共查询到20条相似文献，搜索用时 404 毫秒
1.
The aim of the present paper is to provide sufficient conditions for the existence of periodic solutions of the perturbed attitude dynamics of a rigid dumbbell satellite in a circular orbit. 相似文献
2.
We determine the parameters of a passively gravitating body that satisfy the conditions for the existence of Lagrangian solutions in a plane restricted three-body problem. A example is given. 相似文献
3.
We study the steady-state structure of an accretion disc with a corona surrounding a central, rotating, magnetized star. We
assume that the magneto-rotational instability is the dominant mechanism of angular momentum transport inside the disc and
is responsible for producing magnetic tubes above the disc. In our model, a fraction of the dissipated energy inside the disc
is transported to the corona via these magnetic tubes. This energy exchange from the disc to the corona which depends on the
disc physical properties is modified because of the magnetic interaction between the stellar magnetic field and the accretion
disc. According to our fully analytical solutions for such a system, the existence of a corona not only increases the surface
density but reduces the temperature of the accretion disc. Also, the presence of a corona enhances the ratio of gas pressure
to the total pressure. Our solutions show that when the strength of the magnetic field of the central neutron star is large
or the star is rotating fast enough, profiles of the physical variables of the disc significantly modify due to the existence
of a corona. 相似文献
4.
The formulation of Elliott (1975) is recapitulated somewhat more elegantly for a monenergetic beam of “Top Hat” profile. The mode corresponding most closely to the parallel-polarized mode in a uniform beam is explored for phase velocities less than the beam velocity and frequencies between the hybrid frequencies. The mere existence of solutions indicates the possibility of instability in some real case. Solutions are found for all frequencies except for a range above the gyrofrequency, beyond which a ducted solution exists up to the plasma frequency. In the other range radiative solutions exist.The nature of the results provides a guide for several applications, but more realistic models must be specific to the application. 相似文献
5.
The existence of homographic solutions of the N-body problem with a geneva attraction is verified, and the way which leads to obtaining certain types of homographic solutions is indicated. Basic properties of the solutions, such as the relations between the dynamical quantities and the initial conditions are presented. Furthermore, we proved that, for k is not equal to 3, if a homographic solution is not planar, it must be homothetic. And in this case, another important conclusion is that the configurations corresponding to any homographic solution are central configurations. Finally, we showed that along each homographic solution, motion of any individual mass point observes the same rules as the ones observed by mass points of a certain two-body system. 相似文献
6.
M. Z. Aboelnaga 《Astrophysics and Space Science》1995,225(1):81-91
This paper investigates the regular motions of an axisymmetrical satellite in the field of Newton's attraction of a triaxial body. Both the orbital and the self rotational motions of the two bodies are taken into consideration. The exact solutions are discussed using Poincaré's method of small parameter. In the decomposition of the force function all the harmonic terms up to the third order are taken into account.The results show the existence of eight solutions. The stability of the new group of solutions is discussed using two methods to get the necessary and sufficient conditions required for the stability of these motions. 相似文献
7.
S. G. Zhuravlev 《Celestial Mechanics and Dynamical Astronomy》1981,25(3):297-315
In our article (Zhuravlev, 1979) a formal method of constructing conditionally periodic solutions of canonical systems of differential equations with a quick-rotating phase in the case of sharp commensurability was presented. The existence of stationary (or periodic) solutions of an averaged system of differential equations corresponding to the initial system of differential equations is necessary for an effective application of the method for different problems.Evidently, the stationary solutions do not always exist but in numerous papers on stationary solutions (oscillations or motions), the conditions of existence of such solutions are very often not considered at all. Usually a simple assumption is used that the stationary solutions do exist.Otherwise it is well known that Poincaré's theory of periodic solutions (Poincaré, 1892) let one set up conditions of existence of periodic solutions in different systems of differential equations. Particularly, in papers,Mah (1949, 1956), see alsoexmah (1971), the necessary and sufficient conditions of the existence of periodic solutions of (non-canonical) systems of differential equations which are close to arbitrary non-linear systems are given. For canonical autonomous systems of differential equations the conditions of existence of periodic solutions and a method of calculation are presented in the paperMepmah (1952).In our paper another approach is given and the conditions of existence of stationary solutions of canonical systems of differential equations with a quick-rotating phase are proved. For this purpose Delaunay-Zeipel's transformation and Poincaré's small parameter method are used. 相似文献
8.
