相关论文: New results on orbital resonances

We consider particles with low free or proper eccentricity that are orbiting near planets on eccentric orbits. Via collisionless particle integration we numerically find the location of the boundary of the chaotic zone in the planet's…

In our Solar system, spin-orbit resonances are common under Sun--planet, planet--satellite and binary asteroid configurations. In this work, high-order and secondary spin-orbit resonances are investigated by taking numerical and analytical…

Motivated by the population of multi-planet systems with orbital period ratios 1<P2/P1<2, we study the long-term stability of packed two planet systems. The Hamiltonian for two massive planets on nearly circular and nearly coplanar orbits…

The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…

Context: Resonances in the stellar orbital motion under perturbations from spiral arms structure play an important role in the evolution of the disks of spiral galaxies. The epicyclic approximation allows the determination of the…

The early stages of dynamical evolution of planetary systems are often shaped by dissipative processes that drive orbital migration. In multi-planet systems, convergent amassing of orbits inevitably leads to encounters with rational period…

Robust heteroclinic cycles are known to change stability in resonance bifurcations, which occur when an algebraic condition on the eigenvalues of the system is satisfied and which typically result in the creation or destruction of a…

A condition upon which sporadic bursts (intermittent behaviour) of the relative energy become possible is derived for the motion in the chaotic layer around the separatrix of non-linear resonance. This is a condition for the existence of a…

Modern theoretical methods for estimating the width of the chaotic layer in presence of prominent marginal resonances are considered in the perturbed pendulum model of nonlinear resonance. The fields of applicability of these methods are…

Previous studies have shown that planets that rotate retrograde (backwards with respect to their orbital motion) generally experience less severe obliquity variations than those that rotate prograde (the same direction as their orbital…

The majority of extrasolar planets discovered to date have significantly eccentric orbits, some if not all of which may have been produced through planetary migration. During this process, any planets interior to such an orbit would…

Planets around binary stars and those in multiplanet systems may experience resonant eccentricity excitation and disruption due to perturbations from a distant stellar companion. This "evection resonance" occurs when the apsidal precession…

We test a crossing orbit stability criterion for eccentric planetary systems, based on Wisdom's criterion of first order mean motion resonance overlap (Wisdom, 1980). We show that this criterion fits the stability regions in real exoplanet…

We present a general analysis of the orbit structure of 2D potentials with self-similar elliptical equipotentials by applying the method of Lie transform normalization. We study the most relevant resonances and related bifurcations. We find…

The orbit of a planet is surrounded by a chaotic zone wherein nearby particles' orbits are chaotic and unstable. Wisdom (1980) showed that the chaos is driven by the overlap of mean motion resonances which occurs within a distance…

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…

Our concern here is the nature of secondary resonances--commensurabilities between apsidal and libration periods lying within first-order mean motion resonances [mmr] in the solar system. At the 4/3 and 3/2 mmr in the asteroid belt, we find…

Mean motion resonances (MMRs) are a key phenomenon in orbital dynamics. The traditional disturbing function expansion in celestial mechanics shows that, at low eccentricities, $p$:$p-q$ MMRs exhibit a clear hierarchy of strengths, scaling…

We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under $Z_2 \times Z_2$ symmetry. The rich…

We study two uncoupled oscillators, horizontal and vertical, residing in rectilinear polygons (with only vertical and horizontal sides) and impacting elastically from their boundary. The main purpose of the article is to analyze the…