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1.
Consider a Hamiltonian system of two degrees of freedom at an equilibrium. Suppose that the linearized vectorfield has eigenvaluesi,i,–i,–i ( , >0) and is not semisimple. In this paper we discuss the real normalization of the Hamiltonian function of such a system. We normalize the Hamiltonian up to 4th order and show how to compute its coefficients. For the planar restricted three body problem atL 4 the coefficient that plays an important role in the investigation of the qualitative behaviour of periodic solutions near the equilibrium is explicitly calculated.  相似文献   

2.
A family of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form H=A+B was given in (McLachlan, 1995). We give here a constructive proof that for all integer p, such integrator exists, with only positive steps, and with a remainder of order O(p + 22), where is the stepsize of the integrator. Moreover, we compute the analytical expressions of the leading terms of the remainders at all orders. We show also that for a large class of systems, a corrector step can be performed such that the remainder becomes O(p +42). The performances of these integrators are compared for the simple pendulum and the planetary three-body problem of Sun–Jupiter–Saturn.  相似文献   

3.
In a previous publication (1977) the author has constructed a family () of long-periodic orbits in the Trojan case of the restricted problems of three bodies. Here he constructs the domain of the analytical solution of the problem of the motion, excluding the vicinity of thecritical divisor which vanishes at the exact commensurability of the natural frequencies 1 and 2. In terms of thecritical masses mj(2), or the associatedcritical energies j 2 (m), is the intersection of the intervals ofshallow resonance, of the form. Inasmuch as the intervals |2– j 2 |<j ofdeep resonance aredisjoint, it follows that (1) the disjointed family () embraces the tadpole branch, 021, lying in: and (2) despite the clustering of j 2 (m) atj=, the family () includes, for 2=1, an asymptoticseparatrix that terminates the branch in the vicinity of the Lagrangian pointL 3.In a similar manner, the family () can be extended to the horseshoe branch 1<2 2 2 .  相似文献   

4.
The use of an auxiliary beamsplitter with the Kitt Peak 15-foot spectroheliograph permits spectroheliograms to be taken simultaneously in 4 identical images of the sun. By using two of these images for a Zeeman spectroheliogram, a third image for a Fei 4071 spectroheliogram, and the fourth image for a 6107Å continuum spectroheliogram, simultaneous measurements of magnetic fields and brightness fields have been obtained. Within the limits of intensity variations imposed by doppler shifts and brightness fluctuations of the continuum, a quantitative relation does exist between the measured values of brightness and magnetic field strength of the photospheric network. For intensities measured +0.12 Å from the core of Fei 4071, this relation is ln(1 +I/I) = ¦B ¦, whereB refers to the component of magnetic field normal to the solar surface,I/I is the fractional excess of brightness of the magnetic regions relative to the brightness of non-magnetic regions, and = (6±2)%/100 gauss.Kitt Peak National Observatory Contribution No. 538.Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.Visiting Astronomer, Solar Division, Kitt Peak National Observatory.  相似文献   

5.
The diagramV - log(1 +z e ) as function of (, ) is considered for the quasars. HereV is the apparent visual magnitude,z e is the emission line redshift, and are the equatorial coordinates. Two opposite extreme spots NE and SE are observed on the sky, where the inclination of the straight line fitting the dependenceV - log(1 +z e ) is maximum and minimum. The coordinates of the centres of these extreme spots are ( NE, NE) = (282°, +42°) and ( SE, SE) = (70°, -38°) with errors 5°. A hypothesis of the Superattractor (SA) is proposed to explain such an effect. Two independent tests of this hypothesis are realized. First, the dependence or the frequency a of the absorbers in QSO spectra on (, ) is investigated. A region of the larger a is found. The coordinates of its centre are (, ) = (82°, - 10°) with error 5°. Second, the cases ofz a >z e are plotted in the Mercatorial projection (, ). The most of the casesz -z e > 0.02 are concentrated within the circle with radiusR = 34° and centre (, ) = (50°, - 15°). The both anomalous regions overlap the Southern extreme spot around SE. The SA direction is (, ) = (67°, -21°) with errors about 12°. The redshift of SA isz SA = 1.7 ± 0.3 that corresponds to the distancer SA = (3100 ± 300)h –1 Mpc for the Hubble constantH 0 = 75h kms–1 Mpc–1. The SA mass isM SA ~ 1018-1020 M . The orientation of the normal to the quasiperiodical large-scale sheet structure on the sky occurs near SA.  相似文献   

