共查询到20条相似文献，搜索用时 21 毫秒
1.
O. Kaburaki 《Astrophysics and Space Science》1985,112(1):157-174
A theoretical scheme is developed to deal with the problems of stellar winds in three-dimensional situations, and relativistic fluid equations are integrated formally under isentropic and quasi-stationary conditions, in a flat space-time.The relativistic Euler equation for a one-component plasma is expressed in the same form as the ideal-MHD condition for the effective electromagnetic field which combines the inertial and pressure terms with the true electromagnetic field. This equation and that of mass continuity are integrated formally by introducing Euler-type potentials for the effective magnetic field and for the mass flux in the rotating frame, respectively. Functional form of one of these Euler potentials, which represents the total energy per unit charge in the rotating frame, is specified as an integral of motion. For an electron-proton plasma, the integrals for both components are combined to yield the energy integral of the plasma as a whole and the integrated Ohm's law, in the limit of vanishing mass ratio of an electron to a proton.Maxwell's equations are divided in two parts: i.e., the co-rotational and non-corotational parts. It is shown that the electromagnetic potentials for these parts are derived from a scalar super-potential and a vector super-potential, respectively. 相似文献
2.
We present a three-dimensional technique for the solution of the magnetohydrostatic equations when we are modeling structures
bounded by a current sheet that is free to move to satisfy pressure balance. The magnetic field is expressed in terms of Euler
potentials and the equations are transformed to flux coordinates, greatly simplifying the problem of locating the free boundary.
Multi-grid techniques are used to rapidly solve the resulting nonlinear elliptic partial differential equations. The method
is tested against Low's (1982) exact solution of a bipolar plasma loop. It is shown that fast, accurate solutions can be found. 相似文献
3.
Quaternions and the rotation of a rigid body 总被引：1，自引：0，他引：1
The orientation of an arbitrary rigid body is specified in terms of a quaternion based upon a set of four Euler parameters. A corresponding set of four generalized angular momentum variables is derived (another quaternion) and then used to replace the usual three-component angular velocity vector to specify the rate by which the orientation of the body with respect to an inertial frame changes. The use of these two quaternions, coordinates and conjugate moments, naturally leads to a formulation of rigid-body rotational dynamics in terms of a system of eight coupled first-order differential equations involving the four Euler parameters and the four conjugate momenta. The equations are formally simple, easy to handle and free of singularities. Furthermore, integration is fast, since only arithmetic operations are involved. 相似文献
4.
5.
The effect of an electric field induced by a rapidly decaying ring current on the motion of charged particles in the magnetosphere has been investigated using Euler potentials. For a model consisting of the earth dipole and the symmetric ring current, the electric field satisfies the condition E . B = 0. where and β are Euler potentials.
Under this circumstance, the E × B drift of the particle can be identified as the motion of the magnetic field lines and vice versa. The time dependent electric field induced can be evaluated in a Spherical polar coordinate system by the formula
A model calculation on the particle drift velocity vD = E × B/B2 shows that the radial component of the drift velocity is in good agreement with those deduced from whistler duct studies. 相似文献
6.
Andrzej J. Maciejewski 《Celestial Mechanics and Dynamical Astronomy》1985,37(1):47-57
The Euler-Poinsot equations of rigid body motion are considered. The Euler parameters attitude parametrization is assumed. The Hamiltonian form of these equations is obtained. Two different solutions are shown. A short discussion of free motion in this new treatment is also given. 相似文献
7.
N. Borderies 《Celestial Mechanics and Dynamical Astronomy》1978,18(3):295-307
The mutual gravitational potential ofN solid bodies is expanded without approximation in terms of harmonic coefficients of each body. As an application the Euler dynamical equations for the motion of the axis of figure of the rigid Earth are integrated analytically by the method of variation of parameters. 相似文献
8.
