共查询到20条相似文献，搜索用时 31 毫秒
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A form of planetary perturbation theory based on canonical equations of motion, rather than on the use of osculating orbital elements, is developed and applied to several problems of interest. It is proved that, with appropriately selected initial conditions on the orbital elements, the two forms of perturbation theory give rise to identical predictions for the observable coordinates and velocities, while the orbital elements themselves may be strikingly different. Differences between the canonical form of perturbation theory and the classical Lagrange planetary perturbation equations are discussed. The canonical form of perturbation theory in some cases has advantages when the perturbing forces are velocity-dependent, but the two forms of perturbation theory are equivalent if the perturbing forces are dependent only on position and not on velocity. The canonical form of the planetary perturbation equations are derived and applied to the Lense Thirring precession of a test body in a Keplerian orbit around a rotating mass source. 相似文献
3.
The three-dimensional distribution of change in phase travel time of an active region below the solar surface can be constructed
with the technique of acoustic imaging. The interpretation of the distribution of measured phase travel time perturbation
suffers from the finite spatial resolution of the acoustic lenses. In the ray approximation, the phase travel time perturbation
measured in acoustic imaging can be expressed as an integral of the product of the relative sound-speed perturbation and a
kernel. Forward computations show that the vertical resolution of phase travel time perturbation is poor even in the ray approximation.
In this study, we discuss the inversion of phase travel time perturbations to estimate the relative sound-speed perturbation
with a regularized least-squares inversion method. The tests with model perturbations of sound speed show that the inversion
reasonably recovers the distribution of the model perturbation. We also apply the inversion method to the measured phase travel
time perturbation of active region NOAA 7981. 相似文献
4.
Akira Mizuta Jave O. Kane Marc W. Pound Bruce A. Remington Dmitri D. Ryutov Hideaki Takabe 《Astrophysics and Space Science》2007,307(1-3):183-186
Hydrodynamic instability of an accelerating ionization front (IF) is investigated with 2D hydrodynamic simulations, including
absorption of incident photoionizing photons, recombination in the HII region, and radiative molecular cooling. When the amplitude
of the perturbation is large enough, nonlinear dynamics of the IF triggered by the separation of the IF from the cloud surface
is observed. This causes the second harmonic of the imposed perturbation to appear on the cloud surfaces, whereas the perturbation
in density of ablated gas in the HII region remains largely single mode. This mismatch of modes between the IF and the density
perturbation in the HII region prevents the strong stabilization effect seen in the linear regime. Large growth of the perturbation
caused by Rayleigh-Taylor-like instability is observed late in time. 相似文献
5.
Yoshio Kubo 《Celestial Mechanics and Dynamical Astronomy》2012,112(1):99-106
Kubo (Celest Mech Dyn Astron 110:143–168, 2011) investigated the kinematical structure of the perturbation in the rotation of the elastic Earth due to the deformation caused
by the outer bodies. In that paper, while the mechanism for the perturbation of the figure axis was made clear, that for the
rotational axis was not shown explicitly. In the present study, following the same method, the structure of the perturbation
of the rotational axis is investigated. This perturbation consists of the direct perturbation and the convective perturbation.
First the direct perturbation is shown to be (A − C)/A times as large as that of the figure axis, coinciding with the analytical expressions obtained in preceding studies by other
authors. As for the convective perturbation, which appears only in the perturbation of the rotational axis but not in that
of the figure axis, it is shown to be (A − C)/A times the angular separation between the original figure axis and the induced figure axis produced by the elastic deformation,
A and C being the principal moments of inertia of the Earth. If the perturbing bodies are motionless, the conclusion of Kubo (Celest
Mech Dyn Astron 105:261–274, 2009) holds strictly, i.e. the sum of the direct and the convective perturbations of the rotational axis coincides with the perturbation
of the figure axis. 相似文献
6.
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
7.
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
8.
The lunisolar perturbation is the principal factor that causes variation in the orbit of a GTO (geosychronous transfer orbit) space debris. In the present article the analytical expression of the long-periodic term of the altitude of the GTO orbital perigee caused by the lunisolar perturbation is derived, and the basic characteristics of the variation of the perigee caused by the lunisolar perturbation are analyzed. A method of selecting a launch window that will help to improve the space debris situation is given, and its correctness is tested and verified through simulation calculation. 相似文献
9.
The effect of a weak magnetic field on the adiabatic radial and non-radial oscillations of a stellar configuration is studied by means of a perturbation method. Special attention is devoted to the perturbation of the oscillation frequencies resulting from the change of the boundary conditions caused by the magnetic field. This change is related to the fact that the introduction of a magnetic field removes the singularity at the surface of the equilibrium configuration. The perturbation method is applied to Ferraro's model and the influence of a magnetic field on the frequencies of the different types of oscillation modes is discussed. 相似文献
10.
Three experiments on the initially slightly flattened spheroids (=0.45) have been made. The first one is run without perturbation and the others with perturbation. The results have shown that the spheroid without perturbation will evolve to nearly sphere and the other two will almost keep the originally projected shape after perturbation and relaxation.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984. 相似文献
11.
Stefano Casotto 《Celestial Mechanics and Dynamical Astronomy》1995,62(1):1-22
A new method for calculating the perturbation spectrum in the framework of Kaula's linear satellite theory (LST) is introduced. The novelty of this approach consists in using recent results on the spectral decomposition of the perturbation frequencies in LST to provide a closed formulation for the amplitude and the phase of each line in the perturbation spectrum. The theory presented here can be applied to perturbations in the elements or in the radial and transverse directions due to the geopotential or to the tides. Separate algorithms are developed for application to orbits with circulating or frozen perigee. 相似文献
12.
