302 research outputs found
Resonant periodic orbits in the exoplanetary systems
The planetary dynamics of , , , and 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. Both planar and spatial cases are examined. In the spatial problem,
families of periodic orbits are obtained after analytical continuation of
vertical critical orbits. The linear stability of orbits is also examined.
Concerning initial conditions nearby stable periodic orbits, we obtain
long-term planetary stability, while unstable orbits are associated with
chaotic evolution that destabilizes the planetary system. Stable periodic
orbits are of particular importance in planetary dynamics, since they can host
real planetary systems. We found stable orbits up to of mutual
planetary inclination, but in most families, the stability does not exceed
-, depending on the planetary mass ratio. Most of these
orbits are very eccentric. Stable inclined circular orbits or orbits of low
eccentricity were found in the and resonance, respectively.Comment: Accepted for publication in Astrophysics and Space Science. Link to
the published article on Springer's website was inserte
Vertical instability and inclination excitation during planetary migration
We consider a two-planet system, which migrates under the influence of
dissipative forces that mimic the effects of gas-driven (Type II) migration. It
has been shown that, in the planar case, migration leads to resonant capture
after an evolution that forces the system to follow families of periodic
orbits. Starting with planets that differ slightly from a coplanar
configuration, capture can, also, occur and, additionally, excitation of
planetary inclinations has been observed in some cases. We show that excitation
of inclinations occurs, when the planar families of periodic orbits, which are
followed during the initial stages of planetary migration, become vertically
unstable. At these points, {\em vertical critical orbits} may give rise to
generating stable families of periodic orbits, which drive the evolution
of the migrating planets to non-coplanar motion. We have computed and present
here the vertical critical orbits of the and resonances, for
various values of the planetary mass ratio. Moreover, we determine the limiting
values of eccentricity for which the "inclination resonance" occurs.Comment: Accepted for publication in Celestial Mechanics and Dynamical
Astronom
Inclined asymmetric librations in exterior resonances
Librational motion in celestial mechanics is generally associated with the
existence of stable resonant configurations and signified by the existence of
stable periodic solutions and oscillation of critical (resonant) angles. When
such an oscillation takes place around a value different than 0 or , the
libration is called asymmetric. In the context of the planar circular
restricted three-body problem (CRTBP), asymmetric librations have been
identified for the exterior mean-motion resonances (MMRs) 1:2, 1:3 etc. as well
as for co-orbital motion (1:1). In exterior MMRs the massless body is the outer
one. In this paper, we study asymmetric librations in the 3-dimensional space.
We employ the computational approach of Markellos (1978) and compute families
of asymmetric periodic orbits and their stability. Stable, asymmetric periodic
orbits are surrounded in phase space by domains of initial conditions which
correspond to stable evolution and librating resonant angles. Our computations
were focused on the spatial circular restricted three-body model of the
Sun-Neptune-TNO system (TNO= trans-Neptunian object). We compare our results
with numerical integrations of observed TNOs, which reveal that some of them
perform 1:2-resonant, inclined asymmetric librations. For the stable 1:2 TNOs
librators, we find that their libration seems to be related with the vertically
stable planar asymmetric orbits of our model, rather than the 3-dimensional
ones found in the present study.Comment: Accepted for publication in CeMD
Driving white dwarf metal pollution through unstable eccentric periodic orbits
Context. Planetary debris is observed in the atmospheres of over 1000 white dwarfs, and two white dwarfs are now observed to contain orbiting minor planets. Exoasteroids and planetary core fragments achieve orbits close to the white dwarf through scattering with major planets. However, the architectures that allow for this scattering to take place are time-consuming to explore with N-body simulations lasting ∼1010 yr; these long-running simulations restrict the amount of phase space that can be investigated.
Aims. Here we use planar and three-dimensional (spatial) elliptic periodic orbits, as well as chaotic indicators through dynamical stability maps, as quick scale-free analytic alternatives to N-body simulations in order to locate and predict instability in white dwarf planetary systems that consist of one major and one minor planet on very long timescales. We then classify the instability according to ejection versus collisional events.
