共查询到20条相似文献，搜索用时 578 毫秒
1.
G. Contopoulos E. Grousouzakou C. Polymilis 《Celestial Mechanics and Dynamical Astronomy》1996,64(4):363-381
We study the distribution of regular and irregular periodic orbits on a Poincaré surface of section of a simple Hamiltonian system of 2 degrees of freedom. We explain the appearance of many lines of periodic orbits that form Farey trees. There are also lines that are very close to the asymptotic curves of the unstable periodic orbits. Some regular orbits, sometimes stable, are found inside the homoclinic tangle. We explain this phenomenon, which shows that the homoclinic tangle does not cover the whole area around an unstable orbit, but has gaps. Inside the lobes only irregular orbits appear, and some of them are stable. We conjecture that the opposite is also true, i.e. all irregular orbits are inside lobes. 相似文献
2.
《天文和天体物理学研究(英文版)》2016,(2)
We use a simple dynamical model which consists of a harmonic oscillator and a spherical component, in order to investigate the regular or chaotic character of orbits in a barred galaxy with a central spherically symmetric nucleus. Our aim is to explore how the basic parameters of the galactic system influence the nature of orbits, by computing in each case the percentage of chaotic orbits, as well as the percentages of different types of regular orbits. We also give emphasis to the types of regular orbits that support either the formation of nuclear rings or the barred structure of the galaxy. We provide evidence that the traditional x1 orbital family does not always dominate in barred galaxy models since we found several other types of resonant orbits which can also support the barred structure. We also found that sparse enough nuclei, fast rotating bars and high energy models can support the galactic bars. On the other hand, weak bars, dense central nuclei, slowly rotating bars and low energy models favor the formation of nuclear rings.We also compare our results with previous related work. 相似文献
3.
We study the various approximations used to investigate the eigenmode spectrum for systems with highly elongated stellar orbits. The approximation in which the elongated orbits are represented by thin rotating spokes, with the rotation imitating the precession of real orbits, is the simplest and most natural one. However, we show that using this pictorial approximation does not allow the picture of stability to be properly presented. We show that for stellar systems with a plane disk geometry, this approach does not allow unstable spectral modes to be obtained even in the leading order in small parameter, which characterizes the spread of nearly radial orbits in angular momentum. For spherical systems, where the situation is more favorable, the spectrum can be determined but only in the leading order in this parameter. A rigorous approach based on the solution of more complex integral equations given here should be used to properly investigate the stability of stellar systems. 相似文献
4.
J. C. Muzzio 《Celestial Mechanics and Dynamical Astronomy》2006,96(2):85-97
We created a self-consistent triaxial stellar system through the cold disipationless collapse of 100,000 particles whose evolution was followed with a multipolar code. The resulting system rotates slowly even though its total angular momentum is zero, i.e., it offers an example of figure rotation. The potential of the system was subsequently approximated with interpolating formulae yielding a smooth potential stationary in the rotating frame. The Lyapunov exponents could then be computed for a randomly selected sample of 3,472 of the bodies that make up the system, allowing the recognition of regular and partially and fully chaotic orbits. The regular orbits were Fourier analyzed and classified using their locations on the frequency map. A comparison with a similar non-rotating model showed that the fraction of chaotic orbits is slightly but significantly enhanced in the rotating model; alternatively, there are no significant differences between the corresponding fractions neither of partially and fully chaotic orbits nor of long axis tubes, short axis tubes, boxes and boxlets among the regular orbits. This is a reasonable result because the rotation causes a breaking of the symmetry that may increase chaotic effects, but the rotation velocity is probably too small to produce any other significant differences. The increase in the fraction of chaotic orbits in the rotating system seems to be due mainly to the effect of the Coriolis force, rather than the centrifugal force, in good agreement with the results of other investigations. 相似文献
5.
J. C. Muzzio D. D. Carpintero F. C. Wachlin 《Celestial Mechanics and Dynamical Astronomy》2005,91(1-2):173-190
We created a triaxial stellar system through the cold dissipationless collapse of 100,000 particles whose evolution was followed
with a multipolar code. Once an equilibrium system had been obtained, the multipolar expansion was freezed and smoothed in
order to get a stationary smooth potential. The resulting model was self-consistent and the orbits and Lyapunov exponents
could then be computed for a randomly selected sample of 3472 of the bodies that make up the system. More than half of the
orbits (52.7 % ) turned out to be chaotic. Regular orbits were then classified using the frequency analysis automatic code
of Carpintero and Aguilar (1998, MNRAS 298(1), 1–21). We present plots of the distributions of the different kinds of orbits projected on the symmetry planes of
the system. We distinguish chaotic orbits with only one non-zero Lyapunov exponent from those with two non-zero exponents
and show that their spatial distributions differ, that of the former being more similar to the one of the regular orbits.
