共查询到20条相似文献，搜索用时 406 毫秒
1.
Klaus Jockers 《Solar physics》1968,3(4):603-610
The stability of the solar wind is studied in the case of spherical symmetry and constant temperature. It is shown that the stability problem must be formulated as a mixed initial and boundary-value problem in which are prescribed the perturbation values of velocity and density at an initial time and additionally the velocity perturbation at the base of the corona for all times. The solution is constructed by linear superposition of normal solutions, which contain the time only in an exponential factor. The stability problem becomes a singular eigenvalue problem for the amplitudes of the velocity and pressure perturbations, since additionally to the boundary condition at the base of the corona one must add the condition that the amplitudes behave regularly at the critical point. It is proved that only stable eigenvalues exist. 相似文献
2.
《New Astronomy》2017
We investigate the stability of stationary integral solutions of an ideal irrotational fluid in a general static and spherically symmetric background, by studying the profile of the perturbation of the mass accretion rate. We consider low angular momentum axisymmetric accretion flows for three different accretion disk models and consider time dependent and radial linear perturbation of the mass accretion rate. First we show that the propagation of such perturbation can be determined by an effective 2 × 2 matrix, which has qualitatively similar acoustic causal properties as one obtains via the perturbation of the velocity potential. Next, using this matrix we analytically address the stability issues, for both standing and travelling wave configurations generated by the perturbation. Finally, based on this general formalism we briefly discuss the explicit example of the Schwarzschild spacetime and compare our results of stability with the existing literature, which instead address this problem via the perturbation of the velocity potential. 相似文献
3.
This paper presents a generalized problem of the restricted three body studied in Abdul Raheem and Singh with the inclusion that the third body is an oblate spheroidal test particle of infinitesimally mass. The positions and stability of the equilibrium point of this problem is studied for a model in which the primaries is the binary system Struve 2398 (Gliese 725) in the constellation Draco; which consist of a pair of radiating oblate stars. It is seen that additional equilibrium points exist on the line collinear with the primaries, for some combined parameters of the problem. Hence, there can be up to five collinear equilibrium points. Two triangular points exist and depends on the oblateness of the participating bodies, radiation pressure of the primaries and a small perturbation in the centrifugal force. The stability analysis ensures that, the collinear equilibrium points are unstable in the linear sense while the triangular points are stable under certain conditions. Illustrative numerical exploration is given to indicate significant improvement of the problem in Abdul Raheem and Singh. 相似文献
4.
W. E. Williamson 《Celestial Mechanics and Dynamical Astronomy》1972,5(2):174-188
The perturbation method, a numerical method for solving two point boundary value problems (TPBVP), is modified to attempt to improve inherent instability and sensitivity problems associated with the method. The desired solution to the TPBVP is divided into two time intervals. The differential equations required to define a solution to the two point boundary value problem are integrated independently over these shorter segments rather than consecutively over the entire trajectory. The independent integration of the differential equations over approximately half of the trajectory instead of the entire trajectory substantially decreases sensitivity and stability properties associated with the numerical integration. The equations for both time segments can be integrated simultaneously. By this procedure, a system of twice the dimension of the original problem is integrated for a period of time equal to half of the time interval for the original problem. To show the effectiveness of the method, two impulse trajectories which minimize the total velocity increment required to transfer a spacecraft from an Earth orbit into a lunar orbit are calculated. 相似文献
5.
Jesús Peláez José Manuel Hedo Pedro Rodríguez de Andrés 《Celestial Mechanics and Dynamical Astronomy》2007,97(2):131-150
The special perturbation method considered in this paper combines simplicity of computer implementation, speed and precision, and can propagate the orbit
of any material particle. The paper describes the evolution of some orbital elements based in Euler parameters, which are
constants in the unperturbed problem, but which evolve in the time scale imposed by the perturbation. The variation of parameters
technique is used to develop expressions for the derivatives of seven elements for the general case, which includes any type
of perturbation. These basic differential equations are slightly modified by introducing one additional equation for the time,
reaching a total order of eight. The method was developed in the Grupo de Dinámica de Tethers (GDT) of the UPM, as a tool for dynamic simulations of tethers. However, it can be used in any other field and with any kind of
orbit and perturbation. It is free of singularities related to small inclination and/or eccentricity. The use of Euler parameters
makes it robust. The perturbation forces are handled in a very simple way: the method requires their components in the orbital
frame or in an inertial frame. A comparison with other schemes is performed in the paper to show the good performance of the
method. 相似文献
6.
Alessandro Morbidelli Antonio Giorgilli 《Celestial Mechanics and Dynamical Astronomy》1989,47(2):145-172
The classical problem of the dynamics in the asteroids belt is revisited in the light of recently developed perturbation methods. We consider the spatial problem of three bodies both in the circular and in the elliptic case, looking for families of periodic or quasi periodic orbits. Some criteria for deciding the stability of these families are also indicated. 相似文献
7.