Ahmed Aly Kamel 《Celestial Mechanics and Dynamical Astronomy》1969,1(2):190-199
The theory of perturbation based on Lie transforms is considered. Deprit's equation is reduced to a form which enables us to generate simplified general recursion formulae. These expansions are then modified to speed up the implementation of such perturbation theory in the computerized symbolic manipulation. 相似文献
13.
David Moss 《Astrophysics and Space Science》1978,54(2):445-452
A first-order perturbation theory method developed by Goossens to determine the perturbation to the eigenfrequencies of stellar models caused by the presence of a magnetic field is modified slightly, and applied to models with toroidal and poloidal fields. Some limitations of the analysis are pointed out. 相似文献
14.
含粘滞的弱磁化吸积盘的非轴对称脉动不稳定性 总被引：1，自引：0，他引：1
本文讨论了一种含扩散型粘滞的弱磁化等温吸积盘模型．在作者原有工作的基础上研究了吸积盘对非轴对称扰动（含径向、环向和垂向三个方向的扰动）所表现的脉动不稳定性．结果表明，径向扰动是最重要、最根本的扰动：在无径向扰动时，吸积盘中不存在环向扰动与垂向扰动所产生的脉动不稳定性．在径向扰动存在时，吸积盘除了可能存在纯径向脉动不稳定性外，还可能存在由于径向扰动与垂向扰动的耦合所引起的轴对称脉动不稳定性，以及由于径向扰动与环向扰动的耦合所引起的非轴对称脉动不稳定性．当上述三个方向的扰动并存时，对应的非轴对称脉动不稳定性也可能存在． 相似文献
15.
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
16.
M. S. Ruderman 《Solar physics》2017,292(8):111
We study the excitation of fluting perturbations in a magnetic tube by an initially imposed kink mode. We use the ideal magnetohydrodynamic (MHD) equations in the cold-plasma approximation. We also use the thin-tube approximation and scale the dependent and independent variables accordingly. Then we assume that the dimensionless amplitude of the kink mode is small and use it as an expansion parameter in the regular perturbation method. We obtain the expression for the tube boundary perturbation in the second-order approximation. This perturbation is a superposition of sausage and fluting perturbations. The amplitude of the fluting perturbation takes its maximum at the middle of the tube, and it monotonically decreases with the distance from the middle of the tube. 相似文献
17.
In this investigation, a procedure is described for extending the application of canonical perturbation theories, which have been applied previously to the study of conservative systems only, to the study of non-conservative dynamical systems. The extension is obtained by imbedding then-dimensional non-conservative motion in a 2n-dimensional space can always be specified in canonical form, and, consequently, the motion can be studied by direct application of any canonical perturbation method. The disadvantage of determining a solution to the 2n-dimensional problem instead of the originaln-dimensional problem is minimized if the canonical transformation theory is used to develop the perturbation solution. As examples to illustrate the application of the method, Duffing's equation, the equation for a linear oscillator with cubic damping and the van der Pol equation are solved using the Lie-Hori perturbation algorithm.This research was supported by the Office of Naval Research under Contract N00014-67-a-0126-0013. 相似文献
18.
Effect of Moon perturbation on the energy curves and equilibrium points in the Sun–Earth–Moon system
《New Astronomy》2021
In this paper, we have considered that the Moon motion around the Earth is a source of a perturbation for the infinitesimal body motion in the Sun–Earth system. The perturbation effect is analyzed by using the Sun–Earth–Moon bi–circular model (BCM). We have determined the effect of this perturbation on the Lagrangian points and zero velocity curves. We have obtained the motion of infinitesimal body in the neighborhood of the equivalent equilibria of the triangular equilibrium points. Moreover, to know the nature of the trajectory, we have estimated the first order Lyapunov characteristic exponents of the trajectory emanating from the vicinity of the triangular equilibrium point in the proposed system. It is noticed that due to the generated perturbation by the Moon motion, the results are affected significantly, and the Jacobian constant is fluctuated periodically as the Moon is moving around the Earth. Finally, we emphasize that this model could be applicable to send either satellite or telescope for deep space exploration. 相似文献
19.
The transformational behaviour of Hori's noncanonical perturbation theory (Hori 1971) as well as that of the theory of Krylov-Bogoliubof-Mitropolsky is studied. An integration procedure of the perturbation equations is based on the transformation properties that have been established. 相似文献
20.
Using a Lagrangian approach to the equations describing small amplitude departures from equilibrium of solar prominences, we derive seven quantities which, by analogy to the concepts of energy, momentum and angular momentum, are conserved under circumstances corresponding to ignorable coordinates of classical mechanics. In a pragmatic sense it is expected that these conservation laws will be useful as criteria of accuracy in obtaining eigen-frequencies for the perturbation equations when numerical techniques are employed.We also demonstrate that: (i) the perturbation equations (which are not self-adjoint) follow from an external variation of a Lagrangian; (ii) the equations adjoint to the perturbation equations also follow from an extremal variation of the same Lagrangian; (iii) the Lagrangian approach automatically gives the conserved quantities, together with a variational principle for computing the eigen-frequencies of the perturbation equations.In view of the paucity of analytic solutions (and their eigen-frequencies) to the perturbation equations (due essentially to the complicated spatial dependence of thermodynamic quantities describing the equilibria) we believe that the technique developed here - which is capable of handling complicated spatial dependences and which has internal criteria for assessing accuracy of any given numerical convergence scheme - is a valuable addition to the arsenal of methods used for discussing the equilibria, and their stability, of models thought to represent the basic physical processes underlying the quiescent solar prominence phenomenon. 相似文献