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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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. . ,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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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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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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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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, , . . ( I), ( II). I , () . -, . , , (R/R i)2/3, R/R i- . ( II) . , . , , , . , . , , . , , - , , . , , , , . , . . . 1969 .  相似文献   

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The period of very high energy (E>2×1012 eV) gamma-ray emission of Cyg X-3 by using the data of observations of the source made during 6 years, 1972–1977, was specified. The value of the period is equal to 0.199 683±1×10–6 days. Phase histogram reveals two peaks, one lagging the other by 0.6 of the period. The averaged 6 year data amounts to 1.8×10–10 quanta cm–2 s–1 (peak intensity). It corresponds to luminosity of about 1.2×1037 erg s–1 if one assumes that an emission is isotropical and the distance is equal to 10 kpc.
- E>2×1012 Cyg X-3 . 1972–1977 . - T=0,199 683 ±10–6 . , 0,6 . 1,8×10–10 –2 –1 ( ), 1,2×1037 / 10 .
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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.
, , NP 0532 . , . , . , , NP 0532 50 , .
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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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, , , , ,S , , , S Mg. , . , . , ( , ..). B5 B0; (<1%).  相似文献   

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The normalised Hénon–Heiles family exhibits a degenerate bifurcation when passing through the separable case =0. We clarify the relation between this degeneracy and the integrability at =0. Furthermore we show that the degenerate bifurcation carries over to the Hénon–Heiles family itself.  相似文献   

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