The effect of finite conductivity on the Rayleigh-Taylor instability of an incompressible, viscous rotating fluid through a porous medium has been studied in the presence of a two-dimensional horizontal magnetic field. It has been shown that the solution is characterized by a variational principle. By making use of the existence of the variational principle, proper solutions have been obtained for a semi-infinite fluid in which density has a one-dimensional (exponential) vertical stratification. The dispersion relation has been derived and solved numerically. It is found that finite resistivity and porosity have a destabilizing effect on the Rayleigh-Taylor instability while rotation has a stabilizing effect. 相似文献
9.
Alexander A. Burov Anna D. Guerman Vasily I. Nikonov 《Celestial Mechanics and Dynamical Astronomy》2018,130(9):58
The existence, stability and bifurcation analysis is performed for equilibria of a material point in the gravitational field of three homogeneous penetrable balls fixed in absolute frame. The radii of the balls are assumed finite. In the case when the mass distribution admits a symmetry axis, analytic expressions are written out, allowing one to investigate the properties of equilibrium positions located both on the symmetry axis and outside it. The stability of solutions is studied; domains with different instability degree are described. 相似文献
10.
The effect of Hall currents and collision with neutrals on the instability of a horizontal layer of a self-gravitating partially-ionized plasma of varying density have been studied. It is assumed that the plasma is permeated by a variable horizontal magnetic field stratified vertically. A variational principle is shown to characterize the problem. By making use of the existence of the variational principle, proper solutions have been obtained for a semi-infinite plasma in which density has a one-dimensional (exponential) vertical stratification. The dispersion relation has been derived and solved numerically. It is found that the collisions with neutrals have a stabilizing influence while Hall currents have a destabilizing influence. 相似文献
11.
E. N. Eremenko 《Celestial Mechanics and Dynamical Astronomy》1983,31(4):339-362
The present paper is a continuation of papers by Shinkaric (1972), Vidyakin (1976), Vidyakin (1977), and Duboshin (1978), in which the existence of particular solutions, analogues to the classic solutions of Lagrange and Euler in the circular restricted problem of three points were proved. These solutions are stationary motions in which the centres of mass of the bodies of the definite structures always form either an equilateral triangle (Lagrangian solutions) or always remain on a straight line (Eulerian solutions) The orientation of the bodies depends on the structure of the bodies. In this paper the usage of the small-parameter method proved that in the general case the centre of mass of an axisymmetric body of infinitesimal mass does not belong to the orbital plane of the attracting bodies and is not situated in the libration points, corresponding to the classical case. Its deviation from them is proportional to the small parameter. The body turns uniformly around the axis of symmetry. In this paper a new type of stationary motion is found, in which the axis of symmetry makes an angle, proportional to the small parameter, with the plane created by the radius-vector and by the normal to the orbital plane of the attracting bodies. The earlier solutions-Shinkaric (1971) and Vidyakin (1976)-are also elaborated, and stability of the stationary motions is discussed. 相似文献
12.
The problem of determining all equilibria of a satellite in a circular orbit is solved in the case where the satellite is
subjected to gravitational and aerodynamic torques. The number of isolated equilibria is shown to be no less than eight and
no more than 24. The existence proof of one-parameter families of stationary solutions is given. Using Lyapunov's method sufficient
conditions for stability of isolated equilibria are obtained.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
13.
