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1.
Hanlun Lei Christian Circi Emiliano Ortore Bo Xu 《Celestial Mechanics and Dynamical Astronomy》2018,130(8):53
In this work, periodic attitudes and bifurcations of periodic families are investigated for a rigid spacecraft moving on a stationary orbit around a uniformly rotating asteroid. Under the second degree and order gravity field of an asteroid, the dynamical model of attitude motion is formulated by truncating the integrals of inertia of the spacecraft at the second order. In this dynamical system, the equilibrium attitude has zero Euler angles. The linearised equations of attitude motion are utilised to study the stability of equilibrium attitude. It is found that there are three fundamental types of periodic attitude motions around a stable equilibrium attitude point. We explicitly present the linear solutions around a stable equilibrium attitude, which can be used to provide the initial guesses for computing the true periodic attitudes in the complete model. By means of a numerical approach, three fundamental families of periodic attitudes are studied, and their characteristic curves, distribution of eigenvalues, stability curves and stability distributions are determined. Interestingly, along the characteristic curves of the fundamental families, some critical points are found to exist, and these points correspond to tangent and period-doubling bifurcations. By means of a numerical approach, the bifurcated families of periodic attitudes are identified. The natural and bifurcated families constitute networks of periodic attitude families. 相似文献
2.
A global picture of the families of simple periodic orbits in terms of their characteristics is given in the part of the plane (γ, ξ1) of representation near the singularity corresponding to the small primary, for the case of the restricted problem with a small value of the mass parameter μ. The value used for μ is smaller than the critical value of Routh. The picture is found to be qualitatively different from the one corresponding to μ larger than the critical value. By means of the stability parameters four new families, consisting of asymmetric periodic orbits, are shown to exist as bifurcations of families of symmetric periodic orbits. 相似文献
3.
We consider the BSBM(Bekenstein, Sandvik, Barrow and Magueijo) cosmological model in the presence of tachyon potential with the aim of studying the stability of the model and test it against observations. The phase space analysis shows that from fourteen critical points that represent the state of the universe, only one is stable.With a small perturbation, the universe transits from a state of unstable deceleration to stable acceleration. The stability analysis combined with the best fitting process imposes constraints on the cosmological parameters that are in agreement with observation. In the BSBM theory, the variation of fundamental constants is driven from variation of a scalar field. The tachyonic scalar field, responsible for both variation of fundamental constants and universal acceleration, is reconstructed. 相似文献
4.
G. Contopoulos 《Celestial Mechanics and Dynamical Astronomy》1987,42(1-4):239-250
We study the evolution of families of periodic orbits of simple 3-dimensional models representing the central parts of deformed galaxies. In some cases the evolution is non-unique, i.e. if we follow a closed path in the parameter space we do not return with the same periodic orbit. This happens when the path surrounds a critical point. We found that critical points are generated at particular collisions of bifurcations in limiting cases when the 3-D system is separated into a 2-D system and an independent oscillation along the third axis. The regions of stability and instability of some families of periodic orbits change in remarkable ways near the various collisions of bifurcations and around the critical points. 相似文献
5.
Sławomir Breiter 《Celestial Mechanics and Dynamical Astronomy》2000,77(3):201-214
The resonance C7 is a 1:1 eccentricity (apsidal) resonance between the longitude of a satellite's pericentre and the mean
longitude of the Sun. A previous paper by the author (Breiter, 1999) identified it as the strongest of the lunisolar apsidal
resonances. After the reduction to a single degree of freedom, the problem is studied qualitatively for the prograde orbits
around the Earth and Mars. Pitchfork, saddle-node, and saddle connection bifurcations give rise to a complicated phase flow,
which may involve up to nine critical points.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
R. A. Broucke 《Celestial Mechanics and Dynamical Astronomy》1994,58(2):99-123
We describe a collection of results obtained by numerical integration of orbits in the main problem of artificial satellite theory (theJ
2 problem). The periodic orbits have been classified according to their stability and the Poincaré surfaces of section computed for different values ofJ
2 andH (whereH is thez-component of angular momentum). The problem was scaled down to a fixed value (–1/2) of the energy constant. It is found that the pseudo-circular periodic solution plays a fundamental role. They are the equivalent of the Poincaré first-kind solutions in the three-body problem. The integration of the variational equations shows that these pseudo-circular solutions are stable, except in a very narrow band near the critical inclincation. This results in a sequence of bifurcations near the critical inclination, refining therefore some known results on the critical inclination, for instance by Izsak (1963), Jupp (1975, 1980) and Cushman (1983). We also verify that the double pitchfork bifurcation around the critical inclination exists for large values ofJ
2, as large as |J
2|=0.2. Other secondary (higher-order) bifurcations are also described. The equations of motion were integrated in rotating meridian coordinates. 相似文献
7.
