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1.
The scope of the present paper is to provide analytic solutions to the problem of the attitude evolution of a symmetric gyrostat about a fixed point in a central Newtonian force field when the potential function isV (2).We assume that the center of mass and the gyrostatic moment are on the axis of symmetry and that the initial conditions are the following: (t 0)=0, (t 0)=0, (t 0)=(t 0)=0, 1(t 0)=0, 2(t 0)=0 and 3(t 0)= 3 0 .The problem is integrated when the third component of the total angular momentum is different from zero (B 1 0). There now appear equilibrium solutions that did not exist in the caseB 1=0, which can be determined in function of the value ofl 3 r (the third component of the gyrostatic momentum).The possible types of solutions (elliptic, trigonometric, stationary) depend upon the nature of the roots of the functiong(u). The solutions for Euler angles are given in terms of functions of the timet. If we cancel the third component of the gyrostatic momentum (l 3 r =0), the obtained solutions are valid for rigid bodies.  相似文献   

2.
The exact geometry of the Roche curvilinear coordinates (, , ) in which corresponds to the zero-velocity surfaces is investigated numerically in the plane, as well as in the spatial, case for various values of the mass-ratio between the two point-masses (m 1,m 2) constituting a binary system.The geometry of zero-velocity surfaces specified by -values at the Lagrangian points are first discussed by taking their intersections with various planes parallel to thexy-, xz- andyz-planes. The intersection of the zero-velocity surface specified by the -value at the Lagrangian equilateral-triangle pointsL 4,5 with the planex=1/2 discloses two invariable curves passing through the pointsL 4,5 and situated symmetrically with respect to thexy-plane whose form is independent of the mass-ratio.The geometry of the remaining two coordinates (, ) orthogonal to the zero-velocity surfaces is investigated in thexy- andxz-planes from extensive numerical integrations of differential equations generated from the orthogonality relations among the coordinates. The curves (x, y)=constant in thexy-plane are found to be separated into three families by definite envelopes acting as boundaries whose forms depend upon the mass-ratio only: the inner -constant curves associated with the masspointm 1, the inner -constant curves associated with the mass-pointm 2 and the outer -constant curves. All the -constant curves in thexy-plane coalesce at either of the Lagrangian equilateraltriangle pointsL 4,5, except for a limiting case coincident with thex-axis. The curves (x, z)=constant in thexz-plane are also separated by definite envelopes depending upon the mass-ratio into different families: the inner -constant curves associated with the mass-pointm 1, the inner -constant curves associated with the mass-pointm 2 and the outer -constant curves on both sides out of the envelopes. For larger values ofz, the curves =constant tend asymptotically to the line perpendicular to thex-axis and passing through the centre of mass of the system, except for a limiting case coincident with thex-axis. The geometrical aspects of the envelopes for the curves (x, y)=constant in thexy-plane and the curves (x, z)=constant in thexz-plane are also discussed independently.In the three-dimensional space, the Roche coordinates can be conveniently defined in such a way as to correspond to the polar coordinates in the immediate neighbourhood of the origin, and to the cylindrical coordinates at great distances. From numerical integrations of simultaneous differential equations generating spatial curves orthogonal to the zero-velocity surfaces, the surfaces (x, y, z)=constant and the surfaces (x, y, z)=constant are constructed as groups of such spatial curves with common values of some parameters specifying the respective surfaces.On leave of absence from the University of Tokyo as an Honorary Fellow of the Victoria University of Manchester.  相似文献   

3.
Two spherically symmetric time-dependent Green's functions of the equation of transport for cosmic rays in the interplanetary region are derived by transform techniques. The solar wind velocity is assumed radial and of constant speedV. In the first model the radial diffusion coefficient =0 r (0 constant), and in the second solution =0= constant. The solutions are for monoenergetic, impulsive release of particles from a fixed heliocentric radius. Integration of the solutions over timet, fromt=0 tot=, gives the steady-state Green's functions obtained previously.  相似文献   

