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Some asymptotic solutions in the restricted problem of three bodies by L. G. Lukjanov.
Some particular solutions of the plane restricted problem of three bodies in the form of Liapunov's series are obtained. These solutions asymptotically approach the Lagrange solutions. Convergence is proved.
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, ii (2000–3000 Å) i . , i . i (. 2). i i i i + ( 7–10). ii (. 13). ii i i (, 2400 Å) (. 14 15). i i i , iu , i (. 1). i i ii i i . .  相似文献   

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An exact analysis of the effects of mass transfer on the flow of a viscous incompressible fluid past an uniformly accelerated vertical porous and non-porous plate has been presented on taking into account the free convection currents. The results are discussed with the effects of the Grashof number Gr, the modified Grashof number Sc, the Schmidt number Sc, and the suction parametera for Pr (the Prandtl number)=0.71 representating air at 20°C.Nomenclature a suction parameter - C species concentration - C species concentration at the free stream - g acceleration due gravity - Gc modified Grashof number (vg*(C C )/U 0 3 ) - Pr Prandtl number (C p/K) - T temperature of the fluid near the plate - T dimensionless temperature near the plate ((T-T )/(T -T )) - U(t) dimensionless velocity of the plate (U/U 0) - v normal velocity component - v 0 suction/injection velocity - x, y coordinate along and normal to the plate - v kinematic viscosity (/gr) - C p specific heat at constant pressure - C w species concentration at the plate - C non-dimensional species concentration ((C-C )/(C w -C )) - Gr Grashof number (g(T w -T )/U 0 3 ) - D chemical molecular diffusivity - K thermal conductivity - Sc Schmidt number (/D) - T w temperature of the plate - T free stream temperature - t time variable - t dimensionless time (tU 0 2 /) - U 0 reference velocity - u velocity of the fluid near the plate - u non-dimensional velocity (u/U 0) - v dimensionless velocity (v/U 0) - v 0 non-dimensionalv 0 (v 0 /U0)=–at–1/2 - y dimensionless ordinate (yU 0/) - density of the fluid - coefficient of viscosity  相似文献   

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Evolutionary tracks of 0.9M , 0.7M and 0.6M models for Population II stars have been computed in the post-red giant phase. The stars are initially composed of a helium core containing a mass fraction equal to 0.9 and of a hydrogen-rich envelope. They represent hypothetical remnants of stars after substantial mass loss in previous evolutionary phases or/and at the helium flash.u 0,9M , 0,7M 0,6M . , 90% , . , .Riassunto È stata calcolata per modelli di stelle di 0,9M , 0,7M e 0,6M di Popolazione II l'evoluzione successiva allo stadio di gigante rossa. Inizialmente i modelli constano di un nucleo di elio contenente il 90% della massa totale e di un inviluppo idrogenico. Essi possono interpretarsi come i resti di stelle che abbiano perso una frazione di massa considerevole in fasi evolutive precedenti, o all'innesco violento dell'elio al centro.  相似文献   

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2800 Mgii (. 1). (N +/N 11000) , , (N +/N 110). , . —, , . — . : ; 0.002 1 , 0.1 ; () 100 –3; ; ; , 10 ; 10–4 1 . 2800 Mgii .  相似文献   

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With the Hamiltonian parameters developed for the two-fixed-centers problem a simple and very accurate expression of the quasi-integral can be given for the motion of artificial satellites perturbed by the Earth's zonal harmonics. This motion can be considered as integrable.A theoretical analysis shows that Hénon's semi-ergodic regions or chaotic regions are extremely small in this problem, and almost all orbits are of the regular or quasi-periodic type. Furthermore, the relative difference between the true motion and the corresponding integrable motion remains forever less than 10–14 for all regular orbits even in the vicinity of critical inclinations.For chaotic orbits this very small difference remains verified at least for centuries, nevertheless there are some exceptional orbits that finally diverge from the integrable model.  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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1937 - (, 1938). , , , , . , . . (, 1938), , . - (, 1938; Szebehely, 1967)., , . . - (, 1938), . — — . , , . , . . , . , , . . (, 1944). , .
In 1937, the Celestial Mechanics and Cosmogony section of the Sternberg State Astronomical Institute undertook the task of evaluating the Gylden-Moulton hypothesis on the origin of the Gegenshein from the standpoint of celestial mechanics. That investigation, which the authors themselves considered preliminary, contains nonetheless a series of important results. For example, G. N. Duboshin showed that in the planar, circular, restricted three-body problem, periodic motion of finite amplitude in the neighborhood of a collinear libration point is unstable according to Lyapunov's criterion both in the proper and in the orbital sense. The latter result is incompatible with the above named hypothesis, and thus appears as one of the serious objections among the many known negative conclusions relative to the existence of the Gylden-Moulton cluster.Unfortunately, most of the specific problems which arose in the above named research have not been considered since. One of these, the problem of the stability of three-dimensional periodic orbits in the neighborhood of a collinear libration point is solved in the present paper, within the limits of the three-dimensional, circular, restricted, three-body problem. Major attention is given to the investigation of stability in the orbital sense, since in the proper sense all orbits are unstable according to Lyapunov theory. It is shown that in order to resolve the question of stability, it is sufficient to consider the equations in their variational form. Analysis of the roots of the corresponding characteristic equations determines the orbital stability of planar and three-dimensional solutions, which later can be confirmed by calculation of the characteristic exponents appearing in the periodic solutions of the N. A. Artemiev method. Finally, the possibility of conditional stability in the linear approximation is proved.
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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   

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. . ,e, , . . e, . , .
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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We implement a complex-plane strategy and a multiple partition technique to the computation of polytropic models distorted by very strong and very rapid differential rotation. We also verify with our numerical results a heuristic relation between stability and virial theorem.  相似文献   

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Periodic orbits of stars in axisymmetrical nearly spherical stellar systems have been investigated. Generating orbits have been found among periodic ones relating to the spherically-symmetrical field. The linear approximation appears to be insufficient for constructing periodic trajectories. Possible variants of the generating periodic solutions have been found, which give rise to disturbed periodic orbits in the second approximation.
, . - . , . , .
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Orbital stability of quasiperiodic motions in the many dimensional autonomic hamiltonian systems is considered. Studied motions are supposed to be not far from equilibrium, the number of their basic frequencies may be not equal to the number of degrees of freedom, and the procedure of their construction is supposed to be converged. The stability problem is solved in the strict nonlinear mode.Obtained results are used in the stability investigation of small plane motions near the lagrangian solutions of the three-dimensional circular restricted three-body problem. The values of parameters for which the plane motions are unstable have been found.
. , , . . , . , .
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One component of a three-fluid adiabatic plasma is under certain conditions contained in a restricted region of space by a large-scale electrostatic field generated within the plasma. The containment is discussed here for plasma consisting of ions and two populations of electrons characterized by different pitch angle distribution functions.The bouncing motion of electrons along open fieldlines between a magnetic mirror and an electrostatic mirror produces a velocity distribution function similar to that generated by bouncing particles on closed fieldlines.  相似文献   

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