Related papers: The tale of two centres
This paper presents a more complete version than hitherto published of our explanation of a transition from regular to irregular motions and more generally of the nature of a certain kind of deterministic chaos. To this end we introduced a…
We introduce a novel, two-mass system that slides up an inclined plane while its center of mass moves down. The system consists of two identical masses connected by an ideal string symmetrically placed over a corner-shaped support. This…
In the classical (non-quantum) relativity theory the course of the moving clock is dilated as compared to the course of the clock at rest (the Einstein dilation). Any unstable system may be regarded as a clock. The time evolution (e.g., the…
The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting…
We study the nonlinear classical dynamics of an electron confined in a double dot potential and subjected to a spin-orbit coupling and a constant external magnetic field. It is shown that due to the spin orbit coupling, the energy can be…
We prove the existence of periodic orbits of the two fixed centers problem bifurcating from the Kepler problem. We provide the analytical expressions of these periodic orbits when the mass parameter of the system is sufficiently small.
We obtain the general static solutions of the axially symmetric (2+1)-dimensional Einstein-Maxwell-Dilaton theory by dimensionally reducing it to a 2-dimensional dilaton gravity theory. The solutions consist of the magnetically charged…
We investigate the cosmological solutions coming from the double field theory equations of motion after coupling a matter source to them. Assuming constant dilaton and imposing the section condition with respect to the regular coordinates…
We study the motion of test particles around a center of attraction represented by a monopole (with and without spheroidal deformation) surrounded by a ring, given as a superposition of Morgan & Morgan discs. We deal with two kinds of…
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles…
It is shown that the set of equations known as Maxwell's equations perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices,…
The action of the isometry subgroup which preserves the trivial values of the fields is studied for the stationary D=4 Einstein--Maxwell--Dilaton--Axion theory. The technique for generation of charges and the corresponding procedure for…
We argue that the non gauge invariant coupling between torsion and the Maxwell or Yang-Mills fields in Einstein-Cartan theory can not be ignored. Arguments based in the existence of normal frames in neighbourhoods, and an approximation to a…
Unlike Einstein gravity, dilaton-Maxwell gravity with matter is renormalizable in $2+\epsilon$ dimensions and has a smooth $\epsilon\to 0$ limit.By performing a renormalization- group study of this last theory we show that the gravitational…
A trajectory isomorphism between the two Newtonian fixed center problem in the sphere and two associated planar two fixed center problems is constructed by performing two simultaneous gnomonic projections in $S^2$. This isomorphism converts…
Test particles interact with a medium by means of a bimolecular reversible chemical reaction. Two species are assumed to be much more numerous so that they are distributed according fixed distributions: Maxwellians and Dirac's deltas.…
The Lagrangian, the Hamiltonian and the constant of motion of the gravitational attraction of two bodies when one of them has variable mass is considered. The relative and center of mass coordinates are not separated, and choosing the…
We introduce and discuss a simple Hamiltonian dynamical system, interpretable as a 3-body problem in the complex plane and providing the prototype of a mechanism explaining the transition from regular to irregular motions as travel on…
We give a comprehensive analysis of the Euler-Jacobi problem of motion in the field of two fixed centers with arbitrary relative strength and for positive values of the energy. These systems represent nontrivial examples of integrable…
Dynamics of regular clusters of many non-touching particles falling under gravity in a viscous fluid at low Reynolds number are analysed within the point-particle model. Evolution of two families of particle configurations is determined: 2…