共查询到20条相似文献，搜索用时 46 毫秒
1.
We construct a non-stationary form of the Lagrangian of a material point with a known integral of motion and given monoparametric
family of evolving orbits. An equation for non-stationary space symmetrical ‘potential’ function of such Lagrangian is given
and this stands for the analog of Szebehely's (1974) equation. As an application of the problem, an integrable equation from
celestial mechanics of variable mass with use of non-perturbed orbits of evolving type is constructed. On its basis adiabatic
invariants of non-stationary two-body problem containing a tangential force are found.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
2.
We propose an approximate analytical approach to the problem of the transition of supernova remnants from the adiabatic stage of their evolution to the radiative one. Contrary to the traditional notion, this process turns out to last for a quite long time which is commensurable with the duration of the adiabatic stage. We calculate some parameters of the thermal X-ray radiation of supernova remnants. 相似文献
3.
Mohammad Salmassi 《Celestial Mechanics and Dynamical Astronomy》1985,37(4):359-369
An adiabatic invariant is characterized by the property that its derivative is small and oscillatory. Therefore, assuming that such a quantity is constant does not lead to a cumulative error as t. In this paper, using action and angle variables, adiabatic invariants to 0(1) and 0() are found for the two-body problem with a slowly varying gravitational constant. 相似文献
4.
S. V. Vorontsov 《Solar physics》1983,82(1-2):379-382
Perturbation theory is developed for calculating the influence of slow differential rotation on the adiabatic nonradial modes of stellar oscillations. The effects of Coriolis forces and ellipticity are analysed simultaneously using the perturbation technique for Hermitian operators which is developed up to second order in eigenvalues and to first order in eigenvectors. 相似文献
5.
Some asteroids in Earth‐crossing orbits avoid close approaches by entering in a mean motion resonance whenever the distance between the two orbits is small. These orbits are ‘Toro class’ according to the classification of (Milani et al., 1989). This protection mechanism can be understood by a semi‐averaged model, in which the fast variables are removed and the dynamical variables are the critical argument and the semimajor axis, with dependence upon a slow parameter. The adiabatic invariant theory can be applied to this model and accounts for all the qualitative features of the orbits in this class, including the onset of the libration when the orbit distance is small. Because of the neglected perturbations by the other planets, this theory is approximate and the adiabatic invariant is conserved only with low accuracy moreover, the Toro state can be terminated by a close approach to another planet (typically Venus). “Would you tell me, please, which way I ought to go from here?” “That depends a good deal on where you want to get to,” said the Cat. Alice in Wonderland, L. Carroll 相似文献
6.
Giancarlo Benettin Massimiliano Guzzo Valerio Marini 《Celestial Mechanics and Dynamical Astronomy》2008,101(1-2):203-224
We provide evidences that the angular momentum of a symmetric rigid body in a spin–orbit resonance can perform large scale chaotic motions on time scales which increase polynomially with the inverse of the oblateness of the body. This kind of irregular precession appears as soon as the orbit of the center of mass is non-circular and the angular momentum of the body is far from the principal directions with minimum (maximum) moment of inertia. We also provide a quantitative explanation of these facts by using the theory of adiabatic invariants, and we provide numerical applications to the cases of the 1:1 and 1:2 spin–orbit resonances. 相似文献
7.
We here investigate the motion of particles in a dipole magnetic field under the assumption of conservation of the first two adiabatic invariants. The results are then combined with Liouville's theorem to obtain the variation of the distribution function, and hence the plasma bulk parameters with L-shell. A comparison of the numerical results with recently published analytical approximations is made. Finally, the results are used to describe the structure of the ring current plasma in the outer radiatoin zone, the effects of the Alfvén layers being quantitatively evaluated for a simple electric field model. 相似文献
8.
Vishnu Sharan 《Astrophysics and Space Science》1984,104(2):189-197
By use of the approximate method of Whitham (1958), the propagation of magnetogasdynamic spherical shock waves is considered for adiabatic and isothermal flows in a decreasing density medium. The effect of initial magnetic fields on the shock velocity is discussed; and a comparison made between adiabatic and isothermal cases. 相似文献
9.
An approximate analytical technique for computing the change in the binding energy of a binary due to an incoming third star moving in a distant parabolic orbit is presented. This is an example of a tidal encounter since we assume that the distance of the third star always considerably exceeds the size of the binary. The perturbation is also adiabatic, varying on a time scale much exceeding the binary period, and the change has an exponential form. Different cases arise depending on the choice of the masses and the angle of inclination of the plane in which the star moves. Some numerical experiments are performed as a means of checking the analytical theory. 相似文献
10.
Yu. D. Zhugzhda 《Astrophysics and Space Science》1983,95(2):255-275
The problem of propagation and linear transformation of atmospheric and temperature waves in an isothermal atmosphere with stratified heat exchange has been solved analytically. The cases are discussed where temperature inhomogeneities produced by the waves are either optically thin or optically thick. Formulae have been derived for the absorption, reflection, and transformation of waves when they are transformed from adiabatic into isothermal. The properties of temperature waves are considered. The theory of non-adiabatic atmospheric waves is applied to an analysis of oscillations in a quiet solar atmosphere. 相似文献
11.
We investigate the transport process of electrons in the tail plasma sheet by convection electric fields, under the assumption of conservation of the first two adiabatic invariants. The variation of the electron distribution function, and hence the bulk parameters with distance from the Earth are calculated. The results show that the electron distribution has a pressure anisotropy with p/p< 1 in the plasma sheet. Finally, the effects of the pressure anisotropy are qualitatively considered in terms of the modification of the geomagnetic field structure in the tail plasma sheet and instabilities due to wave-particle interactions. 相似文献
12.
