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1.
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   

2.
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   

3.
The general conception of the critical inclinations and eccentricities for theN-planet problem is introduced. The connection of this conception with the existence and stability of particular solutions is established. In the restricted circular problem of three bodies the existence of the critical inclinations is proved for any values of the ratio of semiaxes . The asymptotic behaviour of the critical inclinations as 1 is investigated.
. . . 1.
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4.
The consequences of a cosmological term varying asS –2 in a spatially isotropic universe with scale factorS and conserved matter tensor are investigated. One finds a perpetually expanding universe with positive and gravitational constantG that increases with time. The hard equation of state 3P>U (U mass-energy density,P scalar pressure) applied to the early universe leads to the expansion lawSt (t cosmic time) which solves the horizon problem with no need of inflation. Also the flatness problem is resolved without inflation. The model does not affect the well known predictions on the cosmic light elements abundance which come from standard big bang cosmology.In the present, matter dominated universe one findsdG/dt=2H/U (H is the Hubble parameter) which is consistent with observations provided <10–57 cm–2. Asymptotically (S) the term equalsGU/2, in agreement with other studies.  相似文献   

5.
Zusammenfassung Es wird gezeigt, daß die unter der Einwirkung einer Momentenimpulsserie entstehende Bewegung eines rotierenden Flugkörpers mit Nutationsdämpfung sich vollständig einem regelmäßigen Polygon entnehmen läßt, das durch das Trägheitsmomentenverhältnis, den Integralwert eines Einzelimpulses, den Drall und eine die Dämpfung charakterisierende KonstanteK 0 bestimmt ist.Die Bewegung setzt sich aus logarithmischen Spiralen zusammen, derenn-ten Anfangsradius man erhält, indem man den Teilungspunkt des im VerhältnisK 0:1 geteilten (n–1)-ten Radius mit der (n+1)-ten Polygonecke verbindet.Es wird bewiesen, daß das Konstruktionsnetz zu einem im äußeren Polygon liegenden ähnlichen inneren Polygon konvergiert, das gegenüber ersterem gedreht ist.Einfache Beziehungen zur Bewegungsbestimmung mit dem Polygonschema werden für Pulsfrequenzen angegeben, die ganzzahlige Vielfache oder Bruchteile der Spinfrequenz sind.
It is shown that the motion of a spinning body with nutation damping due to a series of torque pulses can be completely derived from a regular polygon determined by the ratio of inertias, the integral of one pulse, the momentum and a constantK 0 characterizing damping.The motion is composed of spirals thenth initial radius of which is obtained by connecting the dividing point of the (n–1)th radius with the (n+1)th polygon corner. Each dividing point divides the respective radius in the ratioK 0:1. The net of construction lines converges into an inner polygon turned against the outer one and having the same shape.Simple rules are shown for the application of the scheme on pulse frequencies which are multiples or fractions of spin frequency.
Symbole 1-2-3 Achsen des flugkörperfesten Koordinatensystems - a,b,c Hilfsgrößen zur Bestimmung der Iterationsgrößen - E i i-te Polygonecke - H Drall des Flugkörpers - K i Verhältnis deri-ten Drehzeigerlängen zu Beginn und am Ende eines Impulses - M Iterationsmatrix - Integralwert des Momentenimpulses - P 0 Äußeres Polygon - P 1 Spitze des Drehzeigersr 00e - P Drehpunkt des Drehzeigersr 00 - P Konvergierendes Polygon - P i Teilungspunkt des [i–1]-ten Zeigers - r 0i Drehzeiger aufgrund desi-ten Impulses allein - r 0ia Zeigerr 0i in Anfangslage - r 0ie Zeigerr 0i in Endlage - r i i-ter Summenzeiger - r ia Zeigerr i in Anfangslage - r ie Zeigerr i in Endlage - T Dauer einer Flugkörperumdrehung - t,t, Zeitargumente - x-y-z Achsen eines raumfesten Koordinatensystems - x i ,y i Iterationskoordinaten - n Phase desn-ten Radius gegenüber der anliegenden Polygonseite - Drehung des inneren Polygons gegenüber dem äußeren - Abklingkonstante - Phasenänderung des Drehzeigers innerhalb einer Flugkörperumdrehung - 0 Anteil der über 2 hinausgehenden Phasenänderung des Drehzeigers - 3 Trägheitsmoment um die Spinachse - 12 Trägheitsmoment um die Querachsen - Zahl der Ecken des Konstruktionspolygons - 1,2 Eigenwerte der Iterationsmatrix - Zahl der vollen Umläufe des Konstruktionspolygons - Fortbewegungsachse des Drallvektors - 0 Ausgangsphasenwinkel - i Phasenlage desi-ten Summenzeigers - x, y Drehwinkel nach Einzelimpuls fürt - , Funktionen der Iterationsgrößen - , Drehwinkel umx-bzw.y-Achse - Drehgeschwindigkeit der Spinachse um den Drallvektor - Fiktive Größen bei Pulsfrequenzen kleiner als Spinfrequenz - Fiktive Größen bei Pulsfrequenzen größer als Spinfrequenz  相似文献   