This paper is devoted to the numerical approximation of the discontinuous solutions of the Euler equations for weakly ionized
mixtures of reacting gases. The main difficulty stems from the non conservative formulation of these equations due to a widely
used physical assumption. We show how to derive a well-posed conservative reformulation of the equations from the analysis
of the associated full convective-diffusive system. We then propose an exact Roe-type linearization for the equivalent system
of conservation laws on the basis of an original Lemma for averagings. Our results can be seen as an extension of the classical
Roe average, for nonlinearities that cannot be recast under quadratic form.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
In celestial mechanics the kinematic equation connecting the time and position in orbit is important. This equation is investigated in detail, but the case of nearly-parabolic motion remains little studied. The universal equations were derived by Euler, but he did not investigate then in detail. We present the solution in the form of series with respect to the small Euler parameter, with coefficients depending on time, and we solve the problem on determining the convergence domain of this series that occurs to be more complicated problem. 相似文献
10.
J. A. Docobo 《Astronomy Letters》2003,29(5):344-347
an extension of the Gylden-Meshcherskii problem when the mass depends both on time and distance between two bodies is considered. certain mass loss laws as well as the Meshcherskii position vector and time transformation are used to convert the problem into the cases with equations of motion arising from integrable potentials. 相似文献
11.
John D. Donaldson Donald J. Jezewski 《Celestial Mechanics and Dynamical Astronomy》1977,16(3):367-387
The perturbed motion of a rigid body about its center of mass, is formulated in terms of the six elements:l, the magnitude of the angular momentum vector;h, the total energy; and , two linear functions of the independent variable; and 1 and 1, two Euler angles that orientate the inertial frame with respect to the unperturbed solution. Solutions from the element formulation and the original Euler equations are numerically compared using shuttle-type data. For applied torques smaller than a given magnitude, the element formulation produced the following results: (1) larger step sizes in the numerical integration of the differential equations, resulting in an overall computational time-saving, and (2) more significant figures of accuracy in the computation of the variables describing the state of the rigid body. 相似文献
12.
13.
Mervat El-Sayed Awad 《Earth, Moon, and Planets》1995,69(1):1-12
In this paper an analytical solution for the differential equations governing the motion of Artificial Satellite under the oblateness of the earth will be developed. We start with the differential equations in terms of Euler parameters. To compact algebra, we introduce the Cayley-Klein type complex variables. Comparison between numerical and analytical final states withJ
2 will be given for a test case. 相似文献
14.
R. F. Coker B. H. Wilde J. M. Foster B. E. Blue P. A. Rosen R. J. R. Williams P. Hartigan A. Frank C. A. Back 《Astrophysics and Space Science》2007,307(1-3):57-62
We have conducted experiments on the Omega laser at the University of Rochester that have produced jets of supersonic Ti impacting
and being deflected by a ball of high density plastic. These mm-sized jets of dense plasma are highly complex, have large
Reynolds numbers, and, given sufficient time and shear, should produce a fully turbulent flow. The experiments are diagnosed
with a point-projection backlighter, resulting in a single image per shot. Simulations of the 3D hydrodynamics capture the
large-scale features of the experimental data fairly well while missing some of the smaller scale turbulent-like phenomena.
This is to be expected given the limited characterization of the targets as well as the finite resolution of the 3D simulations.
If Euler scaling holds, these experiments should model larger astrophysical jets in objects such as HH 110 where an outflow
can be seen colliding with a molecular cloud. However, Euler scaling demands that not only the isothermal internal Mach numbers
of the two systems be similar but also that any dissipative mechanisms, such as radiative cooling or viscous dissipation,
be of equal importance relative to each other. Similar equations of state are required as well. We discuss such issues in
the context of these experiments and simulations. 相似文献
15.
