共查询到20条相似文献，搜索用时 109 毫秒
1.
Y. Tanaka 《Astrophysics and Space Science》1993,210(1-2):333-341
Modal coupling oscillation models for the stellar radial pulsation and coupled-oscillators are reviewed. Coupled-oscillators with the second-order and third-order terms seemed to behave non-systematically. Using the equation by Schwarzschild and Savedoff (1949) with the dissipation term of van del Pol's type which is third-order, we demonstrate the effect of each term. The effects can be understood by the terms of the nonlinear dynamics, which is recently developing, that is. phase-locking, quasi-periodicity, period doubling, and chaos. As the problem of stellar pulsation, especially of double-mode cepheids on the period-ratio, we examine the dependence on the stellar structure from which the coupling constants in the second-order terms are derived. Eigen functions for adiabatic pulsations had been used for the calculation of the constants. It is noted that only two set of the constants are available, that is, for the polytrope model withn = 3 and a cepheid model without convection. Some examples of nonlinear dynamical effects will be shown.It is shown that if the constants were suitable values, the period-ratio of double-mode cepheids is probably realized. The possibility is briefly suggested. 相似文献
2.
The regularization of a new problem, namely the three-body problem, using ‘similar’ coordinate system is proposed. For this
purpose we use the relation of ‘similarity’, which has been introduced as an equivalence relation in a previous paper (see
Roman in Astrophys. Space Sci. doi:, 2011). First we write the Hamiltonian function, the equations of motion in canonical form, and then using a generating function,
we obtain the transformed equations of motion. After the coordinates transformations, we introduce the fictitious time, to
regularize the equations of motion. Explicit formulas are given for the regularization in the coordinate systems centered
in the more massive and the less massive star of the binary system. The ‘similar’ polar angle’s definition is introduced,
in order to analyze the regularization’s geometrical transformation. The effect of Levi-Civita’s transformation is described
in a geometrical manner. Using the resulted regularized equations, we analyze and compare these canonical equations numerically,
for the Earth-Moon binary system. 相似文献
3.
In this paper we use a new approach to derive the system of first-order coupled equations governing the propagation of electromagnetic waves in an inhomogeneous magnetized plasma for normal incidence. In this new approach we employ a step model and use Maxwell's equations indirectly. The method we present here possesses simplicity in mathematical manipulation and gives a clearer physical picture of the mechanism of mode-coupling. The variablesE
i used in the coupled equations are directly related to experimental measurements. Our result is shown to be equivalent to that obtained by Budden and Clemmow (1957). 相似文献
4.
In this paper we have proposed certain generalizations of anomalous diffusion equations for fractional order. These diffusion equations are solved by the method of Laplace transform with respect to the time variable and Fourier transform with respect to the space variable. The solutions of some known diffusion equations are also shown to be derived here. 相似文献
5.
S. R. Das Gupta 《Astrophysics and Space Science》1978,56(1):21-49
In this paper we develop a new method, combined with Laplace transformation and Wiener-Hopf technique, to obtain unique solutions of transport equations in finite media. For this purpose we consider the simple transfer equation for diffuse reflection by a plane-parallel finite atmosphere scattering radiation with moderate anisotropy. It is transformed, by Laplace transformation, into two coupled linear integral equations which are then reduced to two uncoupled Fredholm integral equations admitting of unique solutions by the method of iteration for values of the breadth of the atmosphere greater than that specified, depending on the scattering process. 相似文献
6.
Myeong-Gu Park 《Monthly notices of the Royal Astronomical Society》2006,367(4):1739-1745
Radiation interacts with matter via exchange of energy and momentum. When matter is moving with a relativistic velocity or when the background space–time is strongly curved, rigorous relativistic treatment of hydrodynamics and radiative transfer is required. Here, we derive fully general relativistic radiation hydrodynamic equations from a covariant tensor formalism. The equations can be applied to any three-dimensional problems and are rather straightforward to understand compared to the comoving frame-based equations. The current approach is applicable to any space–time or coordinates, but in this work we specifically choose the Schwarzschild space–time to show explicitly how the hydrodynamic and the radiation moment equations are derived. Some important aspects of relativistic radiation hydrodynamics and the difficulty with the radiation moment formalism are discussed as well. 相似文献
7.
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the equations of motion of the unaveraged perturbed two-body problem in terms of planetary orbital elements by using a generalized form of Gauss’ equations. We consider a varied set of position and velocity-dependent perturbations, and also derive relevant specific cases of the equations: when they are averaged over fast variables (the “adiabatic” approximation), and in the prograde and retrograde planar cases. In each instance, we delineate the properties of the equations. As brief demonstrations of potential applications, we consider the effect of Galactic tides. We measure the effect on the widest-known exoplanet orbit, Sedna-like objects, and distant scattered disk objects, particularly with regard to where the adiabatic approximation breaks down. The Mathematica code which can help derive the equations of motion for a user-defined perturbation is freely available upon request. 相似文献
8.
R. Broucke 《Celestial Mechanics and Dynamical Astronomy》1978,18(3):207-222
In this article we study a form of equations of motion which is different from Lagrange's and Hamilton's equations: Pfaff's equations of motion. Pfaff's equations of motion were published in 1815 and are remarkably elegant as well as general, but still they are much less well known. Pfaff's equations can also be considered as the Euler-Lagrange equations derived from the linear Lagrangian rather than the usual Lagrangian which is quadratic in the velocity components. The article first treats the theory of changes of variables in Pfaff's equations and the connections with canonical equations as well as canonical transformations. Then the applications to the perturbed two-body problem are treated in detail. Finally, the Pfaffians are given in Hill variables and Scheifele variables. With these two sets of variables, the use of the true anomaly as independent variable is also considered. 相似文献
9.