The existence of current-interrupting non-linear electrostatic waves in the form of negative solitons is demonstrated. Self-consistent, non-linear electrostatic potentials are constructed assuming that a current may be interrupted by trapping current-carrying electrons in such a potential. A significant fraction of the current-carrying electrons is trapped by the potential if the electron thermal velocity is much less than the electron streaming velocity. In one class of solutions, the negative solitons, the current may be reduced to a fourth of its initial value in the limit of high ion-electron temperature ratio. 相似文献
14.
H. Bruer 《Astronomische Nachrichten》1979,300(1):43-49
For a dynamo model obtained by idealizing features of the Sun, an analytic proof of the existence and a recursion formula for the determination of small time periodic solutions in a finite vicinity of the critical dynamo numbers are given. The nonlinear problem is solved by transforming the boundary value problem of the induction equation into a fixed point problem in an infinite dimensional sequence space and then applying the LYAPUNOV -SCHMIDT method to reduce it to a relationship between dynamo number, amplitude and frequency. 相似文献
15.
Virendra Singh 《Celestial Mechanics and Dynamical Astronomy》1977,16(2):137-142
In this article the existence of periodic solutions in Hill's relativistic problem is demonstrated using Poincaré's small parameter method. This method guarantees the convergence of the series representing the periodic solutions. 相似文献
16.
L. M. Perko 《Celestial Mechanics and Dynamical Astronomy》1976,14(4):395-427
This paper uses the results of second-order asymptotic matching in the restricted three body problem to establish the existence and first-order asymptotic approximation of various families of second species periodic solutions with one near-moon passage during a half-period. In this way, the existence and asymptotic approximation of second species solutions with any number of near-moon passages during a half-period can be established based on higher order asymptotic matching. Second species solutions with near-moon passages have not been studied numerically due to the difficult nature of this problem.This research was supported in part by the National Science Foundation under Grant GP42739 and in part by Northern Arizona University under a university research grant. 相似文献
17.
T. P. Valkering 《Celestial Mechanics and Dynamical Astronomy》1982,28(1-2):119-131
The existence of a one-parameter family of periodic solutions representing longitudinal travelling waves is established for a one-dimensional lattice of identical particles with nearest-neighbour interaction. The potential is not given in closed form but is specified by only a few global properties. The lattice is either infinite or consists ofN particles on a circle with fixed circumference. Waves with low energy are sinusoidal and their properties are studied using bifurcation methods. Waves of high energy, however, are of solitary type, i.e. the excitation is strongly localized.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.Dedicated to Professor Szebehely, for his stimulating enthusiasm. 相似文献
18.
An analytical proof of the existence of some kinds of periodic orbits of second species of Poincaré, both in the Circular and Elliptic Restricted three-body problem, is given for small values of the mass parameter. The proof uses the asymptotic approximations for the solutions and the matching theory developed by Breakwell and Perko. In the paper their results are extended to the Elliptic problem and applied to prove the existence of second-species solutions generated by rectilinear ellipses in the Circular problem and nearly-rectilinear ones in the Elliptic case. 相似文献
19.
V. Singh 《Celestial Mechanics and Dynamical Astronomy》1976,14(2):167-173
The paper discusses the existence of periodic and quasi-periodic solutions in the space relativistic problem of three bodies with the help of Poincaré's small parameter method starting from non-Keplerian generating solutions, i.e., using Gauss's method. The main peculiarity of these periodic orbits is the fact that they close, in general, after many revolutions. It is worth noticing that these periodic orbits give a new class of periodic solutions of the classical circular problem of three bodies, if relativistic effects are neglected. 相似文献
20.
S. G. Zhuravlev 《Celestial Mechanics and Dynamical Astronomy》1979,19(1):77-93
A formal method of constructing of conditionally periodic solutions of canonical systems of differential equations in the vicinity of a commemsurability of frequencies is proposed. The method is a union of the rapid convergence method and (well-known in celestial mechanics) Delaunay-Zeipel's method of canonical transformations. For a successful application of the method an existence of stationary resonant solutions of an averaged system of the differential equations is necessary. 相似文献