Methods. We generalized our previous work by allowing eccentricity and inclination of the periodic orbits to increase, thereby adding more realism but also significantly more degrees of freedom to our architectures. We also carried out a suite of computationally expensive 10 Gyr N-body simulations to provide comparisons with chaotic indicators in a limited region of phase space.
Results. We compute dynamical stability maps that are specific to white dwarf planetary systems and that can be used as tools in future studies to quickly estimate pollution prospects and timescales for one-planet architectures. We find that these maps also agree well with the outcomes of our N-body simulations.
Conclusions. As observations of metal-polluted white dwarfs mount exponentially, particularly in the era of Gaia, tools such as periodic orbits can help infer dynamical histories for ensembles of systems
Driving white dwarf metal pollution through unstable eccentric periodic orbits
Context. Planetary debris is observed in the atmospheres of over 1000 white dwarfs, and two white dwarfs are now observed to contain orbiting minor planets. Exoasteroids and planetary core fragments achieve orbits close to the white dwarf through scattering with major planets. However, the architectures that allow for this scattering to take place are time-consuming to explore with N-body simulations lasting ∼1010 yr; these long-running simulations restrict the amount of phase space that can be investigated.
Aims. Here we use planar and three-dimensional (spatial) elliptic periodic orbits, as well as chaotic indicators through dynamical stability maps, as quick scale-free analytic alternatives to N-body simulations in order to locate and predict instability in white dwarf planetary systems that consist of one major and one minor planet on very long timescales. We then classify the instability according to ejection versus collisional events.
Methods. We generalized our previous work by allowing eccentricity and inclination of the periodic orbits to increase, thereby adding more realism but also significantly more degrees of freedom to our architectures. We also carried out a suite of computationally expensive 10 Gyr N-body simulations to provide comparisons with chaotic indicators in a limited region of phase space.
Results. We compute dynamical stability maps that are specific to white dwarf planetary systems and that can be used as tools in future studies to quickly estimate pollution prospects and timescales for one-planet architectures. We find that these maps also agree well with the outcomes of our N-body simulations.
Conclusions. As observations of metal-polluted white dwarfs mount exponentially, particularly in the era of Gaia, tools such as periodic orbits can help infer dynamical histories for ensembles of systems
On quasi-satellite periodic motion in asteroid and planetary dynamics
Applying the method of analytical continuation of periodic orbits, we study
quasi-satellite motion in the framework of the three-body problem. In the
simplest, yet not trivial model, namely the planar circular restricted problem,
it is known that quasi-satellite motion is associated with a family of periodic
solutions, called family , which consists of 1:1 resonant retrograde orbits.
In our study, we determine the critical orbits of family that are continued
both in the elliptic and in the spatial model and compute the corresponding
families that are generated and consist the backbone of the quasi-satellite
regime in the restricted model. Then, we show the continuation of these
families in the general three-body problem, we verify and explain previous
computations and show the existence of a new family of spatial orbits. The
linear stability of periodic orbits is also studied. Stable periodic orbits
unravel regimes of regular motion in phase space where 1:1 resonant angles
librate. Such regimes, which exist even for high eccentricities and
inclinations, may consist dynamical regions where long-lived asteroids or
co-orbital exoplanets can be found.Comment: Accepted for publication in Celestial Mechanics and Dynamical
Astronom
An illustration of new methods in machine condition monitoring, Part I: Stochastic resonance
There have been many recent developments in the application of data-based
methods to machine condition monitoring. A powerful methodology based on machine learning
has emerged, where diagnostics are based on a two-step procedure: extraction of damage sensitive
features, followed by unsupervised learning (novelty detection) or supervised learning
(classification). The objective of the current pair of papers is simply to illustrate one state-of the-art
procedure for each step, using synthetic data representative of reality in terms of size
and complexity. The first paper in the pair will deal with feature extraction.
Although some papers have appeared in the recent past considering stochastic resonance
as a means of amplifying damage information in signals, they have largely relied on ad hoc
specifications of the resonator used. In contrast, the current paper will adopt a principled
optimisation-based approach to the resonator design. The paper will also show that a discrete
dynamical system can provide all the benefits of a continuous system, but also provide a
considerable speed-up in terms of simulation time in order to facilitate the optimisation
approach
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