6.
The hypothesis that the optical continua of QSOs, BL Lac objects and the nuclei of Seyfert, N and normal galaxies arise due to incoherent synchrotron radiation from electrons and consequently the flux of radiation in the optical continua of these objects is given by the power law:F(v)v is examined. Following Kinman, spectral indices B–V and U–B in(B-V) and(U-B) colours as well as their average and difference have been defined and calculated for samples of 227 QSOs, 32 BL Lac objects and nuclei of 62 Seyfert, 12 N and 7 normal galaxies. Here has been assumed to be an estimate of the spectral index . On the other hand, has been regarded as a measure of departure from the power law. On the basis of this, the distributions of and in QSOs, BL Lac objects and the nuclei of Seyfert, N and normal galaxies have been studied. The value of depends mainly on the balance of the energy loss due to synchrotron radiation and the rate of replenishment of energy by injection of high energy electrons in the radiating region. The increase in the value of and therefore that of indicates that the activity in the object is slowing down and the object is growing older. Assuming that the QSOs, BL Lac objects and the nuclei of Seyfert, N and normal galaxies essentially represent different phases in the evolutionary sequence of extragalactic objects, we suggest that they may be arranged in the sequence: QSOsBL Lac objects Seyferts 1N galaxies Seyferts 2 Normal galaxies in the decreasing order of activity in the core or nuclei of these objects.On leave of absence from the Government Science College, Rajpur, M.P., India.  相似文献   

7.
The H observations of a selected sample of bright Be stars are presented. The available infrared observations at K band (2.2 m) of these stars have been used to find the infrared excess emission. The analysis of the combined data show thatL H, the luminosity of the H emission line, is proportional toL IR, the luminosity of the infrared excess emission. The linear correlation betweenL IR andL H shows that both the infrared excess and the H line originate in a common region. It is also detected that the infrared excess emission is produced throughout the whole envelope whereas the H is emitted in some defined region of the circumstellar (CS) envelope.  相似文献   

8.
The assumption of a linearly expanding universe for the JBD-cosmological equations generates a set of solutions for the barotropic equations of statep= (=const.). These solutions turn out to be valid for closed space-except in the casep= which is for open space. The gravitational constant which is inversely proportional to the scalar field increases with time if >–1/3 and decreases for <–1/3. No solution exists for =1/3. The Brans-Dicke parameter is negative if <–1/3.  相似文献   

9.
The asymptotic properties of a turbulent disk dynamo at large dimensionless numbersR andR characterizing the helicity and the differential rotation are analysed. Three types of generations in the dependence of the relations betweenR andR are found: 2-dynamo and two types of -dynamo. For each of these types the rates of growth are obtained and the forms of solution are pointed out. Boundaries of the disk dynamo approximation are given.  相似文献   

10.
It is shown that, to any change of variables:q i=qi(r, t) (i=1,..., n; =1,...,n+m; mn) increasing the number of variables, it is possible to associate a Mathieu's transformation and conversely. The results are applied to the theory of the osculating plane of motion.
Resumé On montre qu'à toute transformation:q i=qi(r, t)(i=1,..., n; =1,...,n+m; mn) augmentant le nombre de variables, on peut associer une transformation de Mathieu et réciproquement. Les résultats sont appliqués à la théorie du plan osculateur du mouvement.
  相似文献   

11.
The analysis of solar wind He++ and H+ ion distribution functions, collected over five months by the satellite Prognoz 1, shows that these are in general maxwellian but that often tails appear at higher speeds. The existing relation V-T, the observation of ratios of T/Tp 3.83 and V/Vp 1.035 give evidence of preferential He++ ion heating and acceleration. The criteria for heating by dissipation of hydromagnetic waves proposed by Barnes and Hung (1973) are tested experimentally. Finally, multifluid models are likely to predict certain observations such as dependence of the velocity ratio V/Vp on the solar wind flux.  相似文献   

12.
Observations of C100 and C125 atomic carbon recombination lines were made at the Algonquin Radio Observatory, towards the neutral interface separating theHii region DR21 (at RA=20h37m14s, Dec=+42°0900) from its associated molecular cloud. An analysis of the Cn observations in conjunction with a simple model of a neutral interface enabled the derivation of the following parameters: electron density of 300 cm–3, electron temperature of 30 K, microturbulent velocity of 2.3 km s–1, and depth of the neutral interface of 0.01 pc. A single,stimulated emission model is sufficient to reproduce the Cn observations in the wavelength range from 4.6 cm (C100) to 21 cm (C166). All the known Cn data do support a pressure equilibrium between the neutral interface and theHii region, after the usual allowance is made for carbon depletion on grains.  相似文献   

13.
Three different asymptotic branches of the two-fluid equations are found with e m , p n , where, is the inverse distance from the Sun, with (m, n) = (2/7, 2/7), (2/7, 6/7), (4/3, 4/3); other special solutions are also found but they correspond to special choices of density and temperature at the corona. In all the (4/3, 4/3) solutions, the electron and proton temperatures tend to equality at large distances.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

14.
We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec2 at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C min the H- 1.5 Å image (C m 0.1 type I, C m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C m- A scatter diagram, in H and H wings, indicates a wide range of variability for C m in correspondence with very narrow range of variability for A.  相似文献   

