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1.
A largely numerical study was made of families of three-dimensional, periodic, halo orbits near the collinear libration points in the restricted three-body problem. Families extend from each of the libration points to the nearest primary. They appear to exist for all values of the mass ratio , from 0 to 1. More importantly, most of the families contain a range of stable orbits. Only near L1, the libration point between the two primaries, are there no stable orbits for certain values of . In that case the stable range decreases with increasing , until it disappears at =0.0573. Near the other libration points, stable orbits exist for all mass ratios investigated between 0 and 1. In addition, the orbits increase in size with increasing .  相似文献   

2.
A model of a first generation intermediate star of 5M , with Z=0 has been considered. The model is at an advanced stage of its evolution and has a double shell burning. It burns helium in the inner shell, and hydrogen, via CNO cycle, in the outer shell. =(log/log) T and T =(log/logT) were computed allowing for the oscillations of the relative mass abundance of the reagents in nuclear reactions. Including =(log/log) T and =(log/logT) of mean molecular weight and the effect of the oscillations of abundances due to nuclear reactions, stability was studied. Contrary to the results of the static calculations, we found that instability due to the excitation mechanism provided by the high temperature sensitivity of energy generation rate propagates up to the surface. Thus the model in question was found to be unstable against radial adiabatic pulsations, in its fundamental mode.  相似文献   

3.
The scope of the present paper is to provide analytic solutions to the problem of the attitude evolution of a symmetric gyrostat about a fixed point in a central Newtonian force field when the potential function isV (2).We assume that the center of mass and the gyrostatic moment are on the axis of symmetry and that the initial conditions are the following: (t 0)=0, (t 0)=0, (t 0)=(t 0)=0, 1(t 0)=0, 2(t 0)=0 and 3(t 0)= 3 0 .The problem is integrated when the third component of the total angular momentum is different from zero (B 1 0). There now appear equilibrium solutions that did not exist in the caseB 1=0, which can be determined in function of the value ofl 3 r (the third component of the gyrostatic momentum).The possible types of solutions (elliptic, trigonometric, stationary) depend upon the nature of the roots of the functiong(u). The solutions for Euler angles are given in terms of functions of the timet. If we cancel the third component of the gyrostatic momentum (l 3 r =0), the obtained solutions are valid for rigid bodies.  相似文献   

4.
Hong Wei Li 《Solar physics》1986,104(1):131-136
The variations of the growth rates of ECM at first four harmonics in X-, Z-, and O-modes excited by a hollow beam distribution of weakly relativistic electrons with a parameter p / e are presented in this paper. The results show that the second harmonic of ECM in X-mode dominates the instability if < 1, and if 1.2 , 2 or 2.2 3 the third or fourth harmonic will dominate. The second and third harmonics of Z-mode waves grow faster only if 2 2.2 and 3 3.2, respectively, so it would not be a competition in most cases. It is suggested that the ECM emission at these harmonics in X-mode is a possible mechanism to produce solar spike emissions with high brightness temperature at shorter and longer decimetric wavelengths.Proceedings of the Workshop on Radio Continua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.On leave from the Department of Astronomy, Nanjing University, Nanjing, The People's Republic of China.  相似文献   

5.
Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity , , respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values , for modeling such fluctuations. Perturbed values i = i + i ,v i = i + v i were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (= v =0,2 =v 2 = 10–8) grow many times in marginally-stable state.  相似文献   

6.
Families of three-dimensional axisymmetric periodic orbits are determined numerically in the Sun-Jupiter case of the restricted three-body problem. These families bifurcate from the vertical-critical orbits (v = 1,b v = 0) of the basic plane familiesi andI. Further the predictor-corrector procedure employed to reveal these families has been described and interesting numerical results have been pointed out. Also, computer plots of the orbits of these families have been shown in conical projections.  相似文献   

7.
We emphasize the sharp distinctions between different one-body gravitational trajectories made by the ratio of time averagesR(t)–E kin/E pot.R is calculated as a function of the eccentricity (e) and of the energy (E). Whent, independently ofe andE, R1/2 for closed orbits (this clearly illustrates the fulfillment of the virial theorem in classical mechanics); whereasR1, at any time, for open orbits.  相似文献   

