< 1 rad/s) and bounded position…

We study the Bohmian dynamics of a large class of bipartite systems of non-ideal qubit systems, by modifying the basic physical parameters of an ideal two-qubit system, made of coherent states of the quantum harmonic oscillator. First we…

We investigate the relationship between rigid motions and relative equilibria in the N-body problem on the two-dimensional sphere, S2. We prove that any rigid motion of the N-body system on S2 must be a relative equilibrium. Our approach…

Extrasolar planetary systems commonly exhibit planets on eccentric orbits, with many systems located near or within mean-motion resonances, showcasing a wide diversity of orbital architectures. Such complex systems challenge traditional…

We study dynamics of a ball moving in gravitational field and colliding with a moving table. The motion of the limiter is assumed as periodic with piecewise constant velocity - it is assumed that the table moves up with a constant velocity…

We consider the dynamics and symplectic reduction of the 2-body problem on a sphere of arbitrary dimension. It suffices to consider the case for when the sphere is 3-dimensional and where we take the group of symmetries to be $SO(4)$. As…

A 3D-dynamical model is constructed for the study of motion in the central regions of a disk galaxy with a double nucleus. Using the results of the 2D-model, we find the regions of initial conditions in the (x,px,z,py)=EJ, (y=pz=0) phase…

Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…