共查询到20条相似文献，搜索用时 31 毫秒
1.
Summary The integral mean values of gravity on the surface W=W
0
, obtained from satellite observations with the use of harmonic coefficients[3, 7] and from terrestrial gravity measurements[12], are compared. The squares and products of the harmonic coefficients were neglected, with the exception of [J
2
(0)
]
2
, which was taken into account. The Potsdam correction and the geocentric constant are being discussed. The paper ties up with[13–15] and the symbols used are the same. The given problem was treated, e.g., in[2, 4, 6, 8–10]; in the present paper the values of gravity are compared directly. 相似文献
2.
Summary The parameters of the normal gravity field were deduced from the harmonic coefficients[3, 4] upto n=6 and compared with the parameters used hitherto. The symbols used are the same as in papers[5, 6, 8] with which this paper connects up. 相似文献
3.
Summary The evolution of the opinions as to the problem of the triaxiality of the Earth in the period prior to satellite geodesy can be seen, e.g., in[1–18]. Recently the opinion has been voiced that triaxiality is a result of the mathematical treatment of data rather than reality[19–21], especially since this is a comparatively small parameter. This opinion is not in contradiction with the results of satellite observations[22–28], but the non-zero values of the harmonic coefficients of the second degree and second order are a reality, they yield a value of the equatorial flattening of about1/90 000, and the representation of the equatorial section by an ellipse is justified even if the harmonics n=3, k=1 and n=3, k=3 have amplitudes only about half as small, and some other parameters might occur with just as much justification besides triaxiality. 相似文献
4.
Summary The paper presents the solution of the equation of heat conduction with density of heat sources given generally. For two special cases the computed central temperature excesses of model[5] are compared with the results of some authors[1, 6] who deal with convection in the surface layer. 相似文献
5.
Summary The general solution of the direct gravimetric problem for homogeneous and inhomogeneous bodies was derived in[1] in the form of Green-type integrals. In the present paper it is proved that this solution simplifies considerably, if the solution of the external Dirichlet problem, defined by conditions(2), is known for a closed surface bounding the attracting body.Dedicated to RNDr Jan Pícha, CSc., on his 60th Birthday 相似文献
6.
Summary This paper is a continuation of[1]. It is mainly devoted to problems connected with the application of the method of determination of geometrical spreading in laterally inhomogeneous media with curved interfaces based on the solution of eight (in a three-dimensional medium) or two (in a two-dimensional medium) linear ordinary differential equations of the first order. The method of determination of the partial derivatives of velocity with respect to the special coordinates, connected with the ray under investigation, and the methods of determination of the initial values for the system of differential equations at the source and at the interfaces are proposed. 相似文献
7.
Summary The procedure for computation and the numerical results of the first testing of the so-called Mi-operation, which is a construction unit of the model of a convective cloud[1] and represents the formulation of microphysical phenomena occurring in a convective cloud, are described. In this paper the Mi-operation is applied to the case of the liquid stage, restricted to condensation and drop evaporation. The solution of the corresponding system of kinetic equations serves the purpose of an initial test of the applicability of the integration method to the type of equations mentioned. 相似文献
8.
Summary Stokes' constants and, the selenocentric constant, and the angular velocity of the rotation of the Moon define the shape of the external equiselenopotential surfaces, generalized in dependence on the degree N of the harmonics preserved. The scale factor for lengths was computed on the basis of absolute gravity measurement made by the first lunarlanding mission Apollo11 at the landing site[1] under the assumption of a sufficient accuracy of the Stokes' constants used[2, 15]. Anyway, the numerical solution here is only to be considered as an example of the application of the outlined theoretical method, inclusive of the parameters of the lunar reference system, which will be made considerably more accurate when gravity measurements at more points of the lunar surface are available.Presented at the XVth IUGG General Assembly, Moscow, July 30 – August 14, 1971. 相似文献
9.
Summary Using the data in[1], the scale factor for lengths is derived of the geopotential model R
0
=GM/W
0
(W
0
is the potential on a generalized geoid). The resulting value, R
0
==6 363 672.9 m, which is2 m less than the original value[5], is practically the same as that in[6]. 相似文献
10.