Most of the regular orbits are boxes and boxlets, but the minor axis tubes play an important role filling in the wasp waists
of the boxes and helping to give a lentil shape to the system. We see no problem in building stable triaxial models with substantial
amounts of chaotic orbits; the difficulties found by other authors may be due not to a physical cause but to a limitation
of Schwarzschild’s method. 相似文献
6.
A. Kyrala 《Earth, Moon, and Planets》1981,24(3):345-348
The problem of determination of the radial distribution of the planetary orbits is approached under the assumption that the average present radial sizes of the orbits were already determined when the protoplanetary cloud flattened by initial angular momentum aggregated into a set of concentric rings from which the planetary material was ultimately collected. The object of this argument is to derive a consistent stationary distribution of orbits so that the problem of the non-stationary formation of the orbital rings is not here considered. Under the flattening assumption the 3D Poisson equation is replaced by the 2D Helmholtz equation (inhomogeneous) which is solved by use of an averaging theorem generalization of the well-known averaging theorem for the homogeneous Helmholtz equation. Augmenting the ring potentials obtained by specializing the mass distribution in the disk by a solar potential term and a rotational potential, differentiation leads to a generalization of the Kepler 3D law suitable for the many-body problem of a solar system with circular orbits. In this way a system of transcendental equations involving Bessel functions of the first and second kind are obtained which must be satisfied by the orbital radii. Naturally the restriction to circular orbits represents only an approximation to the orbital determination problem, but considering that no arguments have previously been available for the determination even of circular orbits it would seem to represent an advance. 相似文献
7.
Using a consistent perturbation theory for collisionless disk-like and spherical star clusters, we construct a theory of slow
modes for systems having an extended central region with a nearly harmonic potential due to the presence of a fairly homogeneous
(on the scales of the stellar system) heavy, dynamically passive halo. In such systems, the stellar orbits are slowly precessing,
centrally symmetric ellipses (2: 1 orbits). Depending on the density distribution in the system and the degree of halo inhomogeneity,
the orbit precession can be both prograde and retrograde, in contrast to systems with 1: 1 elliptical orbits where the precession
is unequivocally retrograde. In the first paper, we show that in the case where at least some of the orbits have a prograde
precession and the stellar distribution function is a decreasing function of angular momentum, an instability that turns into
the well-known radial orbit instability in the limit of low angular momenta can develop in the system. We also explore the
question of whether the so-called spoke approximation, a simplified version of the slow mode approximation, is applicable
for investigating the instability of stellar systems with highly elongated orbits. Highly elongated orbits in clusters with
nonsingular gravitational potentials are known to be also slowly precessing 2: 1 ellipses. This explains the attempts to use
the spoke approximation in finding the spectrum of slow modes with frequencies of the order of the orbit precession rate.
We show that, in contrast to the previously accepted view, the dependence of the precession rate on angular momentum can differ
significantly from a linear one even in a narrow range of variation of the distribution function in angular momentum. Nevertheless,
using a proper precession curve in the spoke approximation allows us to partially “rehabilitate” the spoke approach, i.e.,
to correctly determine the instability growth rate, at least in the principal (O(α
T−1/2) order of the perturbation theory in dimensionless small parameter α
T, which characterizes the width of the distribution function in angular momentum near radial orbits. 相似文献
8.
Plane, periodic stellar orbits in the spiral gravitational field of the Galaxy superimposed on the axisymmetric background potential are studied in the epicyclic approximation. The superposition of such orbits is illustrated to demonstrate the response of the stellar system to an imposed spiral density perturbation. 相似文献
9.
