Related papers: New Bound Closed Orbits in Spherical Potentials
We study the orbit of a single particle moving under the Yukawa potential and observe the precessing ellipse type orbits. The amount of precession can be tuned through the coupling parameter $\alpha$. With a suitable choice of the coupling…
The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…
In presence of magnetic fields, the orbits of charged particles can be displaced from the equatorial plane. We study circular orbits of electrically charged massive objects around a magnetic black hole in the probe approximation. We show…
Periodic orbits are the central ingredients of modern semiclassical theories and corrections to these are generally non-classical in origin. We show here that for the class of generic polygonal billiards, the corrections are predominantly…
In this paper we study the properties of the periodic orbits of \"x + V'_x(t, x) = 0 with x \in S1 and V(t, x) a T0 periodic potential. Called {\rho} \in (1/T0)Q the frequency of windings of an orbit in S1 we show that exists an infinite…
Bertrand theorem permits closed orbits in 3d Euclidean space only for 2 types of central potentials. These are of Kepler-Coulomb and harmonic oscillator type. Volker Perlick recently extended Bertrand theorem. He designed new static…
We show that in the semiclassical limit, classically chaotic systems have universal spectral statistics. Concentrating on short-time statistics, we identify the pairs of classical periodic orbits determining the small-$\tau$ behavior of the…
The closedness of orbits of central forces is addressed in a three dimensional space in which the Poisson bracket among the coordinates is that of the SU(2) Lie algebra. In particular it is shown that among problems with spherically…
A useful crude approximation for Abelian functions is developed and applied to orbits. The bound orbits in the power-law potentials A*r^{-alpha} take the simple form (l/r)^k = 1 + e cos(m*phi), where k = 2 - alpha > 0 and 'l' and 'e' are…
The nonlinear Schr\"odinger/Gross-Pitaevskii (NLS/GP) equation is considered in the presence of three equally-spaced potentials. The problem is reduced to a finite-dimensional Hamiltonian system by a Galerkin truncation. Families of…
We treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this setting the main result of [4] is applicable. This guarantees…
Bertrand's theorem in classical mechanics of the central force fields attracts us because of its predictive power. It categorically proves that there can only be two types of forces which can produce stable, circular orbits. In the present…
The classical trajectories of the family of complex PT-symmetric Hamiltonians $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) form closed orbits. All such complex orbits that have been studied in the past are PT symmetric (left-right symmetric).…
Coorbital bodies are observed around the Sun sharing their orbits with the planets, but also in some pairs of satellites around Saturn. The existence of coorbital planets around other stars has also been proposed. For close-in planets and…
This paper formalize the existence's proof of first-integrals for any second order ODE, allowing to discriminate periodic orbits. Up to the author's knowledge, such a powerful result is not available in the literature providing a tool to…
We establish a new relation between classical observables for scattering and bound orbits of a massive probe particle in a Kerr background. We find an exact representation of the Hamilton-Jacobi action in terms of the conserved charges…
In the framework of the planar restricted three body problem we study a considerable number of resonances associated to the Kuiper Belt dynamics and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic…
We perform a numerical analysis of the gravitational field of a global monopole coupled nonminimally to gravity, and find that, for some given nonminimal couplings (in constrast with the minimal coupling case), there is an attractive region…
A method is presented for determining the initial conditions of classical orbits from the quantum spectra of the diamagnetic hydrogen atom. Each classical trajectory which is closed at the nucleus produces a sinusoidal fluctuation in the…
The quest of exo-Earths has become a prominent field. In this work, we study the stability of non-coplanar planetary configurations consisting of an inclined inner terrestrial planet in mean-motion resonance with an outer giant planet. We…