Abstract The singular differential equations for finite temperature relativistic magnetohydrodynamic (MHD) winds integrate to two algebraic equations when the source magnetic field is a monopole. This simplification enables an extensive characterization of the asymptotic wind solutions in terms of source parameters. We will consider only the critical solutions-those that pass smoothly through both an intermediate (Alfvenic) and a fast MHD critical point and expand to zero pressure at infinite radial distance from the source. Because the constants of motion must be specified to extremely high accuracy, the critical solutions cannot be found analytically. Synopsis of many numerical solutions reveals a uniform parametric characterization of the asymptotic wind in terms of one combination of source parameters, Z, the mean source particle energy divided by mc2[sgrave]½, where [sgrave] is a generalization of Michel's (1969) cold relativistic wind strength parameter. Cool winds, with Z<1, behave asymptotically much as Michel's cold wind minimum torque solution; Z1 hot winds have quite different, but simply characterized, asymptotic solutions. Thus, the strength of magnetized relativistic outflows can depend critically upon the temperature of the source. 相似文献
11.
Summary Procedures of astrodynamics are used to calculate the actual values of the secular variation of the inclination and eccentricity of the Moon's orbit due to ocean tides. The ocean tide data were taken from the resolution of the ocean tide potential into spherical functions[2] based on cotidal maps[1]. 相似文献
12.
R. W. James 《Pure and Applied Geophysics》1967,68(1):83-89
Summary General recurrence relations between the coefficients in thenth and (n+1)th order spherical harmonic multipole expansions are derived. The particular application presented here is the derivation of the equations concerned with representing the geomagnetic field by magnetic multipoles. The equations up to the 3rd order multipole are given as an example of the method. The main advantage in using these recurrence relations rather than other methods is that the mathematics is reduced to merely a matter of successive substitutions and this allows a fast step by step generation of the required equations, in a form for which there is a simple numerical program for solution. 相似文献
13.
Summary In the present paper the adjustment of the Hradilek's spatial network[3] was carried out in space using the least-squares method according to conditional observations. Triangle, side and base equations of condition are given (see also[1]). In the first method of adjustment (Alternative A) the corrections are assigned to oblique (position) angles and the lengths of sides. In the second method of adjustment (Alternative B) the corrections are assigned to horizontal directions, zenith distances and lengths of sides. The refraction coefficients in both alternatives are introduced as unknown parameters. Neither method of adjustment depends on the directions of the verticals. Theoretically, Alternative B is more correct. However, for practical purposes the results yielded by Alternative A are little better than those yielded by Alternative B. As regards the economical aspect Alternative A is considerably more convenient. Both methods seem suitable for computing the rectangular spatial co-ordinates, less so for determining the refraction coefficients. 相似文献
14.
A. D. Sneyd 《地球物理与天体物理流体动力学》2013,107(1-3):141-151
Abstract Formation of electric current sheets in the corona is thought to play an important role in solar flares, prominences and coronal heating. It is therefore of great interest to identify magnetic field geometries whose evolution leads to variations in B over small length-scales. This paper considers a uniform field B 0[zcirc], line-tied to rigid plates z = ±l, which are then subject to in-plane displacements modeling the effect of photospheric motion. The force-free field equations are formulated in terms of field-line displacements, and when the imposed plate motion is a linear function of position, these reduce to a 4 × 4 system of nonlinear, second-order ordinary differential equations. Simple analytic solutions are derived for the cases of plate rotation and shear, which both tend to form singularities in certain parameter limits. In the case of plate shear there are two solution branches—a simple example of non-uniqueness. 相似文献
15.
Antonín Zeman 《Studia Geophysica et Geodaetica》1991,35(2):75-80
Summary The problem of the constant part of the tidal field is still topical in view of the recommendations of IAG[1, 2] to eliminate the tidal effect of external masses from all geodetic measurements under preservation of the effect of the time-constant tidal deformation of the Earth. The paper discusses the consequences of accepting this recommendation for normal heights, and suggests a solution based on the new definition of the normal gravity field[3]. 相似文献
16.
This paper analytically examines the horizontal vibration of a rigid disk on a saturated poroelastic half-space. The pressure-solid displacement form of the harmonic equations of motion for asymmetric dynamic problem are developed from the form of the equations originally presented by Biot. Making use of a new method the solution of the above equations is obtained. According to the mixed boundary -value conditions, the dual integral equations of the horizontal vibration of a rigid disk on a saturated poroelastic half-space are established. By appropriate transforms, it is shown that the dual integral equations can be reduced to a pair of Fredholm integral equations of the second kind, whose solutions are then computed. Numerical results for the horizontal dynamic compliance coefficient are given at the end of this paper. 相似文献
17.
