共查询到20条相似文献，搜索用时 31 毫秒
1.
The motion of a point mass in the J 2 problem is generalized to that of a rigid body in a J 2 gravity field. The linear and nonlinear stability of the classical type of relative equilibria of the rigid body, which have been obtained in our previous paper, are studied in the framework of geometric mechanics with the second-order gravitational potential. Non-canonical Hamiltonian structure of the problem, i.e., Poisson tensor, Casimir functions and equations of motion, are obtained through a Poisson reduction process by means of the symmetry of the problem. The linear system matrix at the relative equilibria is given through the multiplication of the Poisson tensor and Hessian matrix of the variational Lagrangian. Based on the characteristic equation of the linear system matrix, the conditions of linear stability of the relative equilibria are obtained. The conditions of nonlinear stability of the relative equilibria are derived with the energy-Casimir method through the projected Hessian matrix of the variational Lagrangian. With the stability conditions obtained, both the linear and nonlinear stability of the relative equilibria are investigated in details in a wide range of the parameters of the gravity field and the rigid body. We find that both the zonal harmonic J 2 and the characteristic dimension of the rigid body have significant effects on the linear and nonlinear stability. Similar to the classical attitude stability in a central gravity field, the linear stability region is also consisted of two regions that are analogues of the Lagrange region and the DeBra-Delp region respectively. The nonlinear stability region is the subset of the linear stability region in the first quadrant that is the analogue of the Lagrange region. Our results are very useful for the studies on the motion of natural satellites in our solar system. 相似文献
2.
R.W. Schunk 《Planetary and Space Science》1975,23(3):437-485
In this paper we present results for a general system of transport equations appropriate to a multi-constituent gas mixture. This system includes a continuity, momentum, internal energy, pressure tensor and heat flow equation for each species. The results can be applied to both collision dominated and collisionless plasmas with there being explicit limits derived for the validity of the various expressions. In the limit of very frequent collisions the pressure tensor and heat flow equations give the usual Navier-Stokes results for the viscous stress tensor and heat flow vector. Furthermore, the momentum equation includes thermal diffusion and thermoelectric transport coefficients equivalent to the second approximation of Chapman and Cowling. The basic system of equations has been applied to different regions of the ionosphere and neutral atmosphere. It is found that: (1) The viscous stress tensor and heat flow expressions used in previous studies of the neutral thermosphere may not be appropriate; (2) The transport coefficients normally used for mid-latitude F2-region and topside studies seem to be adequate; (3) The high speed flow of plasma in the polar topside ionosphere is likely to be strongly affected by stresses and heat flow; and (4) E- and F-region ionization at high latitudes is substantially affected by stresses and heat flow. 相似文献
3.
A. V. Dementyev 《Astrophysics》2010,53(3):419-433
A matrix transfer equation for multiple resonance scattering of radiation in a spectral line in a semiinfinite atmosphere
with a uniform distribution of primary radiation sources is examined. A nonlinear matrix integral is obtained for this equation
as a generalization of the Rybicki two-point Q-integral. One special case of the matrix [^(Q)] {\mathbf{\hat{Q}}} -integral is the Volterra equation for the matrix source function of the problem discussed here. The Volterra equation is
solved numerically for a Doppler profile of the absorption coefficient. Several polarization characteristics of the emerging
radiation are obtained. 相似文献
4.
Recently we have derived the equation of polarization transfer in an inhomogeneous magnetized plasma in the case where absorption is so weak that the characteristic modes can be considered to be orthogonal. We extend this investigation to the study of polarization transfer in a plasma where the characteristic polarizations need not be orthogonal. We obtain explicit expressions for the Faraday rotation tensor, the absorption tensor, the mode-coupling tensor and the tensor describing the explicit spatial variation of characteristic polarizations due to plasma inhomogeneity. 相似文献
5.
The aim of this paper is to study the warm inflation during intermediate era in the framework of locally rotationally symmetric Bianchi type I universe model. We assume that the universe is composed of inflaton and imperfect fluid having radiation and bulk viscous pressure. To this end, dynamical equations (first model field equation and energy conservation equations) under slow-roll approximation and in high dissipative regime are constructed. A necessary condition is developed for the realization of this anisotropic model. We assume both dissipation and bulk viscous coefficients variable as well as constant. We evaluate entropy density, scalar (tensor) power spectra, their corresponding spectral indices, tensor–scalar ratio and running of spectral index in terms of inflaton. These cosmological parameters are constrained using recent Planck and WMAP7 probe. 相似文献
6.
In this paper, we study the dynamics of warm inflation in which slow-roll inflation is driven by non-Abelian gauge fields. To this end, we use the geometry of locally rotationally symmetric Bianchi type I universe model. We construct dynamical equations, i.e., first model field equation, energy conservation equations and equation of motion under slow-roll approximation. In order to discuss inflationary perturbations, we evaluate parameters like scalar and tensor power spectra as well as scalar and tensor spectral indices. We also evaluate inflaton, directional Hubble parameter, slow-roll and perturbation parameters as well as tensor-scalar ratio as a function of inflaton during intermediate and logamediate inflationary eras. It is concluded that anisotropic inflationary universe model with non-Abelian gauge fields remains compatible with WMAP7. 相似文献
7.
