On the stability of equilibria of Hamiltonian systems near the main resonances

The equilibrium point O of an autonomous Hamiltonian system of two degrees of freedom is considered for small-oscillation frequencies related as ₂=2₁+. If under the precise resonance (=0) the equilibrium is unstable, the inner diameter () of the domain of stability containing the point O is estimated. It is shown that for the normalized variables ()/b where b is the corresponding resonance coefficient. The estimates () for other main resonances are reported.     

Движение малых частиц в окрестностях протосолнца переменной светимости

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About the stability of the libration points of a rotating triaxial ellipsoid in a degenerate case

The problem of stability of the equilibrium points in the problem of motion of a mass point in the neighbourhood of a rotating triaxial ellipsoid in a degenerate case (the Gaussian of the Hamiltonian is equal to zero) is investigated.It is proved that the equilibrium points in the degenerate case are stable in the strict sence.

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Résumé On étudie le problème de la stabilité des positions d'équilibre relatif dans le problème du mouvement du point matériel au voisinage de l'ellipsoid à trois axes tournant dans un cas dégénéré (le gaussian du Hamiltonian égal zéro).On a démontré que des positions d'équilibre relatif dans le dégénéré sont stables dans le sens rigoureux.

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Поле излучения в полубесконечной атмосфере, содержащей источники энергии

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On the time variation of rotation parameters of pulsar NP 0532

Calculations of the rotation parameters at initial stage of evolution on the basis of the model suggested by Jones and published observational data of NP 0532 were made. It is shown that the observed dependence of the angular velocity of NP 0532 and its first derivative with respect to time can be explained by an increase of the angle between the magnetic moment and the rotation axis. The time variation of rotation parameters essentially depends on the value and time variation of the viscosity of the star. In spite of the fact that the observational data are not extensive enough, it is possible to conclude that initial rotation frequency of NP 0532 did not exceed essentially 50 Hz.

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О спектре релятивистских электронов, ускоряемых в источниках космическиш лучей

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Перенос поляризации излучения В магнитоактивной космической плазме

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О механззме оптического, рентгеновского и гамма-излучения пульсара в краБе

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О ФОрРИРОВНИИИ диаграммы излучения пульсаров

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The virial-based solution for the velocity of gaseous sphere gravitational contraction

It is found that the relationship between the potential energy and the moment of the inertia independent of the radial mass distribution obtained earlier for the sphere also holds in the case of the ellipsoidal mass distribution for the ellipsoid of rotation.The possibility of application of the energy virial relations for solution of the evolutionary problems of the gravitating gaseous sphere, with the help of the relationship found earlier, is demonstrated. The physical conditions on the gaseous sphere boundary are introduced. The existence of two branches of evolution, the proton one and the electron one, is established. The problem of the gravitational contraction velocity during sphere evolution is solved. The relationship between the boundary temperature and the gaseous sphere radius as well as between the luminosity and the body mass is obtained. Some limiting relations for the final stage of the gaseous sphere evolution are found.

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Magnetic reconnection in a high-temperature plasma of solar flares

Simple self-consistent models for non-neutral current sheets are considered. Characteristics of high-temperature turbulent current sheets (HTCS) with a small transverse component of magnetic field are determined for conditions in the solar corona. The energy output of such an HTCS is much larger than that of a neutral sheet. This makes it possible to consider the HTCS as an energy source not only in long-lived X-ray loops but also in flaring loops during the not or main phase of a flare. In this case, the magnetic reconnection velocity agrees with the observed velocity of the loop rise. Thus, these phenomena can be interpreted as a result of magnetic reconnection, for example, between new flux emerging from under the photosphere and an old magnetic field.The role of a longitudinal magnetic field in a current sheet is less important for HTCS. As a result of the compression of a longitudinal field, there appears an electric current circulating around the sheet. This current may induce strong Joule heating, if the compression is large. This additional heating is realized because of the annihilation of the main component, not the longitudinal component of magnetic field. The effect is small for HTCS, but may be significant for preflare current sheets.     

О лагранжевых и зйлеровых решеиях обощенной задачи трех тел

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This paper is a continuation and a generalization of one published earlier (Duboshin, 1969): it discusses the problem whether there exist the Lagrangian and the Eulerian solutions of the generalized three-body (material points) problem. Every point in this generalized problem acts on another, one with a force (attractive or repulsive) directed along the straight line passing through these points, and in an arbitrary manner depending on time, mutual distance and its derivatives, the first and the second. Here, generally speaking, the third axiom of dynamics (law of action and reaction) is not presupposed as fulfilled, that is, it is supposed that every two material points interact in a different way.This most general assumption being made, we establish the conditions which must dictate the laws of the interactions, so that the three points can always remain at the apexes of the equilateral triangle (Langrangian solution), or remain always on a straight line (Eulerian solution).The author believes that such general treatment of the three-body problem can be useful for theoretical studies in celestial mechanics and also for practical applications in the study of isolated stellar systems.

     

ОБ ионизации межзвездного магния

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On the stability of small quasiperiodic motions in the hamiltonian systems

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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Interaction between the interstellar medium and solar wind plasma

The interaction processes governing the penetration of the interstellar gas into the solar neighbourhood are re-examined — as well as photo-ionization and charge-exchange processes, proton elastic collisions and electron ionizations help reduce the nearby gas densities. The total destruction rate varies little during the solar cycle, by perhaps 10%. Particle heating, particularly via the elastic collisions, determines the gas characteristics in the gravitationally focussed tail—enhanced H-density is prevented, while the He-tail is effectively hotter than 10³ K.Termination of the solar wind is rediscussed in the light of both electron heating and the stronger gas/plasma interaction. The spiral interplanetary field is taken to break up and the subsonic plasma flow to be controlled by the pressure of slowly cooling electrons. The terminating collisionless shock is then, if it exists at all, very weak (M ₁<1.4), subcritical, and energetically unimportant. Cosmic rays are little affected by this sonic transition, but at least the electron component should be modulated by plasma turbulence throughout the ionizing flow.

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Перенос резонансного излучения И случайные ълуждания Фотонов

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Transfer of resonance radiation in infinite medium is considered as a process of random walks of photons. Close relation is shown to exist between the problems of transfer of line radiation and the stable distributions of the probability theory. This relation is used as a basis of a new method for the investigation of the asymptotic properties of the radiation field far from the sources.

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Взаимооействие Излучения Рентгеновскооо Истооника с АтмосФерой Нормальной Звезды в Тесных Двойных Системах

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Some fundamental elements of universe mechanics

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.

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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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Hubble expansion in a euclidean framework

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Динамические равновесные плазменные конфигуации и физика магнитосферы

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