Summary In 1967, a series of observations were carried out at Lomnický tít of the intensity of light of the clear sky. Using the de Bary method[1], the observations were used to determine the function of simple dispersion on turbind particles in the atmosphere and compared with theoretical functions, which hold for Jung's power distribution of the particles according to size[7] and for the logarithmic Gauss distribution of the particles[8]. 相似文献
18.
A Bremmer Series decomposition of the solution y(t) to the lossless wave equation in layered media is where the yj(t) are physically meaningful constituents (i.e., y1(t) are primaries, y2(t) are secondaries, etc.). This paper reviews Mendel's state space models for generating the constituents; reviews Bremmer's integral equation models for generating the constituents; and demonstrates how Mendel's state space models can be obtained by a careful decomposition of Bremmer's integral equation models. It shows that Mendel's equations can be viewed as approximate numerical solutions of Bremmer's integral equations. In a lossless homogeneous medium, the approximations become exact. 相似文献
19.
Spherical harmonic coefficients (SHCs) for the daily magnetic variation fields (solar and lunar) and the main field of the earth are usually estimated by the method of least squares applied to a truncated spherical harmonic series. In this paper, an integral method for computing the SHCs for the solar quiet daily magnetic variation fieldSq is described and applied toSq data for May and June 1965. TheSq SHCs thus derived are then compared with the results obtained using both unweighted and weighted versions of the least squares method. The weighting used tends to orthogonalize the least squares terms. The integral and weighted least squares results agree closely for terms up to order 4 and degree 30, but both disagree considerably for the higher degree terms with the results of the unweighted least squares. Errors introduced by the numerical integration can be shown to be small, hence the disagreement between integral and unweighted least squares coefficient sets arises from improper weighting. Also, it is concluded that discrepancies between the geomagnetic northward and eastward component-derived coefficient sets arise from either time-dependent external sources that produce non-local-time, based fields or nonpotential sources and not from truncation of the spherical harmonic series as has previously been suggested.Deceased. 相似文献
20.
A. C. LIAKOPOULOS Dr. Eng. 《水文科学杂志》2013,58(1):69-110
ABSTRACT The one-dimensional transient downward entry of water in unsaturated soils is investigated theoretically. The mathematical equation describing the infiltration process is derived by combining Darcy's dynamic equation of motion with the continuity and thermodynamic state equations adjusted for the unsaturated flow conditions. The resulting equation together with the corresponding initial and boundary conditions constitues a mathematical initial boundary value problem requiring the solution of a nonlinear partial differential equation of the parabolic type. The volumetric water content is taken as the dependent variable and the time and the position along the vertical direction are taken as the independent variables. The governing equation is of such nature that a solution exists for t > 0 and is uniquely determined if two relationships are defined, together with the specified state of the system, at the initial time t = 0 and at the two boundaries. The two required relations are those of pressure versus permeability and pressure versus volumetric water content. Since the partial differential equation has strong non-linear terms, a discrete solution is obtained by approximating the derivatives with finite-differences at discrete mesh points in the solution domain and integrated for the corresponding initial and boundary conditions. The use of an implicit difference scheme is employed in order to generate a system of simultaneous non-linear equations that has to be solved for each time increment. For n mesh points the two boundary conditions provide two equations and the repetition of the recurrence formula provides n—2 equations, the total being n equations for each time increment. The solution of the system is obtained by matrix inversion and particularly with a back-substitution technique. The FORTRAN statements used for obtaining the solution with an electronic digital computer (IBM 704) are presented together with the input data. Analysis of the errors involved in the numerical solution is made and the stability and convergence of the solution of the approximate difference equation to that of the differential equation is investigated. The method applied is that of making a Fourier series expansion of a whole line of errors and then following the progress of the general term of the series expansion and also the behavior of each constituent harmonic. The errors (forming a continuous function of points in an abstract Banach space) are represented by vectors with the Fourier coefficients constituting a second Banach space. The amplification factor of the difference equation is shown to be always less than unity which guarantees the stability of the employed implicit recurrence scheme. Experiments conducted on a vertical column packed uniformly with very fine sand, show a satisfactory agreement between the theoretically and experimentally obtained values. Many experimental results are shown in an attempt to explain the infiltration phenomenon with emphasis on the shape and movement of the wet front, and the effects of the degree of compaction, initial water content and deaired water on the infiltration rate. 相似文献