共查询到20条相似文献，搜索用时 31 毫秒
1.
A plot of spin rate versus orientation when Hyperion is at the pericenter of its orbit (surface of section) reveals a large chaotic zone surrounding the synchronous spin-orbit state of Hyperion, if the satellite is assumed to be rotating about a principal axis which is normal to its orbit plane. This means that Hyperion's rotation in this zone exhibits large, essentially random variations on a short time scale. The chaotic zone is so large that it surrounds the ½ and 2 states, and libration in the 3/2 state is not possible. Stability analysis shows that for libration in the synchronous and ½ states, the orientation of the spin axis normal to the orbit plane is unstable, whereas rotation in the 2 state is attitude stable. Rotation in the chaotic zone is also attitude unstable. A small deviation of the principal axis from the orbit normal leads to motion through all angles in both the chaotic zone and the attitude unstable libration regions. Measures of the exponential rate of separation of nearby trajectories in phase space (Lyapunov characteristic exponents) for these three-dimensional motions indicate the the tumbling is chaotic and not just a regular motion through large angles. As tidal dissipation drives Hyperion's spin toward a nearly synchronous value, Hyperion necessarily enters the large chaotic zone. At this point Hyperion becomes attitude unstable and begins to tumble. Capture from the chaotic state into the synchronous or ½ state is impossible since they are also attitude unstable. The 3/2 state does not exist. Capture into the stable 2 state is possible, but improbable. It is expected that Hyperion will be found tumbling chaotically. 相似文献
2.
Comparative Study of the 2:3 and 3:4 Resonant Motion with Neptune: An Application of Symplectic Mappings and Low Frequency Analysis 总被引：2，自引：1，他引：1
The 2:3 and 3:4 exterior mean motion resonances with Neptune are studied by applying symplectic mapping models. The mappings
represent efficiently Poincaré maps for the 3D elliptic restricted three body problem in the neighbourhood of the particular
resonances. A large number of trajectories is studied showing the coexistence of regular and chaotic orbits. Generally, chaotic
motion depletes the small bodies of the effective resonant region in both the 2:3 and 3:4 resonances. Applying a low frequency
spectral analysis of trajectories, we determined the phase space regions that correspond to either regular or chaotic motion.
It is found that the phase space of the 3:4 resonant motion is more chaotic than the 2:3 one. 相似文献
3.
A full characterization of a nonintegrable dynamical system requires an investigation into the chaotic properties of that system. One such system, the restricted problem of three bodies, has been studied for over two centuries, yet few studies have examined the chaotic nature of some ot its trajectories. This paper examines and classifies the onset of chaotic motion in the restricted three-body problem through the use of Poincaré surfaces of section, Liapunov characteristic numbers, power spectral density analysis and a newly developed technique called numerical irreversibility. The chaotic motion is found to be intermittent and becomes first evident when the Jacobian constant is slightly higher thanC
2. 相似文献
4.
Konstantin Batygin Alessandro Morbidelli 《Celestial Mechanics and Dynamical Astronomy》2011,111(1-2):219-233
As a result of resonance overlap, planetary systems can exhibit chaotic motion. Planetary chaos has been studied extensively in the Hamiltonian framework, however, the presence of chaotic motion in systems where dissipative effects are important, has not been thoroughly investigated. Here, we study the onset of stochastic motion in presence of dissipation, in the context of classical perturbation theory, and show that planetary systems approach chaos via a period-doubling route as dissipation is gradually reduced. Furthermore, we demonstrate that chaotic strange attractors can exist in mildly damped systems. The results presented here are of interest for understanding the early dynamical evolution of chaotic planetary systems, as they may have transitioned to chaos from a quasi-periodic state, dominated by dissipative interactions with the birth nebula. 相似文献
5.
类星体有剧烈、大幅度的光变现象, 光变研究有助于建立与观测相符的理论模型. 这篇文章从密歇根大学射电天文台数据库收集了类星体3C 446射电4.8、8.0和14.5GHz波段的长期观测数据. 传统的线性方法难以分析复杂的光变现象, 文章采用了集合经验模态分解(Ensemble Empirical Mode Decomposition, EEMD)方法和非线性分析方法相结合, 从混沌动力学特性、分形特性和周期性多角度对类星体光变随时间演化的规律进行了较全面的分析, 并重点对比分析了除去周期成分或混沌成分前后, 光变的周期性和非线性特性是否存在明显区别. 分析结果表明, 类星体3C 446射电波段光变资料由周期成分、趋势成分和混沌成分组成, 光变具有周期性、混沌性和分形特性. 除去混沌成分和趋势成分后的光变周期与原始光变资料的周期完全相同, 而两者的混沌和分形特性有明显不同. 从饱和关联维数来看, 重构动力学系统时, 除去周期成分和趋势成分后的光变资料比原始光变资料需要更多的独立参量, Kolmogorov熵值表明前者信息的损失率比后者大, 系统的混沌程度更高, 系统也更复杂, Hurst值表明后者自相似性和长程相关性比前者略强. 相似文献
6.