8.
Galaxies with supermassive binary black holes: (I) a possible model for the centers of core galaxies
The dynamics of galactic systems with central binary black holes is studied. The model is a modification from the restricted three body problem, in which a galactic potential is added as an external potential. Considering the case with an equal mass binary black holes, the conditions of existence of equilibrium points, including Lagrange Points and additional new equilibrium points, i.e. Jiang-Yeh Points, are investigated. A critical mass is discovered to be fundamentally important. That is, Jiang-Yeh Points exist if and only if the galactic mass is larger than the critical mass. The stability analysis is performed for all equilibrium points. The results that Jiang-Yeh Points are unstable could lead to the core formation in the centers of galaxies. 相似文献
9.
Antonis D. Pinotsis 《Earth, Moon, and Planets》2010,107(2-4):225-251
We present a systematic investigation of the parametric evolution of both retrograde and direct families of periodic motions as well as their stability in the inner region of the peripheral primaries of the planar N-body regular polygonal configuration (ring model). In particular, we study the change of the bifurcation points as well as the change of the size and dynamical structure of the rings of stability for different values of the parameters ν = N?1 (number of peripheral primaries) and β (mass ratio). We find some types of bifurcations of families of periodic motions, namely period doubling pitchfork bifurcations, as well as bifurcations of symmetric and non-symmetric periodic orbits of the same period. For a given value of N ? 1, the intervals Δx and ΔC of the rings of stability (where the periodic orbits are stable) of both retrograde and direct families increase with β increasing, while for a given value of β, the interval ΔC decreases with increasing N ? 1. In general, it seems that the dynamical properties of the system depend on the ratio (N ? 1)/β. The size of each ring of stability tends to zero as the ratio (N ? 1)/β → ∞, that is, if N ? 1→∞ or β → 0, the size of each ring of stability tends to zero (Δx → 0 and ΔC → 0) and, in general, the retrograde and direct families tend to disappear. This study gives us interesting information about the evolution of these two families and the changes of the bifurcation patterns since, for example, in some cases the stability index A oscillates between ?1 ≤ Α ≤ + 1. Each time the family becomes critically stable a new dynamical structure appears. The ratios of the Jacobian constant C between the successive critical points, C i /C i+1, tend to 1. All the above depend on the parameters N ? 1, β and show changes in the topology of the phase space and in the dynamical properties of the system. 相似文献
10.
SŁawomir Breiter 《Celestial Mechanics and Dynamical Astronomy》2001,80(1):1-20
The resonance C1 occurs when the longitude of the perigee measured from the equinox becomes a slow angle in the doubly averaged equations of motion. This resonance is one of the critical inclination family with I 46°. For prograde Earth satellite orbits, up to five critical points can be identified. Only simple pitchfork bifurcations occur for the single resonance C1. A two degrees of freedom system is studied to check how a coupling of two lunisolar resonances affects the results furnished by the analysis of an isolated resonance case. In the system with two critical angles (g+h and h,+2 , seven types of critical points have been identified. The critical points arise and change their stability through 11 bifurcations. If the initial conditions are selected close to the critical points, the system becomes chaotic as shown in Poincaré maps. 相似文献
11.
12.