The aim of this paper is to study the global geometry of non-planar 3-body motions in the realms of equivariant Differential
Geometry and Geometric Mechanics. This work was intended as an attempt at bringing together these two areas, in which geometric
methods play the major role, in the study of the 3-body problem. It is shown that the Euler equations of a three-body system
with non-planar motion introduce non-holonomic constraints into the Lagrangian formulation of mechanics. Applying the method
of undetermined Lagrange multipliers to study the dynamics of three-body motions reduced to the level of moduli space [`(M)]{\bar{M}} subject to the non-holonomic constraints yields the generalized Euler-Lagrange equations of non-planar three-body motions
in [`(M)]{\bar{M}} . As an application of the derived dynamical equations in the level of [`(M)]{\bar{M}} , we completely settle the question posed by A. Wintner in his book [The analytical foundations of Celestial Mechanics, Sections
394–396, 435 and 436. Princeton University Press (1941)] on classifying the constant inclination solutions of the three-body problem. 相似文献
16.
J. A. López Ortí A. López García R. López Machí 《Celestial Mechanics and Dynamical Astronomy》1992,53(4):311-322
The equilibrium configurations of close binary systems are analyzed. The autogravitational, centrifugal and tidal potentials are expanded in Clairaut's coordinates. From the set of the total potential angular terms an integral equations system is derived. The reduction of them to ordinary differential equations and the determination of the boundary conditions allow a formulation of the problem in terms of a single variable. 相似文献
17.
B. C. Low 《Solar physics》1980,65(1):147-165
This is a study of the relationship between a magnetic field and its embedding plasma in static equilibrium in a uniform gravity. The ideal gas law is assumed. A system invariant in a given direction is treated first. We show that an exact integral of the equation for force balance across field lines can be derived in a closed form. Using this integral, exact solutions can be generated freely by integrating directly for the distributions of pressure, density and temperature necessary to keep a given magnetic field in equilibrium. Particular solutions are presented for illustration with the solar atmosphere in mind. Extending the treatment to the general system depending on all three spatial coordinates, we arrive at the general form of a theorem of Parker that a magnetic field in static equilibrium must possess certain symmetries. We derive an equation involving the Euler potentials of the magnetic field stipulating these necessary symmetries. Only those magnetic fields satisfying this equation can be in static equilibrium and for these fields, the endowed symmetries make the construction of exact solutions an essentially two dimensional problem as exemplified by the special case of invariance in a given direction. 相似文献
18.
Martin C. Eckstein 《Celestial Mechanics and Dynamical Astronomy》1976,14(3):307-320
The mutual interaction of orbit-attitude maneuvers of spin-stablized satellites is investigated by application of theTwo Variable Expansion Procedure to the Euler equations. The resulting semi-analytical solution describes the short periodic nutation, the long-term attitude variation and the mean linear acceleration of the center of mass. Some applications of the solution are shown by means of a few examples. 相似文献
19.
We briefly describe an advanced 3D gas dynamical model developed for the simulation of theenvironment of active cometary nuclei.
The model canhandle realistic nucleus shapes and alternative physical models for the gas and dust production mechanism.The
inner gas coma structure is computed by solving self-consistently(a) near to the surface the Boltzman Equation(b) outside
of it, Euler or Navier-Stokes equations.The dust distribution is computed from multifluid ``zero-temperature' Euler equations,extrapolated
with the help of a Keplerian fountain model.The evolution of the coma during the nucleus orbital and spin motion,is computed
as a succession of quasi-steady solutions. Earlier versions of the model using simple,``paedagogic' nuclei have demonstrated
that the surface orographyand the surface inhomogeneity contribute similarly to structuring the near-nucleusgas and dust coma,casting
a shadow on the automatic attribution of such structures to ``active areas'.The model was recently applied to comet P/Halley,
for whichthe nucleus shape is available. In the companion paper of this volume,we show that most near-nucleus dust structuresobserved
during the 1986 Halley flybys are reproduced, assuming that the nucleus is strictly homogeneous. Here, we investigate the
effect of shape perturbations and homogeneityperturbations. We show that the near nucleus gas coma structure is robust vis-a-vissuch
effects. In particular, a random distribution of active and inactive areaswould not affect considerably this structure, suggesting that such areas,even if present, could not be easily identified on images
of the coma. 相似文献
20.
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