The stability of a recently proposed general relativistic model of galaxies is studied in some detail. This model is a general relativistic version of the well-known Miyamoto–Nagai model that represents well a thick galactic disc. The stability of the disc is investigated under a general first-order perturbation keeping the space–time metric frozen (no gravitational radiation is taken into account). We find that the stability is associated with the thickness of the disc. We find that flat galaxies have more non-stable modes than the thick ones, i.e. flat galaxies have a tendency to form more complex structures like rings, bars and spiral arms. 相似文献
8.
9.
Shu Si-hui Lu Ben-kui Chen Wu-shen Liu Fu-yao 《Chinese Astronomy and Astrophysics》2004,28(4):432-440
A criterion for the linear stability of the equilibrium points in the perturbed restricted three-body problem is given. This criterion is related only to the coefficients of the characteristic equation of the tangent map of an equilibrium point, and this is convenient to use. With this criterion, we have discussed the linear stability of the equilibrium points in the Robe problem under the perturbation of a drag force, derived the linearly stable region of the equilibrium point in the perturbed Robe's problem with the drag given by Hallen et al., and improved as well the results obtained by Giordano et al. 相似文献
10.
A. R. Bestman 《Astrophysics and Space Science》1992,192(1):133-139
The problem of unsteady flow of a relativistic radiating neutrino gas is studied by imposing a time-dependent perturbation on a basic flow. When the perturbation is small, the problem, which is ill-posed, is reduced to a well-posed spatial value problem for the transverse velocity and the temperature. Subsequently the axial velocity and number density may be obtained by straightforward integration with respect to time and imposition of the initial condition. The solution for the initial value problem is tackled by the Laplace transform technique and the results are discussed quantitatively. 相似文献
11.
This paper studies the motion of a test particle (infinitesimal mass) in the neighborhood of the triangular point L 4 in the framework of the perturbed relativistic restricted three-body problem (R3BP). The problem is perturbed in the sense that a small perturbation is given to the centrifugal force. It is found that the position and stability of the triangular point are affected by both the relativistic factor and a small perturbation in the centrifugal force. 相似文献
12.
Anna M Nobili 《Celestial Mechanics and Dynamical Astronomy》1988,45(1-3):293-304
Modern computer technology allows dynamical astronomers to investigate the long term stability of real systems as thoroughly as ever. However, the process is not straightforward and new problems need to be solved. This work deals with only one such problem: the construction-from the numerical integration- of a secular perturbation theory that is able to describe the dynamical behavior of the system. The discussion refers to the outer planets and is based on the knowledge acquired by the author during her participation in project LONGSTOP. A digital filter is used in order to reduce the output and eliminate short periodic terms. Filtering uncovers long term variations in the semimajor axes. From the filtered output a secular perturbation theory is constructed in the assumption that the solution is regular, as secular perturbation theories can only be constructed for regular solutions. If we succeed, this means that the solution is indeed regular for the computed span of time; if not-and this can be established in a rigorous way-it has to be concluded a posteriori that the solution is not regular. The LONGSTOP 1A and 1B integrations show well that as the timespan of the integration increases it is possible to detect the non-regular behavior of the solution. This happens in the eccentricity of Saturn at the 10–4 level. 相似文献
13.
We studied the stability of the restricted circular three-body problem. We introduced a model Hamiltonian in action-angle Delaunay variables. which is nearly-integrable with the perturbing parameter representing the mass ratio of the primaries. We performed a normal form reduction to remove the perturbation in the initial Hamiltonian to higher orders in the perturbing parameter. Next we applied a result on the Nekhoroshev theorem proved by Pöschel [13] to obtain the confinement in phase space of the action variables (related to the elliptic elements of the minor body) for an exponentially long time. As a concrete application. we selected the Sun-Ceres-Jupiter case, obtaining (after the proper normal form reduction) a stability result for a time comparable to the age of the solar system (i.e., 4.9 · 109 years) and for a mass ratio of the primaries less or equal than 10–6. 相似文献
14.
In this paper, the restricted problem of three bodies is generalized to include a case when the passively gravitating test particle is an oblate spheroid under effect of small perturbations in the Coriolis and centrifugal forces when the first primary is a source of radiation and the second one an oblate spheroid, coupled with the influence of the gravitational potential from the belt. The equilibrium points are found and it is seen that, in addition to the usual three collinear equilibrium points, there appear two new ones due to the potential from the belt and the mass ratio. Two triangular equilibrium points exist. These equilibria are affected by radiation of the first primary, small perturbation in the centrifugal force, oblateness of both the test particle and second primary and the effect arising from the mass of the belt. The linear stability of the equilibrium points is explored and the stability outcome of the collinear equilibrium points remains unstable. In the case of the triangular points, motion is stable with respect to some conditions which depend on the critical mass parameter; influenced by the small perturbations, radiating effect of the first primary, oblateness of the test body and second primary and the gravitational potential from the belt. The effects of each of the imposed free parameters are analyzed. The potential from the belt and small perturbation in the Coriolis force are stabilizing parameters while radiation, small perturbation in the centrifugal force and oblateness reduce the stable regions. The overall effect is that the region of stable motion increases under the combine action of these parameters. We have also found the frequencies of the long and short periodic motion around stable triangular points. Illustrative numerical exploration is rendered in the Sun–Jupiter and Sun–Earth systems where we show that in reality, for some values of the system parameters, the additional equilibrium points do not in general exist even when there is a belt to interact with. 相似文献
15.