Solutions of the equations of the bimetric scalar—tensor theory of gravitation with a variable scalar field are found for
configurations of superdense matter with different versions of the equation of state. The possible existence of static superdense
and supermassive configurations is established for all of the versions of the equation of state of superdense matter used.
Translated from Astrofizika, Vol. 41, No. 1, pp. 131–135, January-March, 1998. 相似文献
8.
The instability of two non-relativistic non-parallel electron-proton plasma shells in quantum plasma is investigated when the perturbation wave propagates perpendicular to the direction of one of the shells. It is assumed that the ions are not affected by the perturbation. The full three-dimensional dispersion tensor is derived by the fluid-Maxwell equations and the dispersion equation has been solved numerically. It is shown that two kinds of instability, the two-stream instability and the filamentation instability, may occur in the system. The effects of the angle between two plasma shells on the growth rate of instabilities and the cut-off wave number have been illustrated. 相似文献
9.
Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker–Planck equation (FPE) is defined on a relatively high dimensional (6-D) state–space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the \(x-y-z\) subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors’ knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral (“super-fast”) convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations. 相似文献
10.
This paper discusses the development of two-stream instability in a collisionless plasma. The plasma is described by velocity moments of Vlasov equation where heat flow tensor has been neglected. A dispersion relation for arbitrary propagation is derived for a collisionless electron fluid. Special cases of propagation parallel and perpendicular to the field lines are discussed. Growth rate is computed for parameters representative of the shear layers of solar wind at one AU. It is found that the shear layers are likely to be overstable. 相似文献
11.
Unrestricted second-order tensor virial equations for linear oscillations of magnetic configurations
M. Goossens 《Astrophysics and Space Science》1979,60(2):401-421
This paper deals with the second-order tensor virial equations for the linear oscillations of a gaseous mass in the presence of a magnetic field. It is shown that the commonly used linearized versions of the tensor virial equations are restricted integral equations that incorporate the linearized equation of motion but not the boundary condition. These restricted equations only allow trial functions that fulfil the boundary condition and are of limited practical value.The unrestricted variational principle for the linear oscillations of a magnetic configuration is used to derive a more general formulation of the second-order tensor virial equations so that the linear trial function i =X
ij
x
j can be used to study the oscillations of a configuration with a magnetic field that extends in the exterior vacuum. The unrestricted virial equations have been applied to Ferraro's model and approximate results for the eigenfrequencies and eigenfunctions have been obtained for nine oscillation modes. 相似文献
12.
E. Evangelidis 《Astrophysics and Space Science》1978,56(1):255-269
The behavioyr of a force-free field has been studied in a Reissner-Nordström metric. An expansion in tensor harmonics of even-odd parity reduced the radial equations in a differential equation of the Sturm-Liouville system which was solved asymptotically in a conveniently defined space coordinate. Further, it has been possible to regularize the singular behaviour of the Reissner-Nordström metric at the event horizon and the modified metric to be given explicitly. 相似文献
13.
S. K. Tripathy S. K. Nayak S. K. Sahu T. R. Routray 《Astrophysics and Space Science》2008,318(1-2):125-131
LRS Bianchi type-I string cosmological models are studied in the frame work of general relativity when the source for the energy momentum tensor is a bulk viscous fluid containing one dimensional strings embedded in electromagnetic field. A barotropic equation of state for the pressure and density is assumed to get determinate solutions of the field equations. The bulk viscosity is assumed to be inversely proportional to the scalar expansion. The physical and kinematical properties of the models are discussed. The effect of viscosity and electromagnetic field on the physical and kinematical properties is also investigated. 相似文献
14.
Sunil Kumar Tripathy Dipanjali Behera Tushar Ranjan Routray 《Astrophysics and Space Science》2010,325(1):93-97
Spatially homogeneous and anisotropic LRS Bianchi type-I string cosmological models are studied in the frame work of general
relativity when the source for the energy momentum tensor is a bulk viscous fluid containing one dimensional strings. A barotropic
equation of state for the pressure and density is assumed to get determinate solutions of the field equations. The bulk viscous
pressure is assumed to be proportional to the energy density. The physical and kinematical properties of the models are discussed.
The role of bulk viscosity in getting an inflationary phase in the universe is studied. 相似文献
15.
Farook Rahaman 《Astrophysics and Space Science》2002,282(4):625-633
Thick domain walls with time dependent displacement vector based on Lyra's geometry are considered. Their exact solutions are obtained in the background of a five-dimensional space time. The field theoretic energy-momentum tensor is considered assuming with $$T_t^t = T_x^x = T_y^y = T_\psi ^\psi .$$ Acceleration due to the domain wall has been evaluated by studyinggeodesic equation. 相似文献
16.