C.-V. Meister 《Astronomische Nachrichten》1995,316(5):295-310
A Langevin equation for charged particles in a plasma with electrostatic turbulence is developed from first principles and in consistency with the kinetic theory in polarization approximation. For the case of ion-acoustic and electrostatic lower-hybrid-drift turbulence approximate expressions for the space-time spectral density of the wave energy are given and estimates of the intensities of the stochastic wave forces are made. The application is done for the plasmas of the earth's magnetosphere, the solar wind and solar flares. It seems, that ion-acoustic and electrostatic lower-hybrid-drift waves can contribute to electron chaotization in different regions of the space plasma. 相似文献
13.
A simple approximate model of the asteroid dynamics near the 3:1 mean–motion resonance with Jupiter can be described by a
Hamiltonian system with two degrees of freedom. The phase variables of this system evolve at different rates and can be subdivided
into the ‘fast’ and ‘slow’ ones. Using the averaging technique, wisdom obtained the evolutionary equations which allow to
study the long-term behavior of the slow variables. The dynamic system described by the averaged equations will be called
the ‘Wisdom system’ below. The investigation of the, wisdom system properties allows us to present detailed classification
of the slow variables’ evolution paths. The validity of the averaged equations is closely connected with the conservation
of the approximate integral (adiabatic invariant) possessed by the original system. Qualitative changes in the behavior of
the fast variables cause the violations of the adiabatic invariance. As a result the adiabatic chaos phenomenon takes place.
Our analysis reveals numerous stable periodic trajectories in the region of the adiabatic chaos. 相似文献
14.
We present a simplified analytic derivation of the capture probabilities for the j+1j and j+2j orbital resonances. We apply Henrard's method which is based on an extension of the theory of adiabatic invariants and recover the results originally obtained by Yoder.Contribution number 3874 from the Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, U.S.A. 相似文献
15.
A. Lemaitre 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):329-341
A possible mechanism to explain the depletion of the Kirkwood gaps in the asteroid belt would be the slow dissipation of the solar nebula at the origin of the Solar System. The effects of this dissipation on a uniform distribution of asteroids are explored by means of the adiabatic invariant theory for the 2/1, 3/1 and 5/2 resonance cases. The framework is the restricted, circular and planar three body problem. 相似文献
16.
R.S. Gomes 《Celestial Mechanics and Dynamical Astronomy》1995,61(1):97-113
The problem of resonance trapping for particles subject to Poynting-Robertson drag is approached initially from an adiabatic regime theory. A simplified Hamiltonian system is presented for simple eccentricity-type resonances up to order 3, and expressions related to the trapping process are deduced. The fast dissipation provoked by Poynting-Robertson leads to the employment of a numerical approach for the computation of resonance capture probabilities, for particles in the size range of practical importance. Some aspects of the dynamical evolution of a particle after capture are noticed from results of numerical integrations. Analytical methods are used in order to confirm the numerical results. 相似文献
17.
The instability of anisotropic disk systems with elongated stellar orbits has been investigated. N-body generalized polytropic models of stellar disks have been constructed. They are shown to be unstable with respect to the bar formation at any degree of anisotropy. This result differs from the results of the studies of such models by other authors. The bar pattern speed and amplitude have been found. The initial distribution of precession rates and the adiabatic invariants of stellar orbits have been calculated. A bar is shown to be formed in such systems due to the radial orbit instability. 相似文献
18.
J. J. Podesta 《Solar physics》2005,232(1-2):1-23
The solar convection zone is modeled as a horizontally stratified atmosphere with a constant gravitational field and an adiabatic
temperature gradient (a neutrally stratified polytrope). At equilibrium, the gas pressure and density decreases to zero at
the solar surface so that the solar surface is treated as a free surface which is bounded by vacuum. The evolution of small
amplitude perturbations about the equilibrium state is described by the linearized Euler equations for an inviscid compressible
fluid with an adiabatic equation of state. A sunquake is initiated at time zero by means of an initial perturbation with a
Gaussian velocity profile and the exact solution of the initial value problem is obtained in terms of a Fourier integral.
Comparisons between theory and observations indicate that this highly simplified model is able to predict the propagation
of sunquake waves across the solar surface with an error of approximately 10% or 20%. 相似文献
19.
本文从完整的MHD方程出发严格推导了一个旋转等离子体系统相对于平衡态作小振动的稳定性条件。该系统具有粘性、可压缩性、有自引力。同前人的工作相比较,由于本文用能量方程代替了近似关系(如绝热关系等),所以结果更加合理并具有普遍性。在一般情况下,前人的结果可以认为是本文结果的特例。同时本文还对文献[1]的稳定性充要条件提出疑义。 相似文献
20.
Series expansions for encounter-type solutions of Hill's problem 总被引：1，自引：0，他引：1
Hill's problem is defined as the limiting case of the planar three-body problem when two of the masses are very small. This paper describes analytic developments for encounter-type solutions, in which the two small bodies approach each other from an initially large distance, interact for a while, and separate. It is first pointed out that, contrary to prevalent belief, Hill's problem is not a particular case of the restricted problem, but rather a different problem with the same degree of generality. Then we develop series expansions which allow an accurate representation of the asymptotic motion of the two small bodies in the approach and departure phases. For small impact distances, we show that the whole orbit has an adiabatic invariant, which is explicitly computed in the form of a series. For large impact distances, the motion can be approximately described by a perturbation theory, originally due to Goldreich and Tremaine and rederived here in the context of Hill's problem. 相似文献