The Sun’s magnetic field is the primary factor determining the structure and evolution of the solar corona. Here, magnetic
topology is used in combination with a Green’s function method to model the global coronal magnetic field with a spherical
photosphere. We focus on the case of three negative flux sources and one positive source, completing our previous categorisation
of the topological states and bifurcations that are present in quadrupolar configurations in a spherical geometry. Three fundamental
varieties of topological state are found, with three types of bifurcation taking one to the other. A comparison to the equivalent
results for a planar photosphere is then carried out, and the differences between the two cases are explained. 相似文献
13.
V. V. Prokof’eva-Mikhailovskaya V. V. Busarev N. N. Gor’kavyi A. N. Rublevskii 《Kinematics and Physics of Celestial Bodies》2011,27(6):291-298
A new spectral-frequency method (SFM) for the study of solid body surfaces is briefly described. This method allows estimation
of the sizes of various spots. Estimates for the sizes of spots on asteroid surfaces made by the SFM and other methods are
compared and discussed. The sizes of spots on the surface of asteroid 1620 Geographos determined by the SFM are well consistent
with those of the craters obtained from radar data. The sizes of hydrosilicate spots on the surface of asteroid 21 Lutetia
found by the SFM agree with those of the craters determined by the Rosetta spacecraft. The size of a blue spot on the surface
of asteroid 4 Vesta found by the SFM is consistent with the size of the well-known crater on the south pole of the asteroid.
It is inferred that the SFM is a promising method for the estimation of the sizes of spots on asteroid surfaces. 相似文献
14.
In this paper, the restricted problem of three bodies is generalized to include a case when the passively gravitating test particle is an oblate spheroid under effect of small perturbations in the Coriolis and centrifugal forces when the first primary is a source of radiation and the second one an oblate spheroid, coupled with the influence of the gravitational potential from the belt. The equilibrium points are found and it is seen that, in addition to the usual three collinear equilibrium points, there appear two new ones due to the potential from the belt and the mass ratio. Two triangular equilibrium points exist. These equilibria are affected by radiation of the first primary, small perturbation in the centrifugal force, oblateness of both the test particle and second primary and the effect arising from the mass of the belt. The linear stability of the equilibrium points is explored and the stability outcome of the collinear equilibrium points remains unstable. In the case of the triangular points, motion is stable with respect to some conditions which depend on the critical mass parameter; influenced by the small perturbations, radiating effect of the first primary, oblateness of the test body and second primary and the gravitational potential from the belt. The effects of each of the imposed free parameters are analyzed. The potential from the belt and small perturbation in the Coriolis force are stabilizing parameters while radiation, small perturbation in the centrifugal force and oblateness reduce the stable regions. The overall effect is that the region of stable motion increases under the combine action of these parameters. We have also found the frequencies of the long and short periodic motion around stable triangular points. Illustrative numerical exploration is rendered in the Sun–Jupiter and Sun–Earth systems where we show that in reality, for some values of the system parameters, the additional equilibrium points do not in general exist even when there is a belt to interact with. 相似文献
15.
The critical inclination in artificial satellite theory 总被引：1，自引：0，他引：1
Shannon L. Coffey André Deprit Bruce R. Miller 《Celestial Mechanics and Dynamical Astronomy》1986,39(4):365-406
Certain it is that the critical inclination in the main problem of artificial satellite theory is an intrinsic singularity. Its significance stems from two geometric events in the reduced phase space on the manifolds of constant polar angular momentum and constant Delaunay action. In the neighborhood of the critical inclination, along the family of circular orbits, there appear two Hopf bifurcations, to each of which there converge two families of orbits with stationary perigees. On the stretch between the bifurcations, the circular orbits in the planes at critical inclinmation are unstable. A global analysis of the double forking is made possible by the realization that the reduced phase space consists of bundles of two-dimensional spheres. Extensive numerical integrations illustrate the transitions in the phase flow on the spheres as the system passes through the bifurcations.A delicacy so very susceptible of offence...—Hester Lynch PIOZZI,Observations and Reflections made in the Course of a Journey through France, Italy and Germany (1789)NAS/NRC Postgraduate Research Associate in 1984–1985. 相似文献
16.
