共查询到20条相似文献，搜索用时 31 毫秒
1.
Abdul Ahmad 《Celestial Mechanics and Dynamical Astronomy》1995,61(2):181-196
The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable. 相似文献
2.
Arthur L. Whipple 《Celestial Mechanics and Dynamical Astronomy》1984,33(3):271-294
Fourteen equilibrium solutions of the restricted problem of 2+2 bodies are shown to exist. Six of these solutions are located about the collinear Lagrangian points of the classical restricted problem of three bodies. Eight solutions are found in the neighborhood of the triangular Lagrangian points. Linear stability analysis reveals that all of the equilibrium solutions are unstable with the exception of four solutions; two in the vicinity of each of the triangular Lagrangian points. These four solutions are found to be stable provided the mass parameter of the primary masses is less than a critical value which depends also on the mass of the minor bodies. 相似文献
3.
In this paper we obtain the general axially symmetric space-times in scalar-tensor theory of gravitation proposed by Sáez and Ballester. The only possible solutions of these space-times in this theory are dust solutions. One of the obtained solutions here has a similar considerations to Van Stockum dust solution. A detailed study of geometric and kinematical properties of the obtained solutions are carried out. Furthermore, closed timelike curves are present in these solutions. 相似文献
4.
L. G. Luk’yanov 《Astronomy Letters》2012,38(3):201-211
Families of conditionally periodic solutions have been found by a slightly modified Lyapunov method of determining periodic
solutions near the libration points of the restricted three-body problem. When the frequencies of free oscillations are commensurable,
the solutions found are transformed into planar or spatial periodic solutions. The results are confirmed by numerically integrating
the starting nonlinear differential equations of motion. 相似文献
5.
给出了以偏近点角为自变量的变引力常数的摄动方程组的解.解包括轨道半长轴的长期和周期变化项,其他轨道根数在一阶解中无长期项,只有周期项.近星点经度和平经度在二阶解中显示长期项变化.给出了由于引力常数变化对双星轨道演变情况的数值估计,对结果做了讨论并给出结论. 相似文献
6.
Salah Haggag 《Astrophysics and Space Science》1995,225(1):137-149
Einstein field equations for a static and spherically symmetric perfect fluid are considered. A formulation given by Patiño and Rago is used to obtain a class of nine solutions, two of them are Tolman solutions I, IV and the remaining seven are new. The solutions are the correct ones corresponding to expressions derived by Patiño and Rago which have been shown by Knutsen to be incorrect. Similar to Tolman solution IV each of the new solutions satisfies energy conditions inside a sphere in some range of two independent parameters. Besides, each solution could be matched to the exterior Schwarzschild solution at a boundary where the pressure vanishes and thus the solutions constitute a class of new physically reasonable stellar models. 相似文献
7.
Vertically critical, planar periodic solutions around the triangular equilibrium points of the Restricted Three-Body Problem are found to exist for values of the mass parameter in the interval [0.03, 0.5]. Four series of such solutions are computed. The families of three-dimensional periodic solutions that branch off these critical orbits are computed for µ = 0.3 and are continued till their end. All orbits of these families are unstable. 相似文献
8.
We explore semicomplete self-similar solutions for the polytropic gas dynamics involving self-gravity under spherical symmetry, examine behaviours of the sonic critical curve and present new asymptotic collapse solutions that describe 'quasi-static' asymptotic behaviours at small radii and large times. These new 'quasi-static' solutions with divergent mass density approaching the core can have self-similar oscillations. Earlier known solutions are summarized. Various semicomplete self-similar solutions involving such novel asymptotic solutions are constructed, either with or without a shock. In contexts of stellar core collapse and supernova explosion, a hydrodynamic model of a rebound shock initiated around the stellar degenerate core of a massive progenitor star is presented. With this dynamic model framework, we attempt to relate progenitor stars and the corresponding remnant compact stars: neutron stars, black holes and white dwarfs. 相似文献
9.
A. Beesham 《Astrophysics and Space Science》1987,132(2):397-399
A simple method of obtaining exact solutions in the scale-covariant theory of gravitation from the corresponding general relativistic solutions is presented. Some comments are made on some special scale-covariant solutions. 相似文献
10.
Two basic problems of dynamics, one of which was tackled in the extensive work of Z. Kopal (see e.g. Kopal, 1978, Dynamics of Close Binary Systems, D. Reidel Publication, Dordrecht, Holland.), are presented with their approximate general solutions. The ‘penetration’ into
the space of solution of these non-integrable autonomous and conservative systems is achieved by application of ‘The Last Geometric Theorem of Poincaré’ (Birkhoff, 1913, Am. Math. Soc. (rev. edn. 1966)) and the calculation of sub-sets of ‘solutions précieuses’ that are covering densely the spaces of all solutions
(non-periodic and periodic) of these problems. The treated problems are: 1. The two-dimensional Duffing problem, 2. The restricted
problem around the Roche limit. The approximate general solutions are developed by applying known techniques by means of which
all solutions re-entering after one, two, three, etc, revolutions are, first, located and then calculated with precision.