4.
Free convection effects on MHD flow past a semi infinite porous flat plate is studied when the time dependent suction velocity changes in step function form. The solution of the problem is obtained in closed form for the fluid with unit Prandtl number. It is observed that for both cooling and heating of the plate the suction velocity enhances the velocity field. The heat transfer is higher with increase in suction velocity.Notations B intensity of magnetic field - G Grashof number - H magnetic field parameter,H=(M+1/4) 1/2–1/2 - M magnetic field parameter - N u Nusselt number - P Prandtl number of the fluid - r suction parameter - T temperature of the fluid - T w temperature of the plate - T temperature of the fluid at infinity - t time - t non-dimensional time - u velocity of the fluid parallel to the plate - u non-dimensional velocity - U velocity of the free stream - suction velocity - 1 suction velocity att0 - 2 suction velocity att>0 - x,y coordinate axes parallel and normal to the plate, respectively - y non-dimensional distance normal to the plate - coefficient of volume expansion - thermal diffusivity - kinematic viscosity - electric conductivity of the fluid - density of the fluid - non-dimensional temperature of the fluid - shear stress at the plate - non dimensional shear stress - erf error function - erfc complementary error function  相似文献   

5.
The selection effects that govern the observations of Visual Binary Stars are investigated, in order to obtain a realistic statistical distribution of the mass-ratioq=M sec/M prim. To this end a numerical simulation programme has been developed, which generates binary stars and looks at them to determine whether an observer on Earth would be able to detect them. The simulations show that for mass-ratiosq>0.35, observations are expected to reveal the realq-distributions, while for mass-ratiosq<0.35 selection effects begin to play a major part. It is found that the observed mass-ratio distribution for Main-Sequence systems, derived from theIndex Catalogue of Visual Binary Stars (IDS), can be explained by a distribution of secondary masses according to the Initial Mass Function (IMF), i.e., (M)M –2.7.From theFourth Catalogue of Orbits of Visual Binary Stars (OVB) authors find aq-distribution that peaks strongly forq-values close toq=1. It is shown that this mass-ratio distribution may be the result of a sampling selection effect. Due to this sampling selection effect, the OVB is a considerably morebiased sample of the binary population in our Galaxy than the IDS. Numerical simulations of biased sampling show that theq-distribution, found from the OVB, is not incompatible with the distribution of secondary masses according to the IMF (forq>0.35), found from the IDS.Because of the selection effects, it is difficult to establish the realq-distribution forq<0.35. If the realq-distribution departs from (q)q –2.7 forq0.35, about 36% of all stars are in visual binaries (i.e., if theq-distribution is assumed to be flat for 0<q<0.35); if the distribution flattens forq0.25, about 60% of the stars must be primaries of visual binaries.  相似文献   

6.
Hall effects on the flow of electrically conducting rarefied gas due to combined buoyant effects of thermal and mass diffusion past an infinite porous plate with constant suction in the presence of strong transverse magnetic field have been investigated. The equations governing the flow poblem have been solved for primary, secondary velocities and temperature. The effects of Hall current, magnetic field and the effect of rarefication have been discussed graphically followed by a discussion.Nomenclature x,y coordinate system - u velocity inx direction - v 0 suction velocity - w velocity inz direction - E Eckert number - G, G* Grashof numbers - h 1 velocity slip coefficient - h 2 temperature jump coefficient - h 3 concentration jump coefficient - M, m magnetic field parameter, Hall parameter - Pr Prandtl number - Sc Schmidt number - T, T w, T temperature in flow regime, plate temperature, temperature outside the boundary layer very away from the plate - C, C w, C concentration of the gas in flow, concentration at the plate, concentration far away from the plate - thermal conductivity - D coefficient of chemical molecular diffusion - coefficient of kinematic viscosity - coefficient of viscosity - electrical conductivity - C p specific heat of gas at constant pressure density  相似文献   

7.
The cooling effect of emission in the spectral lines, which dominates over continuous emission in the chromosphere and becomes important first around the temperature minimum, modifies greatly the radiative relaxation timet r in the solar atmosphere. This rises from low photospheric values to a maximum of 8 min just aboveT min, falls in the low chromosphere to 1.5 min because of line emission, but rises again to 6 min atT 7000–8400 K in the chromosphere where hydrogen ionization increases the specific heat.  相似文献   

8.
An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H 0 applied magnetic field - H magnetic field intensity - (j x , j y , j z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n e electron number density - P Prandtl number - q velocity vector - (T, T w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U 0 uniform velocity - v 0 suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - e charge density - electrical conductivity - e electron collision time  相似文献   