Jun-Hwan Choi Yu Lu H. J. Mo Martin D. Weinberg 《Monthly notices of the Royal Astronomical Society》2006,372(4):1869-1874
We consider the sensitivity of the circular-orbit adiabatic contraction approximation to the baryon condensation rate and the orbital structure of dark matter haloes in the Λ cold dark matter (ΛCDM) paradigm. Using one-dimensional hydrodynamic simulations including the dark matter halo mass accretion history and gas cooling, we demonstrate that the adiabatic approximation is approximately valid even though haloes and discs may assemble simultaneously. We further demonstrate the validity of the simple approximation for ΛCDM haloes with isotropic velocity distributions using three-dimensional N -body simulations. This result is easily understood: an isotropic velocity distribution in a cuspy halo requires more circular orbits than radial orbits. Conversely, the approximation is poor in the extreme case of a radial orbit halo. It overestimates the response of a core dark matter halo, where radial orbit fraction is larger. Because no astronomically relevant models are dominated by low angular momentum orbits in the vicinity of the disc and the growth time-scale is never shorter than a dynamical time, we conclude that the adiabatic contraction approximation is useful in modelling the response of dark matter haloes to the growth of a disc. 相似文献
10.
C. Gontikakis C. Efthymiopoulos A. Anastasiadis 《Monthly notices of the Royal Astronomical Society》2006,368(1):293-304
We consider the possibility of particles being injected at the interior of a reconnecting current sheet (RCS), and study their orbits by dynamical systems methods. As an example we consider orbits in a 3D Harris type RCS. We find that, despite the presence of a strong electric field, a 'mirror' trapping effect persists, to a certain extent, for orbits with appropriate initial conditions within the sheet. The mirror effect is stronger for electrons than for protons. In summary, three types of orbits are distinguished: (i) chaotic orbits leading to escape by stochastic acceleration, (ii) regular orbits leading to escape along the field lines of the reconnecting magnetic component, and (iii) mirror-type regular orbits that are trapped in the sheet, making mirror oscillations. Dynamically, the latter orbits lie on a set of invariant KAM tori that occupy a considerable amount of the phase space of the motion of the particles. We also observe the phenomenon of 'stickiness', namely chaotic orbits that remain trapped in the sheet for a considerable time. A trapping domain, related to the boundary of mirror motions in velocity space, is calculated analytically. Analytical formulae are derived for the kinetic energy gain in regular or chaotic escaping orbits. The analytical results are compared with numerical simulations. 相似文献
11.
We present the results of our numerical simulations of the cyclic brightness modulation in young binary systems with eccentric orbits and low-mass secondary components. We suggest that the binary components accrete matter from the remnants of the protostellar cloud, with the main accretor (according to current models) being the low-mass component. The brightness variations of the primary are attributable to the periodic extinction variations on the line of sight caused by the disk wind from the secondary and by the common envelope produced by this wind. The distribution of matter in the envelope was calculated in the ballistic approximation. When calculating the optical effects produced by the dust component of the disk wind, we adopted the dust-to-gas mass ratio of 1:100 characteristic of the interstellar medium and the optical parameters of the circumstellar dust typical of young stars. Our calculations show that the theoretical light curves for binaries with elliptical orbits exhibit a wider variety of shapes than those for binaries with circular orbits. In this case, the parameters of the photometric minima (their depth, duration, and shape of the light curve) depend not only on the disk-wind parameters and the orbital inclination of the binary to the line of sight, but also on the longitude of the periastron. We investigate the modulation of the scattered radiation from the common envelope with orbital phase in the single-scattering approximation. The modulation amplitude is shown to be at a maximum when the system is seen edge-on and to be also nonzero in binaries seen pole-on. We discuss possible applications of the theory to young stellar objects. In particular, several model light curves have been found to be similar to those of candidate FU Orionis stars (FUORs). 相似文献
12.
Euaggelos E. Zotos Daniel D. Carpintero 《Celestial Mechanics and Dynamical Astronomy》2013,116(4):417-438
We investigate the regular or chaotic nature of star orbits moving in the meridional plane of an axially symmetric galactic model with a disk and a spherical nucleus. We study the influence of some important parameters of the dynamical system, such as the mass and the scale length of the nucleus, the angular momentum or the energy, by computing in each case the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families. Some heuristic arguments to explain and justify the numerically derived outcomes are also given. Furthermore, we present a new method to find the threshold between chaos and regularity for both Lyapunov Characteristic Numbers and SALI, by using them simultaneously. 相似文献
13.
