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Stability of the librational triangular points of the three-dimensional elliptic restricted three-body problem is studied. The problem is solved in the non-linear statement at the small values of eccentricity.For all values ofe, , besides ones which correspond to the resonances of the third and the fourth order the librational points are stable taking into account the terms up to the fourth order in the normal form of the Hamiltonian function of the perturbed motion.At sufficiently smalle and the non-stability in sense of Liapunov has been proved. The approximate equations of the boundary of the stability area in the planee, has been obtained. The cause of the non-stability is an equality of the rotational period of the principal attracting masses in the elliptic orbit and the period of oscillation of indefinitely small mass along the direction perpendicular to the plane of their motion.
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qp qz : (1) -, qi , (2) - (R=0.01–0.1R ) (3) - . qs. (1) - 0.1 10–4 cm –2, . - . (2) 108 . . 1042–43 , (25 ). 10% - (0.1 ). , , , , , . . (3) , , - . . (2×1041 ) (1021 ). - 1038–1039 , 0.25 . , , qq . - , , .
The following three mechanisms of generation of gamma-ray bursts at advanced phases of stellar evolution are considered; (1) gamma-ray bursts as a result of absorption of neutrino propagating through the envelope of a collapsing star, (2) gamma-ray burst due to thermal radiation of external layers of a compact star (R=0.01–0.1R ) heated by powerful shock wave, and (3) gamma-ray burst as a consequence of possible ejection of matter from neutron star at some active phases of its evolution. In the case (1) the gamma-ray flux at the top of the Earth's atmosphere is about 10–4 (0.1 MeV photons) cm–2, if a collapsing star is at Galactic distance (10 kpc). It is considerably less than observed one. The observations of such gamma-bursts however would be an important supplement to the direct detection of neutrino radiation from collapsing stars. In the case (2) external layers of a star are heated up to 108 K. As a result we have a short pulse of thermal radiation with total energy of the order of 1042–43 erg. The main fraction of the radiation is in the X-ray ( 25 keV), about 10% of total energy being radiated in gamma-ray ( 0.1 MeV). The energy of such a burst is sufficient for explaining observed gamma-bursts provided the supernova outburst probably takes place in our Galaxy and as a result we have some trouble with explanation of observed frequency and spectra of gammabursts. In the case (3) ejection from neutron star of chemically nonequilibrium matter results in the intensive gamma-radiation in consequence of superheavy nuclei fission followed by beta-decays and radiative captures of free neutrons. The ejection of matter from neutron stars may be connected with observed jumps of pulsar's periods. The total ejected mass ( 1021 g) can be evaluated from increase of kinetic energy ( 2×1041 erg.) of Crab nebula filaments. The resulting theoretical energy of gammabursts is of the order of 1038–39 erg. It is in accordance with observations provided the mean distance of gamma-ray sources is about 0.25 kpc. Contrary to the supernova-outburst mechanism in this case we have probably no troubles with frequency and spectra of gamma-bursts. Among the three mechanisms considered above ejection of matter from neutron stars seems to be a more suitable one for explanation of observations.
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Nonlinear propagation of strong low-frequency waves, as emitted by pulsars or compact galactic nuclei at their rotation frequencies, in a magnetized plasma is investigated. It is shown that even rather small amplitude waves can drive electrons to ultrarelativistic energies. In the limit when the electrons are ultrarelativistic but the ions are immobile, two types of circularly polarized waves (i.e., ± modes) are excited. In the wave zone of the Crab pulsar, both the electric field ( 3 V m–1) and the wavelength (108 m) of the - mode are larger, by an order of magnitude, than those of the + wave mode. Both ± modes can become modulationally unstable due to their nonlinear interaction with density fluctuations induced by the electrostatic waves.  相似文献   

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. - . . , . - . - , , , -. ., , .
The structure of rotating magnetic polytropes is considered in Roche approximation. Investigation of the influence of poloidal as well as toroidal magnetic fields on the conditions of the beginning of matter outflow due to rotational instability is carried out. The influence of the turbulent convection and twisting of magnetic force-lines on the time of smoothing of differential rotation is considered. The estimate of the magneto-turbulence energy generated by differential rotation is presented. Both maximum possible energy output and duration of the quasi-statical evolution phase up to the appearance of hydrodynamic instability due to the effects of general relativity are calculated for supermassive magnetic polytropes of index three with uniform or differential rotation. The radius-mass relation is obtained for supermassive differentially-rotating magnetic polytropes referring to the longest part of the quasi-statistical evolution stage; some consequences are pointed out, including the period-luminosity relation.The evolution of the considered models of supermassive rotating magnetic polytropes with different character of rotation and different geometry of a magnetic field is discussed.The results obtained are summarized in the last section.