9.
In this paper I present a new evolution model of QSOs luminosity. The model is based on edges distribution of apparent magnitude-redshift of QSOs. After the quasars were formed, the luminosities were increasing until they attained their maximum value atz=2+a, where –0.1a0.6, then the luminosities were decreasing. If the QSOs originate from superconducting cosmic string of same initial massM i 1012 M , the formation epochs are different, most of the quasars start atz cutoff5.6. The most luminous QSOs start at later epochz cutoff5.15. The present sky survey echniques may give us the possibility to see the formation of QSOs at apparent magnitudem V 22.5 by chance of 0.3%.  相似文献   

10.
A selective survey of then-body problem of celestial mechanics is given where the emphasis is on the asymptotic behavior of all solutions ast, the possible configurations the particles can assume in phase space and in physical space, and collision and non-collision singularities.Supported in part by NSF Grant MPS 71-03407 A03.  相似文献   

11.
In this paper the unsteady laminar free-convection flow of a viscous incompressible fluid, past an accelerated infinite vertical porous plate subjected to a constant suction (or injection) in considered. Numerical results for the skin-friction on the plate are obtained for the class of accelerated motions whose velocity is of the formU 0 t n wheret is time,U 0 a constant, andn is a positive integer. The skin friction tends to zero with increasingt when the Grashof number Gr=2, the Prandtl number =1,n=0, and >0 which corresponds to suction.On leave of absence from the Department of Mathematics, University of Dhaka, Bangladesh.On leave from absence from the Department of Mathematics, University of Dar-es-Salaam, Tanzania.  相似文献   

12.
In a simple approximation, the evolution of a stellar system can be described in terms of the solutions to a diffusion equation for motion in a harmonic potential. This paper presents a discussion and characterization of the normal modes for this equation. These solutions are of particular interest in that they provide a simple example of the interplay between dynamical and relaxation phenomena. For the case of a large system, in which the relaxation timet r is much greater than the dynamical timet d,there exists a well-defined sense in which the effects of relaxation may be viewed as a perturbation of motion in the fixed field: the dynamical effects give rise to a purely oscillatory behavior, whereas collisions among stars provide a dissipative mechanism that drives the system towards the unique isothermal equilibrium. Alternatively, the presence of the fixed potential serves to alter the e-folding time for the various modes. In the limit thatt r t d , all characteristic relaxation times are essentially doubled. This suggests a danger in the use of velocity space equations to model the effects of evaporation.  相似文献   

13.
It is shown that the cosmological interpretation of the red shift in the spectra of quasars leads to yet another paradoxical result: namely, that the Earth is the center of the Universe. Consequences of this result are examined.Einstein distinguishes between two main criteria [for a good theory]: (a) theexternal confirmation of a theory, which informs us in experimental checks of the correctness of the theory, and (b) theinner perfection of a theory which judges its logical simplicity or naturalness.  相似文献   

14.
Numerical solution of the effect of current-carrying jets on the temperature of an astrophysical surrounding is carried out using classical magnetohydrodynamic equations. Under the assumption of small hydrodynamic and magnetic Reynolds numbers and invoking a jet magnetic field intensityB , which confines high pressure jets along thez-axis, a non-linear equation is generated and solved by asymptotic approximation. It is found that when the field intensity is large, the temperature of the surrounding is small and vice-versa. The problem is of interest in the astrophysical studies of current-carrying jets or magnetised radio jets.  相似文献   

15.
The paper introduces a new time element to be used with a general time transformation for satellite equations of motion. The purpose of this time element is to reduce the growth of the numerical errors with respect to the time integration. It is characteristic for the new time element , that the relation between the timet and the element does not depend on the independent variables.  相似文献   

16.
We compare families of simple periodic orbits of test particles in the Newtonian and relativistic problems of two fixed centers (black holes). The Newtonian problem is integrable, while the relativistic problem is highly non-integrable.The orbits are calculated on the meridian plane through the fixed centersM 1 (atz=+1) andM 2 (atz=–1) for energies smaller than the escape energyE=1. We use prolate spheroidal coordinates (, , =const) and also the variables =cosh and =–cos . The orbits are inside a curve of zero velocity (CZV). The Newtonian orbits are also limited by an ellipse and a hyperbola, or by two eillipses. There are 3 main types of periodic orbits (1) elliptic type (around both centers), (2) hyperbolic-type, and (3) resonant-type.The elliptic type orbits are stable in the Newtonian case and both stable and unstable in the relativistic case. From the stable orbits bifurcate double period orbits both symmetric and asymmetric with respect to thez-axis. There are also higher order bifurcations. The hyperbolic-type orbits are unstable. The Newtonian resonant orbits are defined by the ratiot µ/t =n/m of oscillations along and during one period, and they are all marginally unstable. The corresponding relativistic orbits are stable, or unstable. The main families are figure eight orbits aroundM 1, or aroundM 2 (3/1 orbits); gamma, or inverse gamma orbits (4/2); higher resonant families 5/1,7/1,...,8/2,12/2,...;, more complicated orbits, like 5/3, and bifurcations from the above orbits. Satellite orbits aroundM 1, orM 2, and their bifurcations (e.g. double period) exist in the relativistic case but not in the Newtonian case. The characteristics of the various families are quite different in the Newtonian and the relativistic cases. The sizes of the orbits and their stabilities are also quite different in general. In the Appendix we study the various types of straight line orbits and prove that some subcases introduced by Charlier (1902) are impossible.  相似文献   