8.
We determine the momentum distribution of the relativistic particles near the Crab pulsar from the observed X- and -ray spectra (103109 eV), provided that the curvature radiation is responsible for it. The power law spectrum for the relativistic electrons,f() –5, reproduces a close fit to the observed high-energy photon spectrum. The theoretically determined upper limit to the momentum (due to radiation damping), M 8×106, corresponds to the upper cut-off energy of the -ray spectrum, 109 eV. The lower limit to the momentum, m 1.8×105, is chosen such that flattening of the X-ray spectrum below 10 keV is simulated. The number density of these electrons is found to be much higher than the Goldreich-Julian density. We also discuss pulse shape and polarization of high-energy photons. The extremely high density of particles and the steep momentum spectrum are difficult to understand. This may imply that another, more efficient, mechanism is in operation.  相似文献   

9.
Analytic structure of high-density steady isothermal spheres is discussed using the TOV equation of hydrostatic equilibrium which satisfies an equation of state of the kind:P = K g , = g c 2.Approximate analytical solutions to the Tolman-Oppenheimer-Volkoff (TOV) equations of hydrostatic equilibrium in (, ), (,U) and (u, v) phase planes in concise and simple form useful for short computer programmes or on small calculator, have been given. In Figures 1, 2, and 3, respectively, we display the qualitative behaviours of the ratio of gas density g to the central density gc , g / gc ; pressureP to the gc ,P/ gc ; and the metric componente –, for three representative general relativistic (GR) isothermal configurations =0.1, 0.2, and 0.3. Figure 4 shows the solution curve (, ) for =0.1, 0.2, and 0.3 (=0 represents the classical (Newtonian) curve). Numerical values of physical quantitiesv (=4r 2 P *(r)), in steps ofu (=M(r)/r)=0.03, and the mass functionU, in steps of =0.2 (dimensionless radial distance), are given, respectively, in Tables I and II. Other interesting features of the configurations, such as ratio of gravitational radius 2GM/c 2 to the coordinate radiusR, mass distributionM(r)/M, pressure (or density) distributionP/P c , binding energy (B.E.), etc., have also been incorporated in the text. It has further been shown that velocity of sound inside the configurations is always less than the velocity of light.Part of the work done at Azerbaijan State University, Baku, U.S.S.R., and Mosul University, Mosul, Iraq, 1985-1986  相似文献   

10.
, , , , , . , , . - . — , , .  相似文献   

11.
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   

12.
The known intervals of possible stability, on the mgr-axis, of basicfamilies of 3D periodic orbits in the restricted three-body problem areextended into -A1 regions for oblate larger primary, A 1 beingthe oblateness coefficient. Eight regions, corresponding to the basicstable bifurcation orbits l1v, l1v, l2v, l3v, m1v, m1v,m2v, i1v are determined and related branching 3D periodic orbits arecomputed systematically and tested for stability. The regions for l1v,m1v and m2v survive the test emerging as the regions allowing thesimplest types of stable low inclination 3D motion. For l1v, l2v,l3v, m1v and m2v oblateness seems to have a stabilising effect,while stability of i1v survives only for a very small range of A 1values.  相似文献   

13.
A 3-D particle simulation of excitation of whistler waves driven by an electron temperature anisotropy (T > T ) is presented. Results show that whistler waves can have appreciable growth driven by the anisotropy. The maximum intensity of the excited whistler waves increases as a quadratic function of the anisotropy. Due to the presence of a threshold, one needs a relatively large electron temperature anisotropy above threshold to generate large-amplitude whistler waves. The average amplitude of turbulence in the context of whistler waves is up to as large as about 1% of the ambient magnetic field when T /T . The total energy density of the whistler turbulence is adequate for production of relativistic electrons in solar flares through stochastic acceleration.  相似文献   

