Related papers: Periodic Orbits and Binary Collisions in the Class…
In this contribution, the optimal stabilization problem of periodic orbits is studied via invariant manifold theory and symplectic geometry. The stable manifold theory for the optimal point stabilization case is generalized to the case of…
We provide a statistical and correlational analysis of the spatial and energetic properties of equilibrium configurations of a few-body system of two to eight equally charged classical particles that are confined on a one-dimensional…
We consider Hamiltonian functions of classical type, namely even and convex with respect to the generalized momenta. A brake orbit is a periodic solution of Hamilton's equations such that the generalized momenta are zero on two different…
The Dirac-Coulomb equation for helium-like ions is solved using the iterative self-consistent field method, with Slater-type spinor orbitals as the basis. These orbitals inherently satisfy the kinetic-balance condition due to their coupling…
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the…
The relativistic quantum mechanics of two interacting particles is considered. We first present a covariant formulation of kinematics and of reduced phase space, giving a short outline of the classical results. We then quantize the systems…
Describing general quantum many-body dynamics is a challenging task due to the exponential growth of the Hilbert space with system size. The time-dependent variational principle (TDVP) provides a powerful tool to tackle this task by…
We consider the planar three-body problem perturbed by a celestial body modeled as a time-dependent perturbation that decays in time. We assume that the motion of the celestial body is given and is unbounded with a non-zero asymptotic…
We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed…
We examine the possible trajectories of a classical particle, trapped in a two-dimensional infinite rectangular well, using the Hamilton-Jacobi equation. We observe that three types of trajectories are possible: periodic orbits, open orbits…
We investigate the secular dynamics of a planetary system composed of the parent star and two massive planets in mutually inclined orbits. The dynamics are investigated in wide ranges of semi-major axes ratios (0.1-0.667), and planetary…
In this paper we present both the classical and quantum periodic-orbits of a neutral spinning particle constrained in two-dimensional central-potentials with a cylindrically symmetric electric-field in addition which leads to an effective…
We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…
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…
The numerical optimized shooting method for finding periodic orbits in nonlinear dynamical systems was employed to determine the existence of periodic orbits in the well-known R\"ossler system. By optimizing the period $T$ and the three…
The description of unstable motions in the Restricted Planar Circular 3-Body Problem, modeling the dynamics of a Sun-Planet-Asteriod system, is one of the fundamental problems in Celestial Mechanics. The goal of this paper is to analyze…
We apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four body problem with masses 1, m, m, 1, and also in a…
We derive, in 2+1 dimensions, classical solutions for metric and motion of two or more spinning particles, in the conformal Coulomb gauge introduced previously. The solutions are exact in the $N$-body static case, and are perturbative in…
The three-body problem is reexamined in the framework of general relativity. The Newtonian three-body problem admits Euler's collinear solution, where three bodies move around the common center of mass with the same orbital period and…
We present an illustrative application of the two famous mathematical theorems in differential topology in order to show the existence of periodic orbits with arbitrary given period for a class of hamiltonians .This result point out for a…