17.
An expression is derived for the fluctuation (t) in emergent intensity (observed at some wavelength in a Fraunhofer line or the continuum) caused by a perturbation in temperature (z, t) in the Sun's atmosphere. If the contribution function for the observed intensity is single-peaked near z and if (z) and p(z) are not too rapidly varying, then (t) m (z , t)+N p(z , t) where m and N depend on the structure of the atmosphere. We compute M, N, and contribution functions for several values of and in the inner wings of the K line (13933 Caii).Presently on leave of absence from the Institute for Astronomy, Honolulu, Hawaii.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

18.
High-resolution filtergrams of the quiet chromosphere, taken at seven wavelengths in H with the aid of a computer-controlled 1/8 Å filter, have been used to derive the contrast of ten bright and dark mottles as functions of wavelength. The contrast profiles of bright and dark mottles are strikingly different. They disagree with Athay's (1970) velocity model but, with an appropriate choice of parameters, can be brought into good agreement with Beckers' (1964) cloud model. Comparison between observation and theory yields values for the source function S, optical thickness t 0, line broadening parameter 0, and line-of-sight velocity V for both bright and dark mottles. The values of S and t 0 obtained for dark mottles are consistent with Beckers' (1968) spicule model.  相似文献   

19.
An exact analysis of the effects of mass transfer on the flow of a viscous incompressible fluid past an uniformly accelerated vertical porous and non-porous plate has been presented on taking into account the free convection currents. The results are discussed with the effects of the Grashof number Gr, the modified Grashof number Sc, the Schmidt number Sc, and the suction parametera for Pr (the Prandtl number)=0.71 representating air at 20°C.Nomenclature a suction parameter - C species concentration - C species concentration at the free stream - g acceleration due gravity - Gc modified Grashof number (vg*(C –C )/U 0 3 ) - Pr Prandtl number (C p/K) - T temperature of the fluid near the plate - T dimensionless temperature near the plate ((T-T )/(T -T )) - U(t) dimensionless velocity of the plate (U/U 0) - v normal velocity component - v 0 suction/injection velocity - x, y coordinate along and normal to the plate - v kinematic viscosity (/gr) - C p specific heat at constant pressure - C w species concentration at the plate - C non-dimensional species concentration ((C-C )/(C w -C )) - Gr Grashof number (g(T w -T )/U 0 3 ) - D chemical molecular diffusivity - K thermal conductivity - Sc Schmidt number (/D) - T w temperature of the plate - T free stream temperature - t time variable - t dimensionless time (tU 0 2 /) - U 0 reference velocity - u velocity of the fluid near the plate - u non-dimensional velocity (u/U 0) - v dimensionless velocity (v/U 0) - v 0 non-dimensionalv 0 (v 0 /U0)=–at–1/2 - y dimensionless ordinate (yU 0/) - density of the fluid - coefficient of viscosity  相似文献   

20.
Ideal and resistive ballooning modes are investigated for different ratios of a two-layer stratified density region representing a model for the photospheric/coronal boundary. Construction of the ballooning equations using a WKB approach is justified by comparison between the values of the growth rate obtained using Hain-Lüst and ballooning equations together with a WKB integral relation. Different values of the density ratio, radius, and resistivity are considered. Sausage-type and kink-type instabilities are found. One of these, depending on the value of r remained unstable for large density ratios. The other instability tended to marginal stability as the density ratio was increased, and allowed parallel and perpendicular flows across the boundary. This is contrary to the predictions of both the rigid-wall and flow-through conditions.  相似文献   

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