Related papers: The dynamics of the spin-spin problem in Celestial…
The motion of a particle with a spin in spherical harmonic oscillator potential with spin-orbit interaction is studied. We have focus our attention on spatial motion of wave packets, giving a description complementary to motion of spin…
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…
We study the dynamics of planetary systems with two planets moving in the same plane, when frictional forces act on the two planets, in addition to the gravitational forces. The model of the general three-body problem is used. Different…
Starting with a post-Newtonian description of compact binary systems, we derive a set of equations that describes the evolution of the orbital angular momentum and both spin vectors during inspiral. We find regions of phase space that…
Co-orbital planets (in a $1:1$ mean motion resonance) can be formed within a Laplace resonance chain. Here, we develop a secular model to study the dynamics of the resonance chain $p:p:p+1$, where the co-orbital pair is in a first-order…
Among the numerous discoveries resulting from the {\it Kepler} mission are a plethora of compact planetary systems that provide deep insights into planet formation theories. The architecture of such compact systems also produces unique…
We study the resonant dynamics in a simple one degree of freedom, time dependent Hamiltonian model describing spin-orbit interactions. The equations of motion admit periodic solutions associated with resonant motions, the most important…
We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities, also we assume that both planets share the same…
To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…
I consider the dynamics of mean motion resonances between pairs of co-planar planets and derive a new integrable Hamiltonian model for planets' resonant motion. The new model generalizes previously-derived integrable Hamiltonians for…
We establish the evolution equations of the set of independent variables characterizing the 2PN rigorous conservative dynamics of a spinning compact binary, with the inclusion of the leading order spin-orbit, spin-spin and mass quadrupole -…
Due to their focalizing properties, elliptic quantum corrals present very interesting physical behaviors. In this work, we analyze static and dynamical properties of these systems. Results are presented for realistic values of the…
We construct time independent configurations of two gravitating elastic bodies. These configurations either correspond to the two bodies moving in a circular orbit around their center of mass or strictly static configurations.
We solve for the dynamics of a pair of spins, coupled to each other and also to an environmental sea of oscillators. The environment mediates an indirect interaction between the spins, causing both mutual coherence effects and dissipation.…
Elliptical instability is due to a parametric resonance of two inertial modes in a fluid velocity field with elliptical streamlines. This flow is a simple model of the motion in a tidally deformed, rotating body. Elliptical instability…
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…
We discuss a model describing the spin orbit resonance cascade. We assume that the primary has a two-layer (core-shell) structure: it is composed by a thin solid crust and an inner and heavier solid core that are interacting due to the…
We study an orbit of the electromagnetic two-body problem that involves a fast (stiff) spinning motion about a circular orbit. We give a multiscale method of solution that solves for the fast timescale first. The solvability condition of…
We study the orbital evolution of a three planet system with masses in the super-Earth regime resulting from the action of tides on the planets induced by the central star which cause orbital circularization. We consider systems either in…
We review the orbital stability of the planar circular restricted three-body problem, in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill…