共查询到20条相似文献，搜索用时 15 毫秒
1.
Lei Chen Shengmiao Wu Feng Yuan 《Monthly notices of the Royal Astronomical Society》2009,398(4):1900-1904
We consider a thin accretion disc warped due to the Bardeen–Petterson effect, presenting both analytical and numerical solutions for the situation in which the two viscosity coefficients vary with radius as a power law, with the two power-law indices not necessarily equal. The analytical solutions are compared with numerical ones, showing that our new analytical solution is more accurate than the previous one, which overestimated the inclination change in the outer disc. Our new analytical solution is appropriate for moderately warped discs, while for extremely misaligned discs only a numerical solution is appropriate. 相似文献
2.
Robert A. Van Gorder 《Celestial Mechanics and Dynamical Astronomy》2011,109(2):137-145
We apply the δ-expansion method to a transformed Lane–Emden equation. The results are then transformed back, and we recover analytical solutions
to the Lane–Emden equation of the second kind (which describes Bonnor–Ebert gas spheres) in a special case. The rapid convergence
of the method results in qualitatively accurate solutions in relatively few iterations, as we see when we compare the obtained
analytical solutions to numerical results. 相似文献
3.
Marianne Greff-Lefftz Laurent Métivier Hilaire Legros 《Celestial Mechanics and Dynamical Astronomy》2005,93(1-4):113-146
Tidal forces acting on the Earth cause deformations and mass redistribution inside the planet involving surface motions and
variation in the gravity field, which may be observed in geodetic experiments. Because for space geodesy it is now necessary
to achieve the mm level in tidal displacements, we take into account the hydrostatic flattening of the Earth in the computation
of the elasto-gravitational deformations. Analytical solutions are derived for the semi-diurnal tides on a slightly elliptical
homogeneous incompressible elastic model. That simple analytical Earth’s model is not a realistic representation of any real
planet, but it is useful to understand the physics of the problem and also to check numerical procedures. We rediscover and
discuss the Love’s solutions and obtain new analytical solutions for the tangential displacement. We extend these analytical
results to some geodetic responses of the Earth to tidal forces such as the perturbation of the surface gravity field, the
tilt and the deviation of the vertical with reference to the Earth’s axis. 相似文献
4.
We consider two classical celestial-mechanical systems: the planar restricted circular three-body problem and its simplification, the Hill’s problem. Numerical and analytical analyses of the covering of a Hill’s region by solutions starting with zero velocity at its boundary are presented. We show that, in all considered cases, there always exists an area inside a Hill’s region that is uncovered by the solutions. 相似文献
5.
Based on the fundamental P – ω dynamo equation, using spherical polar coordinates, we carry out a study of turbulent plasma wave dynamo effect. For
various rotation laws, different analytical solutions are derived. In the cases of no rotation and rigid rotation, the dynamo
generates poloidal field only, while with differential rotation, regardless the differential rotation is radial or latitudinal,
poloidal and toroidal fields are all generated. We may think that the solutions are the analytical forms of the magnetic field
in a turbulent source region of celestial bodies.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
Robert A. Van Gorder 《New Astronomy》2011,16(2):65-67
Perturbation solutions are obtained for the Lane–Emden equation of the second kind which describe Bonnor–Ebert gas spheres. In particular, we employ the field-theoretic perturbative procedure due to Bender et al. to obtain analytical solutions to the nonlinear initial value problem. We find that the method allows one to construct perturbation solutions which converge rapidly to the true solutions in many cases, as it allows one to more accurately represent the influence of nonlinear terms in the linearized equations. The rapid convergence of the method results in qualitatively accurate solutions in relatively few iterations. 相似文献
7.
We apply the Boubaker Polynomials Expansion Scheme (BPES) in order to obtain analytical–numerical solutions to two separate Lane–Emden problems: the Lane–Emden initial value problem of the first kind (describing the gravitational potential of a self-gravitating spherically symmetric polytropic gas), the Lane–Emden initial value problem of the second kind (describing isothermal gas spheres embedded in a pressurized medium at the maximum possible mass allowing for hydrostatic equilibrium). Both types of problems are simultaneously singular and nonlinear, and hence can be challenging to solve either numerically or analytically. We find that the BPES allows us to compute numerical solutions to both types of problems, and an error analysis demonstrates the accuracy of the method. In all cases, we demonstrate that relative error can be controlled to less than 1%. Furthermore, we compare our results to those of Hunter (2001). [Hunter, C., 2001. Series solutions for polytropes and the isothermal sphere. Monthly Notices of the Royal Astronomical Society, 328 839–847] and Mirza (2009). Approximate analytical solutions of the Lane–Emden equation for a self-gravitating isothermal gas sphere. Monthly Notices of the Royal Astronomical Society, 395 2288–2291. in order to demonstrate the accuracy of our method. 相似文献
8.
J. Gracia N. Vlahakis K. Tsinganos 《Monthly notices of the Royal Astronomical Society》2006,367(1):201-210
We perform a numerical simulation of magnetohydrodynamics (MHD) radially self-similar jets, whose prototype is the Blandford & Payne analytical example. The final steady state that is reached is valid close to the rotation axis and also at large distances above the disc where the classical analytical model fails to provide physically acceptable solutions. The outflow starts with a subslow magnetosonic speed, which subsequently crosses all relevant MHD critical points and corresponding magnetosonic separatrix surfaces. The characteristics are plotted together with the Mach cones and the superfast magnetosonic outflow satisfies MHD causality. The final solution remains close enough to the analytical one, which is thus shown to be topologically stable and robust for various boundary conditions. 相似文献
9.
M. A. Vashkov’yak 《Astronomy Letters》2006,32(10):707-715
Based on the ideas of Lyapunov’s method, we construct a family of symmetric periodic solutions of the Hill problem averaged over the motion of a zero-mass point (a satellite). The low eccentricity of the satellite orbit and the sine of its inclination to the plane of motion of the perturbing body are parameters of the family. We compare the analytical solution with numerical solutions of the averaged evolutionary system and the rigorous (nonaveraged) equations of the restricted circular three-body problem. 相似文献
10.
Yu-Qing LouNational Astronomical Observatories Chinese Academy of Sciences Beijing Department of Physics & Tsinghua Center for Astrophysics 《中国天文和天体物理学报》2005,5(1):6-20
We develop a theoretical formulation for the large-scale dynamics of galaxy clusters involving two spherical ‘isothermal fluids‘ coupled by their mutual gravity and derive asymptotic similarity solutions analytically. One of the fluids roughly approximates the massive dark matter halo, while the other describes the hot gas, the relatively small mass contribution from the galaxies being subsumed in the gas. By properly choosing the self-similar variables, it is possible to consistently transform the set of time-dependent two-fluid equations of spherical symmetry with serf-gravity into a set of coupled nonlinear ordinary differential equations (ODEs). We focus on the analytical analysis and discuss applications of the solutions to galaxy clusters. 相似文献
11.
The significant orbital eccentricities of most giant extrasolar planets may have their origin in the gravitational dynamics of initially unstable multiple planet systems. In this work, we explore the dynamics of two close planets on inclined orbits through both analytical techniques and extensive numerical scattering experiments. We derive a criterion for two equal mass planets on circular inclined orbits to achieve Hill stability, and conclude that significant radial migration and eccentricity pumping of both planets occurs predominantly by 2:1 and 5:3 mean motion resonant interactions. Using Laplace-Lagrange secular theory, we obtain analytical secular solutions for the orbital inclinations and longitudes of ascending nodes, and use those solutions to distinguish between the secular and resonant dynamics which arise in numerical simulations. We also illustrate how encounter maps, typically used to trace the motion of massless particles, may be modified to reproduce the gross instability seen by the numerical integrations. Such a correlation suggests promising future use of such maps to model the dynamics of more coplanar massive planet systems. 相似文献
12.
E. Falize C. Michaut C. Cavet S. Bouquet M. Koenig B. Loupias A. Ravasio C. G. Gregory 《Astrophysics and Space Science》2009,322(1-4):71-75
In this paper we study specific classes of radiating shocks which are widely spread in astrophysical environments. We present new analytical solutions available for any exponents of typical power-law cooling function which generalize the five special cases (corresponding to specific values of these exponents) of radiating shocks structure and proceed to the analytical determination of physical quantities. Then an application of the results for the accretion shock in polar is realized. A discussion of the reproducibility of cooling layer in laboratory is proposed using scaling laws. 相似文献
13.
We provide a 2.5-dimensional solution to a complete set of viscous hydrodynamical equations describing accretion-induced outflows and plausible jets around black holes/compact objects. We prescribe a self-consistent advective disk-outflow coupling model, which explicitly includes the information of vertical flux. Inter-connecting dynamics of an inflow-outflow system essentially upholds the conservation laws. We provide a set of analytical family of solutions through a self-similar approach. The flow parameters of the disk-outflow system depend strongly on the viscosity parameter α and the cooling factor f. 相似文献
14.
Specialized to the Lie series based perturbation method of Kirchgraber and Stiefel (1978) a new computer algebra package called
ANALYTOS has been developed for constructing analytical orbital theories either in noncanonical or canonical form. We present
results on the (extended) Main Problem of orbital theory of artificial earth satellites and related issues. The order of the
solutions achieved is generally one order higher than those known from literature. Moreover, the analytical orbits have been
checked succesfully against precise numerical ephemerides.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
15.
K. Tsinganos N. Vlahakis S.V. Bogovalov C. Sauty E. Trussoni 《Astrophysics and Space Science》2004,293(1-2):55-66
A brief review is given of some results of our work on the construction of (I) steady and (II) time-dependent MHD models for nonrelativistic and relativistic astrophysical outflows and jets, analytically and numerically. The only available exact solutions for MHD outflows are those in separable coordinates, i.e., with the symmetry of radial or meridional self-similarity. Physically accepted solutions pass from the fast magnetosonic separatrix surface in order to satisfy MHD causality. An energetic criterion is outlined for selecting radially expanding winds from cylindrically expanding jets. Numerical simulations of magnetic self-collimation verify the conclusions of analytical steady solutions. We also propose a two-component model consisting of a wind outflow from a central object and a faster rotating outflow launched from a surrounding accretion disk which plays the role of the flow collimator. We also discuss the problem of shock formation during the magnetic collimation of wind-type outflows into jets. 相似文献
16.
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
17.
Three methods are proposed in this paper to lessen the complexity in the derivation and the resulting expressions of second-order analytical solutions of artificial satellite orbits while retaining the advantages of analytical solutions. Of the three, the one combining the theories of elliptical perturbation and of intermediate orbits is noteworthy for its simplicity. It can also be used with advantage in first-order and third- or higher order solutions. 相似文献
18.
We investigate the characteristics of magneto-acoustic surface waves propagating at a single density interface, in the presence of an inclined magnetic field. For linear wave propagation, the dispersion relation is obtained and analytical solutions are derived for small inclination angle. The inclination of the field renders the frequency of the waves complex, where the imaginary part describes wave attenuation, due to lateral energy leakage. 相似文献
19.
Gabriel Mititelu 《Celestial Mechanics and Dynamical Astronomy》2009,103(4):327-342
A practical and important problem encountered during the atmospheric re-entry phase is to determine analytical solutions for
the space vehicle dynamical equations of motion. The author proposes new solutions for the equations of trajectory and flight-path
angle of the space vehicle during the re-entry phase in Earth’s atmosphere. Explicit analytical solutions for the aerodynamic
equations of motion can be effectively applied to investigate and control the rocket flight characteristics. Setting the initial
conditions for the speed, re-entering flight-path angle, altitude, atmosphere density, lift and drag coefficients, the nonlinear
differential equations of motion are linearized by a proper choice of the re-entry range angles. After integration, the solutions
are expressed with the Exponential Integral, and Generalized Exponential Integral functions. Theoretical frameworks for proposed
solutions as well as, several numerical examples, are presented. 相似文献
20.
火星非球形引力位田谐项联合摄动分析解 总被引：2，自引：0，他引：2
火星非球形引力场模型与地球有明显差别,其非球形引力位中的田谐项系数基本都要比地球的相应值大一个量级,尤其是J2,2项（赤道椭率项）的大小接近它的动力学扁率项J2.对于低轨探测器,若要使轨道外推1 d弧段的精度达到500 m(相当于标准单位10-4量级),在构造环火探测器的轨道分析解时,田谐项与J2项以及田谐项与田谐项之间的联合摄动不容忽视.根据摄动量级分析和构造的摄动分析解证实,上述联合摄动对轨道沿迹方向的影响可超过10-4,并给出了数值验证.结果表明,与地球低轨卫星不同,在类似的问题中,构造环火卫星摄动分析解时,必须考虑这些联合摄动项的影响. 相似文献