S. A. Wagner 《Monthly notices of the Royal Astronomical Society》2006,370(4):1915-1920
The linear analysis of hydrodynamic stability of the local thermal balance in a homogeneous moving gas is revisited to get information about the development of a spatially limited perturbation as seen at a fixed location. The consideration concerns both the evolution of the perturbed quantities inside a domain where the perturbation initially localizes and spreading the perturbation outside this domain. Inside the initial perturbation domain, the conditions for the exponential growth/decay are found to coincide with the well-known Field's criteria, ensuing the analysis of the normal modes. However, as soon as the modal isentropic stability criterion is satisfied the perturbation outside its initial domain asymptotically spreads out with a subsonic velocity not depending on the initial perturbation field. It enables the gas flow to carry the disturbances away and leads to an improved stability criterion for inhomogeneous thermally balanced flows where the modally unstable region appears to be spatially bounded. The spreading velocity, playing a key role in the new stability criterion, is calculated as a function of the same derivatives of the heating/cooling function as the modal instability criteria exploit. 相似文献
16.
The Sitnikov problem is one of the most simple cases of the elliptic restricted three body system. A massless body oscillates
along a line (z) perpendicular to a plane (x,y) in which two equally massive bodies, called primary masses, perform Keplerian orbits around their common barycentre with
a given eccentricity e. The crossing point of the line of motion of the third mass with the plane is equal to the centre of gravity of the entire
system. In spite of its simple geometrical structure, the system is nonlinear and explicitly time dependent. It is globally
non integrable and therefore represents an interesting application for advanced perturbative methods. In the present work
a high order perturbation approach to the problem was performed, by using symbolic algorithms written in Mathematica. Floquet
theory was used to derive solutions of the linearized equation up to 17th order in e. In this way precise analytical expressions for the stability of the system were obtained. Then, applying the Courant and
Snyder transformation to the nonlinear equation, algebraic solutions of seventh order in z and e were derived using the method of Poincaré–Lindstedt. The enormous amount of necessary computations were performed by extensive
use of symbolic programming. We developed automated and highly modularized algorithms in order to master the problem of ordering
an increasing number of algebraic terms originating from high order perturbation theory. 相似文献
17.
The locations and linear stability of the main libration points in Robe's restricted three-body problem under perturbed Coriolis and centrifugal forces are investigated. The perturbed locations of these points are given. The perturbation magnitude of their locations and linear stability are estimated. The results obtained by Shrivastava and Garain[10] are improved. 相似文献
18.
The Symmetrical One-dimensional Newtonian Four-body Problem: A Numerical Investigation 总被引：3，自引：1，他引：2
Winston L. Sweatman 《Celestial Mechanics and Dynamical Astronomy》2002,82(2):179-201
Numerical simulations of the one-dimensional Newtonian four-body problem have been conducted for the special case in which the bodies are distributed symmetrically about the centre of mass. Simulations show a great similarity between this problem and the one-dimensional Newtonian three-body problem. As in that problem the orbits can be divided into three different categories which form well-defined regions on a Poincaré section: there is a region of quasiperiodic orbits about a Schubart-like periodic orbit, there is a region of fast-scattering encounters and in between these two regions there is a chaotic scattering region. The Schubart-like periodic orbit's stability to perturbation is studied. It is apparently stable in one-dimension but is unstable in three-dimensions.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
19.
Ferdinand Verhulst 《Celestial Mechanics and Dynamical Astronomy》1975,11(1):95-129
The main theorems of the theory of averaging are formulated for slowly varying standard systems and we show that it is possible to extend the class of perturbation problems where averaging might be used. The application of the averaging method to the perturbed two-body problem is possible but involves many technical difficulties which in the case of the two-body problem with variable mass are avoided by deriving new and more suitable equations for these perturbation problems. Application of the averaging method to these perturbation problems yields asymptotic approximations which are valid on a long time-scale. It is shown by comparison with results obtained earlier that in the case of the two-body problem with slow decrease of mass the averaging method cannot be applied if the initial conditions are nearly parabolic. In studying the two-body problem with quick decrease of mass it is shown that the new formulation of the perturbation problem can be used to obtain matched asymptotic approximations. 相似文献
20.
We consider the stability of a compressible shear flow separating two streams of different speeds and temperatures. The velocity and temperature profiles in this mixing layer are hyperbolic tangents. The normal mode analysis of the flow stability reduces to an eigenvalue problem for the pressure perturbation. We briefly describe the numerical method that we used to solve this problem. Then, we introduce the notions of the absolute and convective instabilities and examine the effects of Mach number, and the velocity and temperature ratios of each stream on the transition between convective and absolute instabilities. Finally, we discuss the implication of the results presented in this paper for the heliopause stability. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献