共查询到20条相似文献，搜索用时 31 毫秒
1.
S. K. El-Labany E. F. El-Shamy S. A. El-Warraki 《Astrophysics and Space Science》2008,315(1-4):287-295
Nonlinear properties of the dust acoustic (DA) solitary waves in a dusty plasma consisting of negatively variable-charged dust particles, vortex-like distributed ions and two-temperature isothermal electrons are reported. A reductive perturbation theory has been used to derive a modified Korteweg-de Vries (mKdV) equation for the first-order perturbed potential and a linear inhomogeneous mKdV-type equation for the second-order perturbed potential. The renormalization method is used to obtain stationary solutions of these coupled equations. The modifications in the amplitude and width of the solitary wave structure due to the inclusion of two different types of isothermal electrons, external oblique magnetic field, higher-order nonlinearity, and vortex-like distributed ions are investigated. Also a method based on energy consideration was used to obtain the stability condition. Moreover, the numerical results are applied to investigate some nonlinear characteristics of the DA solitary waves. 相似文献
2.
The purpose of the present work is to investigate some nonlinear properties of the dust ion-acoustic (DIA) solitary waves in a four-component hot-magnetized dusty plasma consisting of charged dust grains, positively charged ions and two-temperature isothermal electrons. Applying a reductive perturbation theory, a nonlinear Korteweg-de Vries (KdV) equation for the first-order perturbed potential and a linear inhomogeneous KdV-type equation for the second-order perturbed potentials are derived. Stationary solutions of these coupled equations are obtained using a renormalization method. A method based on energy consideration is used to obtain a condition for stable solitons. The effects of two different types of isothermal electrons, external oblique magnetic field, concentration of negatively (positively) charged dust grains and higher-order nonlinearity on the nature of the DIA solitary waves are discussed. The numerical results are applied to Saturn's E-ring. 相似文献
3.
《Planetary and Space Science》2007,55(14):2192-2202
Nonlinear propagating dust-acoustic solitary waves (DASWs) in a warm magnetized dusty plasma containing different size and mass negatively charged dust particles, isothermal electrons, high- and low-temperature ions are investigated. For this purpose, a reasonable normalization of the hydrodynamic and Poisson equations is used to derive the Zakharov–Kuznetsov (ZK) equation for the first-order perturbed potential. As the wave amplitude increases, the width and the velocity of the solitons deviate from the prediction of the ZK equation, i.e., the breakdown of the ZK approximation. To describe the soliton of larger amplitude, a linear inhomogeneous Zakharov-Kuznetsov-type (ZK-type) equation for the second-order perturbed potential is derived. Stationary solutions of both equations are obtained using the renormalization method. Numerically, the effect of power law distribution on the higher-order corrections is examined. It is found that the soliton amplitude in case of power law distribution is smaller than that of monosized dust grains. The higher-order corrections play a role to reduce the strength of the nonlinearity for power law distribution case. The relevance of the present investigation to Saturn's F-ring and laboratory experiment is discussed. 相似文献
4.
Properties of dust-acoustic solitary waves in a warm dusty plasma are analyzed by using the hydrodynamic model for massive dust grains, electrons, ions, and streaming ion beam. For this purpose, Korteweg-de Vries (KdV) equation for the first-order perturbed potential and linear inhomogeneous KdV-type equation for the second-order perturbed potential have been derived and their analytical solutions are presented. In order to show the characteristics of the dust-acoustic solitary waves are influenced by the plasma parameters, the relevant numerical analysis of the KdV and linear inhomogeneous KdV-type equations are obtained. The dust-acoustic solitary waves, as predicted here, may be associated with the nonlinear structures caused by the interaction of polar jets with the interstellar medium, which is known as Herbig-Haro objects. 相似文献
5.
Giuseppe Pucacco 《New Astronomy》2012,17(5):475-482
We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the dynamics in the Hill synodic system where, by means of the tidal expansion of the potential, the equations of motion take the form of perturbed harmonic oscillators in a rotating frame. In the unperturbed, purely Keplerian case, the post-epicyclic solutions produced with the normal form coincide with those obtained from the expansion of the solution of the Kepler equation. In all cases where the perturbed problem can be cast in autonomous form, the solution is easily obtained as a perturbation series. The generalization to the spatial problem and/or the non-autonomous case is straightforward. 相似文献
6.
Alex Konopliv 《Celestial Mechanics and Dynamical Astronomy》1989,47(4):305-320
For differential equations with one fast variable, a perturbation method is introduced that transforms a solution valid over only a short time interval to a new solution composed of averaged variables plus a periodic function of the averaged variables. The averaged variables are governed by a set of differential equations where the fast variable has been removed and thus can be numerically integrated quickly or solved directly. This method is applied to a perturbed harmonic oscillator with a cubic perturbation, van der Pol's equation, coorbital motion in the restricted three-body problem, and to nearly circular motion of a particle near one of the primaries in the restricted three-body problem. 相似文献
7.