14.
The stars in the Main Sequence are seen as a hierarchy of objects with different massesM and effective dynamical radiiR eff=R/ given by the stellar radii and the coefficients for the inner structure of the stars.As seen in a previous work (Paper I), during the lifetime in the Main SequenceR eff(t) remains a near invariant when compared to the variation in the time ofR(t) and (t).With such an effectiveR eff one obtains the amounts of actionA c(M), the effective densities eff(M)=(M)3(M), the densities of action and of energy (or mean presures in the stellar interior)a c(M),e c(M), and the potential energiesE p(M).The amounts of action areA cM k withk1.87 for the M stars,k5/3 for the KGF stars, andk1.83 for the A and earlier stars, representing very simples conditions for the other dynamical parameters. For instancek5/3 means a near invariant effective density eff for the KGF stars, while for such stars the mean densities and coefficients present the strongest variations with masses (M)M –1.81, (M)M0.6.The cases for the M stars (e c(M)M –1) and for the A and earlier stars (betweena c(M)=constant and eff(M)M –1) and also discussed. These conditions for the earlier stars also represent reasonable mean values for the whole stellar hierarchy in the range of masses 0.2M M25M .With all this, one can build dynamical HR diagrams withA c(M), Ep(M), eff M –p , etc., whose characteristics are analogous to these in the photometrical HR diagram. A comparison is made betweenA c(M) from the models here and the HR diagram with the best known stars of luminosity classes IV, V, and white dwarfs.The comparison of the potential energiesE p(M)M –p according to the stellar models used here and the observed frequency function (MM –q (number of stars in a given interval of masses) from different authors suggests the possibility that the productE p(M)(M) is a constant, but this must be confirmed with further studies of the function (M) and its fine structure.There are analogies between the formulation used here for the stellar hierarchy and other physical processes, for instance, in modified forms of the Kolmogorov law of turbulence and in the formulation used for the hierarchy of molecular clouds in gravitational equilibrium. Besides, the function of actionA c(M) for the stars has analogous properties to the relations of angular momenta and massesJ(M) for different types of objects. The cosmological implications of all this are discussed.  相似文献   

15.
-- () ., , , , , . , , . , .  相似文献   

16.
An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H 0 applied magnetic field - H magnetic field intensity - (j x , j y , j z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n e electron number density - P Prandtl number - q velocity vector - (T, T w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U 0 uniform velocity - v 0 suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - e charge density - electrical conductivity - e electron collision time  相似文献   

17.
As a possible mechanism for particle acceleration in the impulsive phase of solar flares, a new particle acceleration mechanism in shock waves is proposed; a collisionless fast magnetosonic shock wave can promptly accelerate protons and electrons to relativistic energies, which was found by theory and relativistic particle simulation. The simultaneous acceleration of protons and electrons takes place in a rather strong magnetic field such that ce pe . For a weak magnetic field ( ce pe ), strong acceleration occurs to protons only. Resonant protons gain relativistic energies within the order of the ion cyclotron period (much less than 1 s for solar plasma parameters). The electron acceleration time is shorter than the ion-cyclotron period.  相似文献   

18.
The mean lifetime of a particle distribution, driven to isotropy by intense pitch-angle diffusion, is calculated by analytical means for conditions applicable to the Earth's magnetosphere. The resulting algebraic expressions reduce to [64La/35v c 2 (1–)] in the limit of a small equatorial loss cone (half-angle c ), wherev is the particle speed,L is the magnetic shell parameter,a is the radius of the Earth, and is the particle albedo from the atmosphere at either foot of the field line. Distinction is made in the full expressions for between complete isotropy (caused by strong pitch-angle diffusion all along the field line) and incomplete isotropy (caused by strong diffusion that is localized at the magnetic equator) over the upward hemisphere in velocity space.  相似文献   

19.
We study the bifurcations of families of double and quadruple period orbits in a simple Hamiltonian system of three degrees of freedom. The bifurcations are either simple or double, depending on whether a stability curve crosses or is tangent to the axis b=–2. We have also generation of a new family whenever a given family has a maximum or minimum or .The double period families bifurcate from simple families of periodic orbits. We construct existence diagrams to show where any given family exists in the control space (, ) and where it is stable (S), simply unstable (U), doubly unstable (DU), or complex unstable (), We construct also stability diagrams that give the stability parameters b1 and b2 as functions of (for constant ), or of (for constant ).The quadruple period orbits are generated either from double period orbits, or directly from simple period orbits (at double bifurcations). We derive several rules about the various types of bifurcations. The most important phenomenon is the collision of bifurcations. At any such collision of bifurcations the interconnections between the various families change and the general character of the dynamical system changes.  相似文献   

20.
In a previous publication (1977) the author has constructed a family () of long-periodic orbits in the Trojan case of the restricted problems of three bodies. Here he constructs the domain of the analytical solution of the problem of the motion, excluding the vicinity of thecritical divisor which vanishes at the exact commensurability of the natural frequencies 1 and 2. In terms of thecritical masses mj(2), or the associatedcritical energies j 2 (m), is the intersection of the intervals ofshallow resonance, of the form. Inasmuch as the intervals |2– j 2 |<j ofdeep resonance aredisjoint, it follows that (1) the disjointed family () embraces the tadpole branch, 021, lying in: and (2) despite the clustering of j 2 (m) atj=, the family () includes, for 2=1, an asymptoticseparatrix that terminates the branch in the vicinity of the Lagrangian pointL 3.In a similar manner, the family () can be extended to the horseshoe branch 1<2 2 2 .  相似文献   

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