6.
Infrared continuum observations of the Sun at wavelengths between 10 and 30 show a nonisothermal response of the upper photosphere to compression waves associated with the five-minute oscillations. Observations were made with four broad-band filters with effective transmission wavelengths between 10 and 26 and with a 10 aperture. Further observations at submillimeter wavelengths with a 2 aperture did not resolve oscillatory fluctuations of five-minute period.Comparisons with velocity field data of Howard (1976) suggest that the relaxation time of the photosphere exceeds (300/2) seconds at the height of formation of the 26 continuum (5000Å 10-2). The photosphere reponds to 3 mHz oscillatory motion with considerably less compression than expected for simple acoustic modes in an adiabatically responsive atmosphere, confirming the evanescent character of the five-minute oscillations.  相似文献   

7.
We emphasize the sharp distinctions between different one-body gravitational trajectories made by the ratio of time averagesR(t)–E kin/E pot.R is calculated as a function of the eccentricity (e) and of the energy (E). Whent, independently ofe andE, R1/2 for closed orbits (this clearly illustrates the fulfillment of the virial theorem in classical mechanics); whereasR1, at any time, for open orbits.  相似文献   

8.
The potential of a body of revolution is expanded in a series of spherical functions. It is proved that, for a body with analytical density limited by an analytical surface the coefficients of expansion decrease in geometrical progression.
. , , , .
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9.
The 5-dimensional Jordan-Brans-Dicke cosmologies in vacuum are found for the Bianchi type I metric, their relation with general relativity cosmologies is studied. Two solutions are possible, both produce effective pressure and energy density in the 4-dimensional G.R.-universes. One is a power-law relation, with two cases, the first one is forp eff=eff and the other forp eff=eff(– 1 < < 1) has a behaviour as the open flat universe. The second solution is an exponential only valid forp eff=–eff. In all cases the three-space expansion reaches infinity ast and the fifth dimension can be made to decrease approaching zero. The scalar field can increase or decrease with time.  相似文献   

10.
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   

11.
,   相似文献   

12.
-- () ., , , , , . , , . , .  相似文献   

13.
, , , , , . , , . - . — , , .  相似文献   

14.
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   

15.
, . () . , , , . ( ), , , . . (2.7). ( 1 k 1 ,V — , — .) (k 1) (k) §2 ( (2.14)). , (3.6) (3.4), (3.8) . (3.9)–(3.13) ( (3.9), (3.10) (3.11) , (3.12)–(3.13) ). (3.14), (3.16)–(3.19). - . (3.15). ( (4.14)–(4.15)). (4.23)–(4.25). (4.26)–(4.28). §5. , . ((5.5)–(5.6)). , . (5.10) .  相似文献   

16.
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   

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.
It is suggested that the minimum mass of a star at the time of its formation is approximately 0.01M . Making use of this fact and the stellar mass functionF(M) M –, it is found that the hidden mass (or the missing mass) in the solar neighborhood may be explained by the presence of a large number of invisible stars of very low mass (0.01M M<0.07M ).  相似文献   

19.
. , , . , t>1010 ( z<105) .
In this paper we continue the work of Weymann, investigating the causes of distortion of the spectrum of the residual radiation from the Planck curve. We discuss the distortion to the spectrum, resulting from recombination of primeval plasma.We then derive an analytic expression for the distortion to the equilibrium spectrum due to Compton scattering by hot electrons. On the basis of the observational data we conclude that a period of the existence of neutral hydrogen is inescapable in the hot model of the universe. It is concluded that any injection of energy att>1010 sec (red shiftz<105) give the distortions of the equilibrium spectrum.
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20.
In the quasi-linear theory of pitch angle scattering the power spectrum of magnetic field fluctuations is related to the shape of the pitch angle diffusion coefficient D(), the absolute value of the mean free path , and the rigidity dependence of the mean free path (R). We discuss these relations in detail during the solar particle event of 11 April, 1978 which was observed on HELIOS-2 at a distance of 0.49 AU from the Sun. Magnetic field measurements obtained during the time of the event are used as a basis for the layer model in which the method of particle trajectories in an actually measured field is used to simulate pitch angle diffusion. The values of D() and based on the trajectory simulation for 100 MeV protons (field approach) are compared with results obtained from solar proton data (particle approach) and with predictions from quasi-linear theory based on the additional assumption of the slab model for magnetic field fluctuations (QLT approach). The time of the event is characterized by a high level of field fluctuations, the observed mean free path of about 0.03 AU for 100 MeV protons is smaller than the average value near 1 AU. Results from the field and particle approaches agree surprisingly well. The remaining difference in the mean free path of about a factor of 2 could be due to tangential discontinuities which are measured by the magnetometer, but not seen by the real particles traveling along the average field. The results from the field and QLT approaches based on the same set of magnetic field measurements differ by about a factor of 4. One of the reasons for this discrepancy is that the conditions for resonance scattering are only marginally valid. In addition, the wave vectors representing Alfvén-type fluctuations may not be totally field aligned. This deviation from the slab model would cause an increase of the theoretically predicted mean free path and lead to better agreement with the other two approaches.  相似文献   

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