In our preceding paper we found solutions for the equations of the bimetric scalar—tensor theory of gravitation for neutron
stars, in which the scalar field is constant while the metric tensor satisfies the equations of the general theory of relativity.
In the present paper we find analogous solutions for different versions of the equation of state of the matter of a neutron
star.
Translated from Astrofizika, Vol. 41, No. 2, pp. 297–301. April-June, 1998. 相似文献
17.
Cosmological solutions that obey the perfect fluid equation of state in Wesson's gravitational theory are presented assuming that the fifth dimension subspace is also homogeneous and isotropic like the usual homogeneous isotropic cosmological model. It is shown that the scale factor scales as
for the vanishing fifth component of the energy momentum tensor. The role of the fifth component as a cosmological constant is remarked, and an inflationary model is thus obtained. 相似文献
18.
S. I. Grachev 《Astrophysics》2001,44(3):369-381
General equations of the Wiener-Hopf type for a matrix source function with nonsymmetrical kernel matrices are considered in the form of continuous superpositions of exponentials. Certain problems in the transfer of polarized radiation reduce to equations of this kind. In general there are two different H-matrices in the theory (which are a generalization of the Ambartsumian-Chandrasekhar scalar H-function), generated by an initial equation of the Wiener-Hopf type and its analog, but with the kernel matrix and the unknown matrix of the source function being transposed. In addition there are two corresponding I-matrices, actually consisting of Laplace transforms of the matrix source functions, through which the Stokes vector of the escaping radiation is directly determined. In the problem of diffuse reflection from a half-space, the I-matrices are expressed in terms of a product of these two H-matrices, and for the latter there is a system of nonlinear equations which is a generalization of the corresponding Ambartsumian-Chandrasekhar scalar equation. In the problem of the emission of partially polarized radiation from a half-space containing uniformly distributed internal sources we have obtained a system of two nonlinear equations for the I-matrices directly. In the special case of a symmetrical kernel matrix, this system of two equations reduces to one equation. It is shown that in the case of resonance scattering in a weak magnetic field (the Hanle effect) in the approximation of complete frequency redistribution, the system of two nonlinear equations for the I-matrices (of dimension 6×6) also reduces to one nonlinear equation, although the kernel matrix for the main integral equation for the matrix source function () is not symmetrical. For this case we have found a matrix generalization of the so-called
law, consisting of an equation of the type (0)Â
T
(0) =
(where T denotes transposition) at the boundary of a half-space containing uniformly distributed primary sources of partially polarized radiation. 相似文献
19.
Margarita Petkova Volker Springel 《Monthly notices of the Royal Astronomical Society》2009,396(3):1383-1403
We present a novel numerical implementation of radiative transfer in the cosmological smoothed particle hydrodynamics (SPH) simulation code gadget . It is based on a fast, robust and photon-conserving integration scheme where the radiation transport problem is approximated in terms of moments of the transfer equation and by using a variable Eddington tensor as a closure relation, following the Optically Thin Variable Eddington Tensor suggestion of Gnedin & Abel. We derive a suitable anisotropic diffusion operator for use in the SPH discretization of the local photon transport, and we combine this with an implicit solver that guarantees robustness and photon conservation. This entails a matrix inversion problem of a huge, sparsely populated matrix that is distributed in memory in our parallel code. We solve this task iteratively with a conjugate gradient scheme. Finally, to model photon sink processes we consider ionization and recombination processes of hydrogen, which is represented with a chemical network that is evolved with an implicit time integration scheme. We present several tests of our implementation, including single and multiple sources in static uniform density fields with and without temperature evolution, shadowing by a dense clump and multiple sources in a static cosmological density field. All tests agree quite well with analytical computations or with predictions from other radiative transfer codes, except for shadowing. However, unlike most other radiative transfer codes presently in use for studying re-ionization, our new method can be used on-the-fly during dynamical cosmological simulation, allowing simultaneous treatments of galaxy formation and the re-ionization process of the Universe. 相似文献
20.
Sunil K. Tripathy Subodha K. Nayak Subrat K. Sahu Tushar R. Routray 《Astrophysics and Space Science》2009,323(3):281-287
Spatially homogeneous and anisotropic LRSBianchi type-I string cosmological models are studied in the frame work of general relativity when the source for the energy momentum tensor is a bulk viscous fluid containing one dimensional strings embedded in a magnetic field. A barotropic equation of state for the pressure and density is assumed to get determinate solutions of the field equations. The bulk viscous pressure is assumed to be proportional to the energy density. The effects of viscosity and electromagnetic field on the properties of the model are investigated. The role of bulk viscosity and electromagnetic field in getting an inflationary phase and in establishing a string phase in the universe is studied. 相似文献