In this article we study for first time the motion of charged particleswith neglected mass under the influence of Lorentz and Coulomb forces offour moving celestial bodies. For this problem we give the equations ofmotion, variational equations and energy integral. Also we give theequilibrium configurations demonstrating an extensive numericalinvestigation of the equilibrium points with comments about theirappearance. 相似文献
10.
Interaction of Alfvén waves with plasma inhomogeneities generates phase mixing which can lead to dissipate Alfvén waves and to heat the solar plasma. Here we study the dissipation of Alfvén waves by phase mixing due to viscosity and resistivity variations with height. We also consider nonlinear magnetohydrodynamic (MHD) equations in our theoretical model. Non-linear terms of MHD equations include perturbed velocity, magnetic field, and density. To investigate the damping of Alfvén waves in a stratified atmosphere of solar spicules, we solve the non-linear MHD equations in the x–z plane. Our simulations show that the damping is enhanced due to viscosity and resistivity gradients. Moreover, energy variations is influenced due to nonlinear terms in MHD equations. 相似文献
11.
J.R. Jasperse 《Planetary and Space Science》1977,25(8):743-756
Using the Boltzmann-Fokker-Planck method and the local approximation we derive coupled non-linear equations for the electron and ion concentrations and the energy-dependent electron distribution function in the Earth's lower ionosphere. These equations are new and give the appropriate generalization of the standard electron-ion continuity equations in the local approximation when electron-neutral particle impact ionization is treated rigorously. We report stable, numerical solutions to these equations and compare our calculated electron concentration to the experimentally determined result for a rocket experiment where the electron concentration and solar EUV spectral flux were measured simultaneously. 相似文献
12.
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
13.
《Chinese Astronomy and Astrophysics》1982,6(1):60-63
We discuss the excitation of polar motion by earthquake displacement field. Instead of the usual static equilibrium equations in the literature, we use an improved set as given in /1/, which guarantee continuity at the core-mantle boundary. We take the parameter values of three earthquakes from /2/.To obviate the singularity at r = 0, we use asymptotic solutions by power series within a small sphere around the centre. Outisde this sphere, the equations are numerically integrated by the Runge-Kutta algorithm. Our equations /1/ gave polar shifts some 3 times larger than Dahlen's equations /2/. 相似文献
14.
Recently, Innaiah and Reddy (1985) obtained a flat Robertson-Walker-type solution for the Einstein field equations with the trace-free energy-momentum tensor of a conformally invariant scalar field as source. Here we show that the field equations force the scalar field to be independent of time. Furthermore, we obtain open and closed Robertson-Walker-type solutions and observe that, once again, the scalar field has to be independent of time. 相似文献
15.
Paolo Lanzano 《Earth, Moon, and Planets》1990,48(3):251-278
We establish the equations of motion for a fluid spherical shell which constitutes the upper-most layer of a rotating body and which is heated from below because of radiogenic decay occurring in the lower layers. We solve these equations in terms of series of products of Bessel functions and Gegenbauer polynomials. By the step-wise solution of an infinite-order determinant equation we determine those values for the Taylor and Rayleigh numbers of the flow, up to the 1016 order, that will give rise to convective cells in the liquid layer.Using these eigenvalues, we solve linear systems of equations to determine the coefficients of the series solutions. 相似文献
16.
Starting with the Einstein-Maxwell field equations, we obtain the post-Newtonian equations of motion ofn massive-charged particles in general relativity. 相似文献
17.
In the present paper we study some new aspects of the Bianchi type-V space time. The Electric and Magnetic parts of Weyl tensors are calculated in terms of tilted congruence and discussed the purely magnetic Weyl tensor. Einstein field equations for purely magnetic space time are obtained and solution of such field equations called purely magnetic solution. To get deterministic solutions of the field equations we consider a new law of variation of average scale factor which yields time dependent deceleration parameter. Certain physical and geometrical properties of the model are also discussed. 相似文献
18.
The secular effect of YORP torque on the rotational dynamics of an asteroid in non-principal axis rotation is studied. The
general rotational equations of motion are derived and approximated with an illumination function expanded up to second order.
The resulting equations of motion can be averaged over the fast rotation angles to yield secular equations for the angular
momentum, dynamic inertia and obliquity. We study the properties of these secular equations and compare results to previous
research. Finally, an application to several real asteroid shapes is made, in particular we study the predicted rotational
dynamics of the asteroid Toutatis, which is known to be in a non-principal axis state. 相似文献
19.
D.-E. Liebscher 《Astronomische Nachrichten》1988,309(4):277-279
If we require the effective field equations for a local system to be second order partial differential equations, an affinely invariant theory (not presuming the existence of a metric tensor beforehand) has to be non-local, the action being a multiple integral over the manifold considered. 相似文献
20.
For application to the mid-latitude topside ionosphere, we have derived diffusion and heat flow equations for a gas mixture composed of two major ions, electrons and a number of minor ions. These equations were derived by expanding the velocity distribution of each constituent about its 13 lower order velocity moments. As a consequence, each constituent was allowed to have its own temperature and drift velocity. The restriction to mid-latitudes results because we have assumed that the species temperature and drift velocity differences were small. In deriving the diffusion and thermal conduction equations, we have discovered some new transport effects. For the major ions, we have found that: (1) a temperature gradient in either gas causes thermal diffusion in both gases; (2) a temperature gradient in either gas causes heat to flow in both gases; and (3) a relative drift between the major ion gases induces a heat flow in both gases. Similar transport effects have also been found for the minor ions. 相似文献