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We study the influence of perturbations in the three dimensional isotropic harmonic oscillator problem considering different perturbing force laws and apply our results in the context of celestial mechanics, particularly in the movement of…
We study the stability and chaos of three compact objects using post-Newtonian (PN) equations of motion derived from the Arnowitt-Deser-Misner-Hamiltonian formulation. We include terms up to 2.5 PN order in the orbital part and the leading…
The Maupertuis principle allows us to regard classical trajectories as reparametrized geodesics of the Jacobi-Maupertuis (JM) metric on configuration space. We study this geodesic reformulation of the planar three-body problem with both…
For $n$-body problem with arbitrary positive masses, we prove there are regularizable collinear periodic solutions for any ordering of the masses, going from a simultaneous binary collision to another in half of a period with half of the…
We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the Brutus N-body code to include Post-Newtonian pairwise terms…
In this paper we clarify and generalise previous work by Moser and Belbruno concerning the link between the motions in the classical Kepler problem and geodesic motion on spaces of constant curvature. Both problems can be formulated as…
The invariance of the Lagrangian under time translations and rotations in Kepler's problem yields the conservation laws related to the energy and angular momentum. Noether's theorem reveals that these same symmetries furnish generalized…
We study the classical dynamics of the collinear positron-hydrogen scattering system below the three-body breakup threshold. Observing the chaotic behavior of scattering time signals, we in- troduce a code system appropriate to a coarse…
We study dynamical constraints arising from Embedded Contact Homology (ECH) in the spatial isosceles three-body problem. For energies below the critical level, the dynamics on the energy surface is identified with a Reeb flow on the tight…
This paper presents a study of the Poincar\'e-Hough model of rotation of the synchronous natural satellites, in which these bodies are assumed to be composed of a rigid mantle and a triaxial cavity filled with inviscid fluid of constant…
We consider equal-mass periodic Toda oscillators with balanced loss-gain for two and three particles. The two-particle system is integrable with the Hamiltonian and the genralized total momentum being two integrals of motion. The model in…
By introducing a new coordinate system, we prove that there are abundant new periodic orbits near relative equilibrium solutions of the N-body problem. We consider only Lagrange relative equilibrium of the three-body problem and…
Three-body systems of scalar bosons are described in the framework of relativistic constraint dynamics. With help of a change of variables followed by a change of wave function, two redundant degrees of freedom get eliminated and the…
The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more…
Short time existence of classical solutions is proved for a system of equations that involves a three excitations kinetic operator. The system is related to the description of a gas of bosons below but close to the critical temperature,…
The motion of a relativistic test electron in a free electron laser can be altered significantly by an ideal coaxial wiggler field and uniform axial guide field. I have investigated the group I, group II and group III (the new group that,…
Within the framework of Bonnor's exact solution describing a massive magnetic dipole, we study the motion of neutral and electrically charged test particles. In dependence on the Bonnor spacetime parameters, we determine regions enabling…
As shown by Johannes Kepler in 1609, in the two-body problem, the shape of the orbit, a given ellipse, and a given non-vanishing constant angular momentum determines the motion of the planet completely. Even in the three-body problem, in…
If you are given a simple three-dimensional autonomous quadratic system that has only one stable equilibrium, what would you predict its dynamics to be, stable or periodic? Will it be surprising if you are shown that such a system is…
A new coordinate system is defined for the Four-Body dynamical problem with general masses, having as its origin of coordinates the center of mass. The transformation from the inertial coordinate system involves a combination of a rotation…