We study the regular or chaotic character of orbits in a 3D dynamical model,describing a triaxial galaxy surrounded by a spherical dark halo component.Our numerical experiments suggest that the percentage of chaotic orbits decreases exponentially as the mass of the dark halo increases.A linear increase of the percentage of the chaotic orbits was observed as the scale length of the halo component increases. In order to distinguish between regular and chaotic motion,we chose to use the total angular momentum ... 相似文献
7.
We present a quasar model with a rotating disk and a massive nucleus. We use this model in order to characterize the motion in the model (regular or chaotic) and to connect the extent of the chaotic regions to the physical parameters of the model. Numerical experiments suggest that, there are connections between the extent of the chaotic areas and the parameters of the system. Furthermore, it is shown that the form of numerically found relationships can be expressed analytically. Comparison to previous work is also made. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
8.
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
9.
Lei Liu Institute of Particle Physics Huazhong Normal University Wuhan 《中国天文和天体物理学报》2006,6(6):663-668
Some nonlinear dynamical techniques, including state-space reconstruction and correlation integral, are used to analyze the light curve of 3C 273. The result is compared with a chaotic model. The similarities between them suggest there is a low-dimension chaotic attractor in the light curve of 3C 273. 相似文献
10.
A mixture of periodic and chaotic components makes the detection of chaos difficult. The periodic components are sought in the solar UV time series by the Maximum Entropy Method and are removed by a digital notch filter. The filtered output is subjected to investigation for chaotic behavior by three different techniques. (1) Fixed-size method for attractor dimension determination; (2) sensitive initial dependence via prediction error; (3) trajectory direction estimation. All the investigation points to the existence of a chaotic attractor of fractional dimension. 相似文献
11.
We investigate the regular and chaotic motion in a model potential found using the recent developments of the Inverse Problem
of Dynamics. The potential describes the motion in the central parts of a barred galaxy. In the absence of rotation chaotic
motion is observed when the perturbation strength is near the escape perturbation for a fixed value of the energy. In the
rotating cases one observes that the area of chaotic motion on the surface of section decreases as the angular velocity Ω
increases and finally all orbits become regular. The character of motion is also checked by computing the Liapunov characteristic
exponents in all cases.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
12.
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
13.
Jacques Laskar 《Celestial Mechanics and Dynamical Astronomy》1996,64(1-2):115-162
Large scale chaos is present everywhere in the solar system. It plays a major role in the sculpting of the asteroid belt and in the diffusion of comets from the outer region of the solar system. All the inner planets probably experienced large scale chaotic behavior for their obliquities during their history. The Earth obliquity is presently stable only because of the presence of the Moon, and the tilt of Mars undergoes large chaotic variations from 0° to about 60°. On billion years time scale, the orbits of the planets themselves present strong chaotic variations which can lead to the escape of Mercury or collision with Venus in less than 3.5 Gyr. The organization of the planets in the solar system thus seems to be strongly related to this chaotic evolution, reaching at all time a state of marginal stability, that is practical stability on a time-scale comparable to its age.This lecture was given at the XIth International Congress of Mathematical Physics, Paris, july 1994 相似文献
14.
Xiyun Hou Daniel J. Scheeres Lin Liu 《Celestial Mechanics and Dynamical Astronomy》2014,119(2):119-142
The dynamics of the two Jupiter triangular libration points perturbed by Saturn is studied in this paper. Unlike some previous works that studied the same problem via the pure numerical approach, this study is done in a semianalytic way. Using a literal solution, we are able to explain the asymmetry of two orbits around the two libration points with symmetric initial conditions. The literal solution consists of many frequencies. The amplitudes of each frequency are the same for both libration points, but the initial phase angles are different. This difference causes a temporary spatial asymmetry in the motions around the two points, but this asymmetry gradually disappears when the time goes to infinity. The results show that the two Jupiter triangular libration points should have symmetric spatial stable regions in the present status of Jupiter and Saturn. As a test of the literal solution, we study the resonances that have been extensively studied in Robutel and Gabern (Mon Not R Astron Soc 372:1463–1482, 2006). The resonance structures predicted by our analytic theory agree well with those found in Robutel and Gabern (Mon Not R Astron Soc 372:1463–1482, 2006) via a numerical approach. Two kinds of chaotic orbits are discussed. They have different behaviors in the frequency map. The first kind of chaotic orbits (inner chaotic orbits) is of small to moderate amplitudes, while the second kind of chaotic orbits (outer chaotic orbits) is of relatively larger amplitudes. Using analytical theory, we qualitatively explain the transition process from the inner chaotic orbits to the outer chaotic orbits with increasing amplitudes. A critical value of the diffusion rate is given to separate them in the frequency map. In a forthcoming paper, we will study the same problem but keep the planets in migration. The time asymmetry, which is unimportant in this paper, may cause an observable difference in the two Jupiter Trojan groups during a very fast planet migration process. 相似文献
15.