English translation will appear in the next issue ofAstrophys. Space Sci.

Receipt delayed by postal strike in Great Britain  相似文献   

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Stability of the libration points of a rotating triaxial ellipsoid   总被引:1,自引:0,他引:1  
The problem of stability of the equilibrium points (the libration points) in the problem of motion of a mass point in the neighbourhood of a rotating triaxial ellipsoid is investigated in the strict sense.In the plane of parameters, depending on the form and dynamical characteristics of the ellipsoids, the regions of stability and instability of the libration points are obtained.It is shown that the libration points of the ellipsoids, the form and dynamical characteristics of which are close to the planets of the solar system, are stable.
( ) . , , . , , , .
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In the first part of this paper [Marchal, Yoshida, Sun Yi-Sui 1985] we have analyzed three-body systems satisfying the condition rkR where k is a suitable constant, r the mutual distance of the two masses of the binary and R the distance between the center of mass of the binary and the third mass.That condition rkR puts limits on the acceleration of the third mass and these limits allow us to determine the corresponding escape velocities.In this second part we look for initial conditions under which the inequality rkR will remain forever satisfied and we develop the corresponding tests of escape and their applications.This leads to a major improvement of the knowledge of the nature of three-body motions especially in the vicinity of triple close approaches.The region of bounded motions is much smaller than was generally expected and numerical computations of particular solutions show that we approach very near to the true limit.  相似文献   

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An essential part in the mechanics under study is taking into consideration the effect of motions of the Universe objects upon that of an individual one surrounded by them including those infinitely far from it. Only macro-objects of the Universe are meant here.
Zusammenfassung Ein wesentlicher Bestandteil der Mechanik unter unserer Betrachtung ist die Berechnung des Einflusses auf die Bewegung eines individuellen Objektes von Bewegungen der Universum Objekte die es umringen einschließlich jene Objekte, die unendlich entfernt sind. Nur Makroobjekte des Weltalles sind in der Absicht dabei.

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Some attempts of polarimetric sounding of Comet Halley will be undertaken from the flyby probes. In order to facilitate the final planning and the future interpretation of these experiments we have done a thorough analysis of practically all available polarimetric observations. An emphasis is made on interpretation attempts and their discussion. The results of the phase dependence of polarization investigations are presented covering a wide range of phase angles . The chief peculiarities of this dependence are: maximum polarization at = 90, diminishing through zero at 20, negative values up to several per cent and a final growth to zero at zero . A division into gaseous and dusty comets on polarimetric basis is revealed. The wavelength dependence of polarization is discussed. The numerous results of detailed polarimetry are compared to the negative results of attempts to detect the elliptical polarization. New observational problems arising from the evidence given by the negative polarization at small phase angles and by the opposition effect recently discovered are discussed.  相似文献   

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The general conception of the critical inclinations and eccentricities for theN-planet problem is introduced. The connection of this conception with the existence and stability of particular solutions is established. In the restricted circular problem of three bodies the existence of the critical inclinations is proved for any values of the ratio of semiaxes . The asymptotic behaviour of the critical inclinations as 1 is investigated.
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In the framework of non-linear fluid theory we use a lower hybrid (LH) wave of the form as a pump which interacts with the small fluctuations with the low-frequency vibrations i or =0, where i , is the hydrogen ion-cyclotron (HIC) gyrofrequency. The ponderomotive force generated by the beating of the high-frequency pump wave 0 and the sideband LH waves (±0) produces a non-linear coupling between the high- and low-frequency motions of electrons and ions. Under certain conditions the HIC waves and the zero-frequency waves both become parametrically unstable and start to grow. These excited waves then heat the ions by stochastic acceleration in the transverse direction, thus explaining the formation of ion comics along the auroral field lines. Electrons would be heated in the parallel direction directly by the pump field as well as by low-frequency waves. Thus a single mechanism can explain the existence of ion-cyclotron waves, zero-frequency waves, ion conics, and energetic electrons along the auroral field lines.  相似文献   

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We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec2 at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C min the H- 1.5 Å image (C m 0.1 type I, C m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C m- A scatter diagram, in H and H wings, indicates a wide range of variability for C m in correspondence with very narrow range of variability for A.  相似文献   

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