15.
Light-element abundances are compiled for six peculiar A stars (3 CenA, 2 CVn, HR 1732,v For, Cnc, and 112 Her) with Heilines very weak for their colours. The abundances are interpreted on the theory that peculiar A stars were once secondaries in binary systems in which the primaries exploded as type II supernovae. During the explosions of the primaries, protons were accelerated to high energies (>20 MeV) in shock waves at the secondaries, and spallation of He, C, N, and O occurred. This was followed by the arrival of heavier elements from the primaries. Abundances on 2 CVn, HR 1732, andv For were subsequently modified by surface nuclear reactions involving protons and -particles accelerated to lower energies (10 MeV), probably by magnetic fields. Successive (, ) reactions formed Si28 from Ne20, and (p, ) reactions acting on A40 and Ca40 may have contributed to the excesses of Cl observed on 2 CVn and HR 1732. These proposals have interesting implications with regard to the relative abundances of the iron-peak elements found on peculiar A stars and in the Solar System.  相似文献   

16.
We use the Cerenkov line emission mechanism to give a new explanation of the observed intensity ratios, particularly the L/H ratio, of the emission lines of quasars. We give equations that restrict the choice of the parameter values. The parameters are the characteristic energy of the relativistic electrons, the number density of neutral hydrogen and its relative level populations. With reasonable choice of the parmaeters, we can obtain calculated L/H, H/H, P/H ratios in agreement with observed values. Our estimate for the gas density in the broad line region of quasars is 1015 cm–3, very different from previous estimates. Unlike previous theories, such a high density causes no difficulties with the Cerenkov line emission.  相似文献   

17.
We prove existence and multiplicity of T-periodic solutions (for any given T) for the N-body problem in m (any m 2) where one of the bodies has mass equal to 1 and the others have masses 2,..., N , small. We find solutions such that the body of mass 1 moves close to x = 0 while the body of mass i moves close to one of the circular solutions of the two body problem of period T/k i, where ki is any odd number. No relation has to be satisfied by k 2,...,k N.  相似文献   

18.
We have compared the structures seen on X-ray images obtained by a flight of the NIXT sounding rocket payload on July 11, 1991 with near-simultaneous photospheric and chromospheric structures and magnetic fields observed at Big Bear. The X-ray images reflect emission of both Mgx and Fexvi, formed at 1 × 106 K and 3 × 106 K, respectively. The brightest H sources correspond to a dying sub-flare and other active region components, all of which reveal coronal enhancements situated spatially well above the H emission. The largest set of X-ray arches connected plages of opposite polarity in a large bipolar active region. The arches appear to lie in a small range of angle in the meridian plane connecting their footpoints. Sunspots are dark on the surface and in the corona. For the first time we see an emerging flux region in X-rays and find the emission extends twice as high as the H arches. Many features which we believe to correspond to X-ray bright points (XBPs) were observed. Whether by resolution or spectral band, the number detected greatly exceeds that from previous work. All of the brighter XBPs correspond to bipolar H features, while unipolar H bright points are the base of more diffuse comet-like coronal arches, generally vertical. These diverge from individual features by less than 30°, and give a good measure of what the canopies must do. The H data shows that all the H features were present the entire day, so they are not clearly disappearing or reappearing. We find a new class of XBPs which we call satellite points, elements of opposite polarity linked to nearby umbrae by invisible field lines. The satellite points change rapidly in X-ray brightness during the flight. An M1.9 flare occurred four hours after the flight; examination of the pre-flare structures reveals nothing unusual.  相似文献   

19.
We consider the effect that coherent motion has on the observed brightness of moving clouds above the photosphere. We find that steady state clouds (constant N e and T e ) that are moving perpendicular to the line of sight will appear brighter in H for speeds between 8 and 100 km/sec and dimmer for speeds greater than 135 km/sec. The brightening and dimming are due to apparent Doppler shifts of the respective H absorption and the Lyman- emission profiles seen by the absorption profile of the moving cloud.We apply this analysis, along with optical depth and geometrical considerations, to the observed brightness variations of the 1 March 1969 limb eruptive prominence. We find that all of the observed brightening and dimming can be explained by the motions, and that no significant change in the prominence N e or T e was necessary during the observed H event. This conclusion is significant in interpreting an X-ray burst that began as the prominence velocity increased abruptly at the time of maximum H intensity. The thermal X-ray peak occurred 150 sec later when the prominence had become faint again. There was no associated flare that was visible in H. We discuss the relative brightness of H and D 3 in a specific moving prominence knot.We note that the observed range of limb speeds (30–150 km/sec) may be due to the combined H Doppler brightening and Lyman- dimming effects. We also discuss generally the H brightness of disk surges (bright and dark) and flares, and sprays and puffs that occur at or near the limb.Now at the Dept. of Physics and Astrophysics, University of Colorado, and High Altitude Observatory (NCAR) Boulder, Colo., U.S.A.  相似文献   

20.
The Oppenheimer-Penney theory to calculate the polarization of L lines from hydrogen-like ions, when the impact electrons are distributed such that their probability is more in the regions close to the magnetic field (f(cos n ), is applied by Chandra and Joshi (1984). The work of Chandra and Joshi (1984) has been reinvestigated for the pitch-angle distributionf()sin n . The degrees of polarization are still found to be independent of the atomic number of a hydrogen-like ion.  相似文献   

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