J. C. Muzzio H. D. Navone A. F. Zorzi 《Celestial Mechanics and Dynamical Astronomy》2009,105(4):379-395
We used a multipolar code to create, through dissipationless collapses of systems of 106 particles, two cuspy self-consistent triaxial stellar systems with γ ≈ 1. One of the systems has an axial ratio similar to that of an E4 galaxy and it is only mildly triaxial (T = 0.914), while the other one is strongly triaxial (T = 0.593) and its axial ratio lies in between those of Hubble types E5 and E6. Both models rotate although their total angular
momenta are zero, i.e., they exhibit figure rotation. The angular velocity is very small for the less triaxial model and,
while it is larger for the more triaxial one, it is still comparable to that found by Muzzio (Celest Mech Dynam Astron 96(2):85–97,
2006) to affect only slightly the dynamics of a similar model. Except for minor evolution, probably caused by unavoidable
relaxation effects of the N-body code, the systems are highly stable. The potential of each system was subsequently approximated
with interpolating formulae yielding smooth potentials, stationary in frames that rotate with the models. The Lyapunov exponents
could then be computed for randomly selected samples of the bodies that make up the two systems, allowing the recognition
of regular and of partially and fully chaotic orbits. Finally, the regular orbits were Fourier analyzed and classified using
their locations on the frequency map. Most of the orbits are chaotic, and by a wide margin: less than 30% of the orbits are
regular in our most triaxial model. Regular orbits are dominated by tubes, long axis ones in the less triaxial model and short
axis tubes in the more triaxial one. Most of the boxes are resonant (i.e., they are boxlets), as could be expected from cuspy
systems. 相似文献
14.
We distinguish between regular orbits, that bifurcate from the main families of periodic orbits (those that exist also in the unperturbed case) and irregular periodic orbits, that are independent of the above. The genuine irregular families cannot be made to join the regular families by changing some parameters. We present evidence that all irregular families appear inside lobes formed by the asymptotic curves of the unstable periodic orbits. We study in particular a dynamical system of two degrees of freedom, that is symmetric with respect to the x-axis, and has also a triple resonance in its unperturbed form. The distribution of the periodic orbits (points on a Poincaré surface of section) shows some conspicuous lines composed of points of different multiplicities. The regular periodic orbits along these lines belong to Farey trees. But there are also lines composed mainly of irregular orbits. These are images of the x-axis in the map defined on the Poincaré surface of section. Higher order iterations of this map , close to the unstable triple periodic orbit, produce lines that are close to the asymptotic curves of this unstable orbit. The homoclinic tangle, formed by these asymptotic curves, contains many regular orbits, that were generated by bifurcation from the central orbit, but were trapped inside the tangle as the perturbation increased. We found some stable periodic orbits inside the homoclinic tangle, both regular and irregular. This proves that the homoclinic tangle is not completely chaotic, but contains gaps (islands of stability) filled with KAM curves. 相似文献
15.
George Voyatzis John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》2006,95(1-4):259-271
We study the dynamics of 3:1 resonant motion for planetary systems with two planets, based on the model of the general planar three body problem. The exact mean motion resonance corresponds to periodic motion (in a rotating frame) and the basic families of symmetric and asymmetric periodic orbits are computed. Four symmetric families bifurcate from the family of circular orbits of the two planets. Asymmetric families bifurcate from the symmetric families, at the critical points, where the stability character changes. There exist also asymmetric families that are independent of the above mentioned families. Bounded librations exist close to the stable periodic orbits. Therefore, such periodic orbits (symmetric or asymmetric) determine the possible stable configurations of a 3:1 resonant planetary system, even if the orbits of the two planets intersect. For the masses of the system 55Cnc most of the periodic orbits are unstable and they are associated with chaotic motion. There exist however stable symmetric and asymmetric orbits, corresponding to regular trajectories along which the critical angles librate. The 55Cnc extra-solar system is located in a stable domain of the phase space, centered at an asymmetric periodic orbit. 相似文献
16.
Richard Scuflaire 《Celestial Mechanics and Dynamical Astronomy》1998,71(3):203-228
We study the regular families of periodic orbits in an analytical planar galactic potential, using the method of Lindstedt.
We obtain analytical expressions describing these orbits, validity of which is not limited to small amplitudes. We can delimit,
in the space of the parameters, the domain of existence of each family of orbits.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
17.
Florent Deleflie Gilles Métris Pierre Exertier 《Celestial Mechanics and Dynamical Astronomy》2006,94(1):83-104
This paper studies the long period variations of the eccentricity vector of the orbit of an artificial satellite, under the
influence of the gravity field of a central body. We use modified orbital elements which are non-singular at zero eccentricity.