I. M. Belen'kii 《Celestial Mechanics and Dynamical Astronomy》1981,23(1):9-32
This paper deals with a method of regularization and linearization of the equations of motion in the central force-field, when the potential is given.This method of regularization of the equations of motion is known (Sundman, 1913), and is based on the transformation of time by means of introducing a new independent variable.In this article a condition has been obtained for the regularizing function when the potential is given.Some examples of the perturbed Keplerian motions are discussed. 相似文献
8.
The perturbation dynamics of an unbounded nonthermal self-gravitating inhomogeneous viscoelastic system composed of two-component constitutive fluids is theoretically investigated. The role of fluid turbulence, which is a highly nonlinear hydrodynamic vorticity-driven phenomenology, is included via the Larson logatropic equation of state describing nonlinear fluid pressure effects. The thermodynamics of the variable-temperature bulk fluid is included with the help of a proper heat diffusion equation. The system is coupled by the electro-gravitational Poisson equations in a closed form. A generalized linear dispersion relation (cubic in degree) is procedurally obtained using a standard technique of linear normal mode analysis. The dispersion relation stems from the rudimentary condition of non-vanishing perturbed gravitational potential in a linear order. The propagatory and dispersive features of the composite fluid perturbations are numerically explored with a special attention to the nonthermality effects. Their growth characteristics are analyzed alongside promising indication to applicability in the astro-cosmo-plasmic context. 相似文献
9.
We study the problem of the reconstruction of a non-stationary space symmetrical regular planar potential of the gravitating system on a family of evolving types of orbits being used in the dynamics of stationary stellar systems. An application of such an inverse problem to the dynamical evolution of stellar systems with variable masses is given. The general form of the evolving orbit which we use when writing out the differential equations for non-stationary potential may also be interpreted as an osculating orbit of the perturbed Keplerian motion. In this case we are making an additional transformation of the basic equation of the problem and demonstrating an appropriate example of the construction of a non-stationary potential of a gravitating system. In connection with the stellar dynamical character of our inverse problem, we also give a generalized form of its basic equation in a rotating coordinate system. 相似文献
10.
A necessary and sufficient condition for the ideal magnetohydrodynamic stability of 2D current sheet models of prominences suspended in a potential coronal field with line-tying is developed using the energy method. This condition takes the form of two simple coupled second-order differential equations which may be integrated along a field line to find marginal stability. The two conditions (85) and (86) of Anzer (1969) are now only sufficient for stability. Two current sheet models are investigated and it is shown that for a potential coronal field allowing perturbed electric currents to flow, line-tying can completely stabilize the equilibria for realistic heights. 相似文献
11.
J. Baumgarte 《Celestial Mechanics and Dynamical Astronomy》1972,5(4):490-501
A stabilization of the classical equations of two-body motion is offered. It is characterized by the use of the regularizing independent variable (eccentric anomaly) and by the addition of a control-term to the differential equations. This method is related to the KS-theory (Stiefel, 1970) which performed for the first time a stabilization of the Kepler motion. But in contrast to the KS-theory our method does not transform the coordinates of the particle. As far as the theory of stability and the numerical experiments are concerned we restrict ourselves to thepure Kepler motion. But, of course, the stabilizing devices will also improve the accuracy of the computation of perturbed orbits. We list, therefore, also the equations of the perturbed motion. 相似文献
12.
When the elimination of the parallax and the elimination of the perigee is applied to the zonal problem of the artificial satellite, a one-degree of freedom Hamiltonian is obtained. The classical way to integrate this Hamiltonian is by applying the Delaunay normalization, however, changing the time to the perturbed true anomaly and the variable to the inverse of the distance, the Hamilton equations become a perturbed harmonic oscillator. In this paper we apply the Krylov—Bogoliubov—Mitropolsky (KBM) method to integrate the perturbed harmonic oscillator as an alternative method to the Delaunay normalization. This method has no problem with small eccentricities and inclinations, and shows good numerical results in the evaluation of ephemeris of satellites.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
13.
V. A. Brumberg 《Celestial Mechanics and Dynamical Astronomy》1978,18(4):319-336
For treating the perturbed two-body problem in rectangular coordinates a new method is developed. The method is based on the reduction of the variational equations of the two-body problem with arbitrary elements to the Jordan system. The equations of perturbed motion rewritten in the quasi-Jordan form are subjected to a transformation excluding fast variables and leading to a system governing the long term evolution of motion. The method may be easily extended to the problem of the heliocentric motion of the major planets. For performing this method on computer it is suitable to use facilities of Poissonian and Keplerian processors. 相似文献
14.