In this paper, we show the important role of chaotic transients in Celestial Mechanics through the Sitnikov problem. We compare
the two kinds of chaos, permanent and transient, and provide the chaotic saddle of the Sitnikov problem giving also some important
quantitative properties of this fractal set. Additionally, we present a link between the stickiness effect of tori and chaotic
scattering. 相似文献
16.
《Icarus》1986,65(1):70-82
The chaotic regions of the phase space in the vicinity of the 2:1 and 3:2 jovian resonances are identified by using a mapping technique derived from a second-order expansion of the disturbing function for the planar elliptical restricted three-body problem. It is shown that both resonances have extensive chaotic regions which in some cases can lead to large changes in the eccentricity of asteroid orbits. Although the 3:2 resonance is shown to be more chaotic than the 2:1 resonance, the existence of the Hilda group of asteroids and the Hecuba gap may be explained by distinct differences in the location of the high-eccentricity regions at each resonance. The problem of the convergence of the expansion of the disturbing function in the outer asteroid belt is also discussed. 相似文献
17.
M. N. Kremliovsky 《Solar physics》1995,159(2):371-380
The study of a nonlinear chaotic map of 11-year cycle maxima evolution recently derived from observations is presented with the purpose of predicting the features of the long-term variability of solar activity. It is stressed that dynamical forecast is limited by the Lyapunov time and a statistical approach can be justified due to the ergodic properties of the chaotic evolution. The Gleissberg variation is described as a chaotic walk and its distribution over length is shown to be broad. The global minima are identified as laminar slots of temporal intermittency and their typical distribution over length is also given. We note that a long sunspot cycle can be used as a precursor of the global minimum and a close sequence of global minima (once in approximately 1500–2000 years) may be responsible for the climatic changes (Little Ice Ages). 相似文献
18.
Shinichi Watari 《Solar physics》1996,168(2):413-422
Two new techniques were applied to search for chaotic behavior in solar activity. A mixture of periodic and chaotic components in a time series makes it difficult to find chaotic behavior. The singular spectrum analysis (SSA) method (Broomhead and King, 1986) was used to separate periodic and irregular components in solar activity (e.g., sunspot number and 10.7 cm flux). The nonlinear prediction method (Sugihara and May, 1990) was applied for each component to examine whether it has a chaotic characteristic. The result suggests that are are dominant periodic components and highly irregular (random) components in solar activity. 相似文献
19.
V.V. Kouprianov 《Icarus》2005,176(1):224-234
The problem of observability of chaotic regimes in the rotation of planetary satellites is studied. The analysis is based on the inertial and orbital data available for all satellites discovered up to now. The Lyapunov spectra of the spatial chaotic rotation and the full range of variation of the spin rate are computed numerically by integrating the equations of the rotational motion; the initial data are taken inside the main chaotic layer near the separatrices of synchronous resonance in phase space. The model of a triaxial satellite in a fixed elliptic orbit is adopted. A short Lyapunov time along with a large range of variation of the spin rate are used as criteria for observability of the chaotic motion. Independently, analysis of stability of the synchronous state with respect to tilting the axis of rotation provides a test for the physical opportunity for a satellite to rotate chaotically. Finally, a calculation of the times of despinning due to tidal evolution shows whether a satellite's spin could evolve close to the synchronous state. Apart from Hyperion, already known to rotate chaotically, only Prometheus and Pandora, the 16th and 17th satellites of Saturn, pass all these four tests. 相似文献
20.
Miloš Šidlichovský 《Celestial Mechanics and Dynamical Astronomy》1999,73(1-4):77-86
The twenty most chaotic objects found among first hundred of numbered asteroids are studied. Lyapunov time calculated with
and without inner planets indicates that for eleven of those asteroids the strongest chaotic effect results from the resonances
with Mars. The filtered semimajor axis displays an abrupt variation only when a close approach to Mars takes place. The study
of the behaviour of the critical argument for candidate resonances can reveal which is responsible for the semimajor axis
variation. We have determined these resonances for the asteroids in question. For the asteroids chaotic even without the inner
planets we have determined the most important resonances with Jupiter, or three-body resonances.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献