We expand the long periodic part of the corresponding Lagrange equations as power series of the eccentricity. The coefficients
characterizing the differential system depend on the zonal coefficients of the geopotential, and on initial semi-major axis,
inclination, and eccentricity. The differential equations for the components of the eccentricity vector are then integrated
analytically, with a definition of the period of the perigee based on the notion of “free eccentricity”, and which is also
valid for circular orbits. The analytical solution is compared to a numerical integration. This study is a generalization
of (Cook, Planet. Space Sci., 14, 1966): first, the coefficients involved in the differential equations depend on all zonal coefficients (and not only on
the very first ones); second, our method applies to nearly circular orbits as well as to not too eccentric orbits. Except
for the critical inclination, our solution is valid for all kinds of long period motions of the perigee, i.e., circulations
or librations around an equilibrium point. 相似文献
18.
Orbit classification in arbitrary 2D and 3D potentials 总被引：1，自引：0，他引：1
Daniel D. Carpintero & Luis A. Aguilar 《Monthly notices of the Royal Astronomical Society》1998,298(1):1-21
A method of classifying generic orbits in arbitrary 2D and 3D potentials is presented. It is based on the concept of spectral dynamics introduced by Binney &38; Spergel that uses the Fourier transform of the time series of each coordinate. The method is tested using a number of potentials previously studied in the literature and is shown to distinguish correctly between regular and irregular orbits, to identify the various families of regular orbits (boxes, loops, tubes, boxlets, etc.), and to recognize the second-rank resonances that bifurcate from them. The method returns the position of the potential centre and, for 2D potentials, the orientation of the principal axes as well, should this be unknown. A further advantage of the method is that it has been encoded in a FORTRAN program that does not require user intervention, except for 'fine tuning' of search parameters that define the numerical limits of the code. The automatic character makes the program suitable for classifying large numbers of orbits. 相似文献
19.
Now there are two basic observational techniques to investigate a gravitational potential at the Galactic Center, namely, (a) monitoring the orbits of bright stars near the Galactic Center to reconstruct a gravitational potential; (b) measuring the size and shape of shadows around black hole giving an alternative possibility to evaluate black hole parameters in mm-band with VLBI-technique. At the moment, one can use a small relativistic correction approach for stellar orbit analysis (however, in the future the approximation will not be precise enough due to enormous progress of observational facilities) while for smallest structure analysis in VLBI observations one really needs a strong gravitational field approximation. We discuss results of observations, their conventional interpretations, tensions between observations and models and possible hints for a new physics from the observational data and tensions between observations and interpretations. We discuss an opportunity to use a Schwarzschild metric for data interpretation or we have to use more exotic models such as Reissner–Nordstrom or Schwarzschild–de-Sitter metrics for better fits. 相似文献
20.
Roberto O. Aquilano Juan C. Muzzio Hugo D. Navone Alejandra F. Zorzi 《Celestial Mechanics and Dynamical Astronomy》2007,99(4):307-324
We used a multipolar code to create, through the dissipationless collapses of systems of 1,000,000 particles, three self-consistent
triaxial stellar systems with axial ratios corresponding to those of E4, E5 and E6 galaxies. The E5 and E6 models have small,
but significant, rotational velocities although their total angular momenta are zero, that is, they exhibit figure rotation;
the rotational velocity decreases with decreasing flattening of the models and for the E4 model it is essentially zero. Except
for minor changes, probably caused by unavoidable relaxation effects, the systems are highly stable. The potential of each
system was subsequently approximated with interpolating formulae yielding smooth potentials, stationary for the non-rotating
model and stationary in the rotating frame for the rotating ones. The Lyapunov exponents could then be computed for randomly
selected samples of the bodies that make up the different systems, allowing the recognition of regular and partially and fully
chaotic orbits. Finally, the regular orbits were Fourier analyzed and classified using their locations on the frequency map.
As it could be expected, the percentages of chaotic orbits increase with the flattening of the system. As one goes from E6
through E4, the fraction of partially chaotic orbits relative to that of fully chaotic ones increases, with the former surpassing
the latter in model E4; the likely cause of this behavior is that triaxiality diminishes from E6 through E4, the latter system
being almost axially symmetric. We especulate that some of the partially chaotic orbits may obey a global integral akin to
the long axis component of angular momentum. Our results show that is perfectly possible to have highly stable triaxial models
with large fractions of chaotic orbits, but such systems cannot have constant axial ratios from center to border: a slightly
flattened reservoir of highly chaotic orbits seems to be mandatory for those systems. 相似文献