Joachim W. Baumgarte 《Celestial Mechanics and Dynamical Astronomy》1976,13(2):247-251
In order to reduce the error growth during a numerical integration, a method of stabilization, of the differential equations of the Keplerian motion is offered. It is characterized by the use of the eccentric anomaly as independent variable in such a way that the time transformation is given by a generalized Lagrange formalism. The control terms in the equations of motion obtained by this modified Lagrangian give immediately a completely Lyapunov-stable set of differential equations. In contrast to other publications, here the equation of time integration is modified by a control term which leads to an integral which defined the time element for the perturbed Keplerian motion.This paper was supported by the National Research Council and the National Aeronautics and Space Administration and also by the Deutsche Forschungsgemeinschaft. It was presented at the Flight Mechanics/Estimation Theory Symposium, Goddard Space Flight Center, Greenbelt, Md., April 15–16, 1975. 相似文献
15.
S. V. Ferronsky 《Celestial Mechanics and Dynamical Astronomy》1983,30(1):71-83
New physical principles for an explanation of seasonal variations in the Earth's rate of rotation are proposed. It is thought that the variations are caused by a variation of the total energy of the Earth's atmosphere in the course of the planet's revolution about the Sun in elliptic orbit. Jacobi's virial equation for the Earth's atmosphere is derived from the Eulerian equations. The virial theorem is obtained. The existence of the relationship between Jacobi's function and potential energy of the atmosphere is confirmed. In the framework of this relationship, Jacobi's equation is reduced to the equation of unperturbed virial oscillations. The solution of the above-mentioned equation expresses the periodic virial oscillations of Jacobi's function (moment of inertia) of the Earth's atmosphere with time. The solution of the perturbed virial oscillation problem of the atmosphere-solid Earth system is obtained. The perturbation term in Jacobi's virial equation regards, in explicit form, the energy changes occurring in the atmosphere in the course of the planet's revolution about the Sun in elliptic orbit. The annual and semi-annual periodic variations in the Earth's rate of rotation can be considered as an astrometrical result following from the obtained solution. A satisfactory accord of the theoretical results with experimental data is shown. 相似文献
16.
We have investigated the nonlinear interaction between a 3D kinetic Alfvén wave (KAW) and an ion acoustic wave (IAW) in solar wind plasmas. A set of dimensionless equations was developed that describes the pump KAW perturbed by a low-frequency ion acoustic wave. The dependence of the growth rate of the modulational instability on the perturbation wave number was studied. We simulated numerically the dynamical equation of KAW with a pseudo-spectral method, taking ponderomotive nonlinearity into account. The 3D KAW itself propagates in the form of a vortex beam in a magnetised plasma, which manifests the presence of orbital angular momentum of the wave eigenmodes. We discuss the evolution of these vortex structures. Our results reveal that the Kolmogorov scaling is followed by a steeper scaling of power spectra, which is consistent with the solar wind observations by the Cluster spacecraft. We discuss the relevance of our investigation for solar wind plasmas. 相似文献
17.
K. T. Alfriend R. Dasenbrock H. Pickard A. Deprit 《Celestial Mechanics and Dynamical Astronomy》1977,16(4):441-458
The Vinti problem, motion about an oblate spheroid, is formulated using the extended phase space method. The new independent variable, similar to the true anomaly, decouples the radius and latitude equations into two perturbed harmonic oscillators whose solutions toO(J
2
4
) are obtained using Lindstedt's method. From these solutions and the solution to the Hamilton-Jacobi equation suitable angle variables, their canonical conjugates and the new Hamiltonian are obtained. The new Hamiltonian, accurate toO(J
2
4
) is function of only the momenta. 相似文献
18.
An appropriate generalization of the Jacobi equation of motion for the polar moment of inertia I is considered in order to study the N-body problem with variable masses. Two coupled ordinary differential equations governing the evolution of I and the total energy E are obtained. A regularization scheme for this system of differential equations is provided. We compute some illustrative
numerical examples, and discuss an average method for obtaining approximate analytical solutions to this pair of equations.
For a particular law of mass loss we also obtain exact analytical solutions. The application of these ideas to other kind
of perturbed gravitational N-body systems involving drag forces or a different type of mass variation is also considered.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
19.
This study investigates the stability of a class of radiating viscous self-gravitating stars with axial symmetry having anisotropic pressure. We use perturbation technique to establish the perturbed form of the Einstein field equations and dynamical equations. The instability range in the Newtonian and post-Newtonian eras has been analyzed by constructing the collapse equation. It is found that the adiabatic index has a key role in the discussion of instability ranges which depends upon the physical parameters, i.e., energy density, anisotropic pressure and shear viscosity of the fluid and heat flux. We conclude that the shear viscosity decreases the instability range and makes the system more stable. 相似文献
20.
J. N. Tokis 《Astrophysics and Space Science》1975,36(2):427-438
The general equations of angular momentum and kinetic energy of a rotating deformable (or not rigid) body are discussed for a fixed and a rotating coordinate system. A new system of equations is developed for a deformable body of arbitrary form using the Lagrangian (vector) cisplacement up to the first order terms. The equations are, then, illustrated for a self-gravitating ceformable body perturbed by tides. 相似文献