Giuseppe Pucacco 《Monthly notices of the Royal Astronomical Society》2009,399(1):340-348
We investigate an analytical treatment of bifurcations of families of resonant 'thin' tubes in axisymmetric galactic potentials. We verify that the most relevant bifurcations are due to the (1:1) resonance producing the 'inclined' orbits through two different mechanisms: from the disc orbit and from the 'thin' tube associated with the vertical oscillation. The closest resonances occurring after these are the (4:3) resonance in the oblate case and the (2:1) resonance in the prolate case. The (1:1) resonances are treated in a straightforward way using a second-order truncated normal form. The higher order resonances are instead cumbersome to investigate, because the normal form has to be truncated to a high degree and the number of terms grows very rapidly. We therefore adopt a further simplification giving analytical formulae for the values of the parameters at which bifurcations ensue and compare them with selected numerical results. Thanks to the asymptotic nature of the series involved, the predictions are reliable well beyond the convergence radius of the original series. 相似文献
17.
E. A. Perdios 《Celestial Mechanics and Dynamical Astronomy》2007,99(2):85-104
This paper deals with the Sitnikov family of straight-line motions of the circular restricted three-body problem, viewed as
generator of families of three-dimensional periodic orbits. We study the linear stability of the family, determine several
new critical orbits at which families of three dimensional periodic orbits of the same or double period bifurcate and present
an extensive numerical exploration of the bifurcating families. In the case of the same period bifurcations, 44 families are
determined. All these families are computed for equal as well as for nearly equal primaries (μ = 0.5, μ = 0.4995). Some of the bifurcating families are determined for all values of the mass parameter μ for which they exist. Examples of families of three dimensional periodic orbits bifurcating from the Sitnikov family at double
period bifurcations are also given. These are the only families of three-dimensional periodic orbits presented in the paper
which do not terminate with coplanar orbits and some of them contain stable parts. By contrast, all families bifurcating at
single-period bifurcations consist entirely of unstable orbits and terminate with coplanar orbits. 相似文献
18.
E. J. Weber 《Astrophysics and Space Science》1973,20(2):401-415
An isothermal hydrodynamic model of the motions of a multi-ion plasma in a gravitational field is developed and the properties of the flow are discussed for the case of major astrophysical interest in which the gas undergoes a subsonic-supersonic transition. It is shown that the existence of critical points thorough which the plasma has to pass will determine a large number of the plasma parameters, especially the temperature of the minor ions. The equation of motion of a two ion gas (hydrogen-helium) are solved numerically and yield the interesting result that the bulk velocity of the plasma constituents are not equal at 1 AU.Operated by the Association of Universities for Research in Astronomy, under contract with the National Science Foundation. 相似文献
19.
Lidia Jiménez-Lara Adolfo Escalona-Buendía 《Celestial Mechanics and Dynamical Astronomy》2001,79(2):97-117
We present some qualitative and numerical results of the Sitnikov problem, a special case of the three-body problem, which offers a great variety of motions as the non-integrable systems typically do. We study the symmetries of the problem and we use them as well as the stroboscopic Poincarée map (at the pericenter of the primaries) to calculate the symmetry lines and their dynamics when the parameter changes, obtaining information about the families of periodic orbits and their bifurcations in four revolutions of the primaries. We introduce the semimap to obtain the fundamental lines l
1. The origin produces new families of periodic orbits, and we show the bifurcation diagrams in a wide interval of the eccentricity (0 0.97). A pattern of bifurcations was found.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
20.
R. Broucke J. D. Anderson L. Blitzer E. Davoust H. Lass 《Celestial Mechanics and Dynamical Astronomy》1981,24(1):63-82
The article describes the solutions near Lagrange's circular collinear configuration in the planar problem of three bodies with three finite masses. The article begins with a detailed review of the properties of Lagrange's collinear solution. Lagrange's quintic equation is derived and several expressions are given for the angular velocity of the rotating frame.The equations of motion are then linearized near the circular collinear solution, and the characteristic equation is also derived in detail. The different types of roots and their corresponding solutions are discussed. The special case of two equal outer masses receives special attention, as well as the special case of two small outer masses.Finally, the fundamental family of periodic solutions is extended by numerical integration all the wap up to and past a binary collision orbit. The stability and the bifurcations of this family are briefly enumerated. 相似文献