The properties of these general solutions, such as the morphology of their constituent periodic solutions and their stability
for both problems are discussed. Calculations of Poincaré sections verify the presence of chaos, but this does not bear on
the computability of the general solutions of the problems treated. The procedure applied seems efficient and sufficient for
developing approximate general solutions of conservative and autonomous dynamical systems that fulfil the PoincaréBirkhoff
theorems. The same procedure does not apply to the sub-set of unbounded solutions of these problems. 相似文献
11.
Following the formalism on the polarization transfer equation presented recently by the same authors, solutions to this transfer equation under several special cases of interest are discussed in this paper. Analytic solutions for the Stokes parameters for several special cases of interest are given, and numerical solutions to these parameters for arbitrary propagation direction and two types of inhomogeneity of the medium are presented. 相似文献
12.
H. Alinejad 《Astrophysics and Space Science》2011,332(2):325-329
We look for particular solutions to the restricted three-body problem where the bodies are allowed to either lose or gain
mass to or from a static atmosphere. In the case that all the masses are proportional to the same function of time, we find
analogous solution to the five stationary solutions of the usual restricted problem of constant masses: the three collinear
and the two triangular solutions, but now the relative distance of the bodies changes with time at the same rate. Under some
restrictions, there are also coplanar, infinitely remote and ring solutions. 相似文献
13.
D. J. Heath 《Astrophysics and Space Science》1989,154(2):207-216
The general solutions to the density perturbation equation derived by Bonnor are pressented for the zero-pressure Friedmann-Lemaître universes in terms of elliptic functions. The particular solutions already published to this equation in terms of elementary functions are exhibited as special cases arising from the general solutions. These occur when the elliptic functions simplify to either trigonometric or hyperbolic functions. 相似文献
14.
S. M. El-Shaboury 《Celestial Mechanics and Dynamical Astronomy》1990,50(3):199-208
The restricted problem of 2 + 2 homogenous axisymmetric ellipsoids such that their equatorial planes coincide with the orbital plane of the centers of mass is considered. The equilibrium solutions of this problem are shown to exist. Six of these solutions are located about the collinear points of the restricted problem of three axisymmetric ellipsoids. A special case of this problem is studied and sixteen solutions are found in the neighborhood of the triangular Lagrangian points. 相似文献
15.
Gabriel Mititelu 《Celestial Mechanics and Dynamical Astronomy》2009,103(4):327-342
A practical and important problem encountered during the atmospheric re-entry phase is to determine analytical solutions for
the space vehicle dynamical equations of motion. The author proposes new solutions for the equations of trajectory and flight-path
angle of the space vehicle during the re-entry phase in Earth’s atmosphere. Explicit analytical solutions for the aerodynamic
equations of motion can be effectively applied to investigate and control the rocket flight characteristics. Setting the initial
conditions for the speed, re-entering flight-path angle, altitude, atmosphere density, lift and drag coefficients, the nonlinear
differential equations of motion are linearized by a proper choice of the re-entry range angles. After integration, the solutions
are expressed with the Exponential Integral, and Generalized Exponential Integral functions. Theoretical frameworks for proposed
solutions as well as, several numerical examples, are presented. 相似文献
16.
Various representations of the Jordan-Brans-Dicke (JBD) theory arising in conformal transformations of the metric are considered. Propositions are formulated that establish the mathematical equivalence of these representations, making it possible from known exact solutions in one representation to generate new ones in another. It is shown, in particular, how to obtain new solutions in the general theory of relativity from known solutions in the JBD theory and vice versa. 相似文献
17.
A procedure to generate new exact solutions to Einstein equations for perfect fluids is applied to LRS Bianchi type I line-element. Starting from some known solutions a class of new perfect fluid solutions of Bianchi type I are presented. The physical and kinematical properties of spatially homogeneous and anisotropic cosmological models are studied. 相似文献
18.
A. R. Bestman 《Astrophysics and Space Science》1991,179(2):189-202
The oscillatory boundary layer past a porous flat plate for a two-component plasma is studied for the case of large suction. Perturbation series expansion solution is developed for the problem and the various approximate solutions are integrated in closed form. It is possible to obtain higher approximate solutions where steady state streaming solutions appear. These steady-state streaming solutions have generated a lot of mathematical and physiological interest in recent times. 相似文献
19.
The equations of gas dynamics are solved, quasi-analytically by applying McVittie's method for spherical, cylindrical and plane configurations. The hypothesis of linear wave flow is applied and it is assumed that the final state of collapsing clouds is a hydrostatic equilibrium state, determined by complete polytropes. Complete analytical solutions are found when the generalized (to the three symmetries) Emden equation admits of analytical solutions. Otherwise the solutions are left in terms of the numerical solutions of the Emden equation. Numerical solutions to the Emden equation in the plane case are found and tabulated. A strong dependence of amplification, of density, pressure and temperature of the gas, on the symmetry is found. In addition, it is conclude that the flow remains subsonic, during the collapse, except toward the boundaries of the collapsing clouds. 相似文献
20.
R. Chan 《Astrophysics and Space Science》1994,220(1):57-64
In this work we present new solutions of Einstein's equations assuming a spherically symmetric anisotropic fluid with shear in comoving coordinates. We study two limit cases: when the tangential pressure vanishes and when the radial pressure vanishes. The new solutions are based on the Tolman's solutions. 相似文献