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1.
In this article we study the conditions for obtaining canonical transformationsy=f(x) of the phase space, wherey(y 1,y 2,...,y 2n ) andx(x 1,x 2,...,x 2m ) in such a way that the number of variables is increased. In particular, this study is applied to the rotational motion in functions of the Eulerian parameters (q 0,q 1,q 2,q 3) and their conjugate momenta (Q 0,Q 1,Q 2,Q 3) or in functions of complex variables (z 1,z 2,z 3,z 4) and their conjugate momenta (Z 1,Z 2,Z 3,Z 4) defined by means of the previous variables. Finally, our article include some properties on the rotational motion of a rigid body moving about a fixed point.  相似文献   

2.
Perturbation equations of the elements a, e, s, Ms, Ψs,Ωsof Vinti's intermediate orbit are derived here correct to the second-order. Poisson terms have been eliminated from these equations.  相似文献   

3.
The effect of small perturbation in the Coriolis and centrifugal forces on the location of libration point in the ‘Robe (1977) restricted problem of three bodies’ has been studied. In this problem one body,m 1, is a rigid spherical shell filled with an homogeneous incompressible fluid of densityϱ 1. The second one,m 2, is a mass point outside the shell andm 3 is a small solid sphere of densityϱ 3 supposed to be moving inside the shell subject to the attraction ofm 2 and buoyancy force due to fluidϱ 1. Here we assumem 3 to be an infinitesimal mass and the orbit of the massm 2 to be circular, and we also suppose the densitiesϱ 1, andϱ 3 to be equal. Then there exists an equilibrium point (−μ + (ɛ′μ)/(1 + 2μ), 0, 0).  相似文献   

4.
We have used photometric images of ten barred galaxies in the B and I bands to infer the geometrical and dynamical parameters of their bars: Their length, (R bar), their strengths, (S b), and their corotation radii, (R CR).These parameters have been obtained studying azimuthal profiles from the B and I band images of the galaxies. We find that R CR is in all cases slightly larger than R bar, with mean values close to 1.2 R bar. We have also found a dependence of the ratio R CR/R bar on S bar. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

5.
This paper considers the integrability of generalized Yang-Mills system with the HamiltonianH a (p, q)=1/2(p 1 2 +p 2 2 +a 1 q 1 2 +a 2 q 2 2 )+1/4q 1 4 +1/4a 3 q 2 4 + 1/2a 4 q 1 2 q 2 2 . We prove that the system is integrable for the cases: (A)a 1=a 2,a 3=a 4=1; (b)a 1=a 2,a 3=1,a 4=3; (C)a 1=a 2/4,a 3=16,a 4=6. Our main result is the presentation of these integrals. Only for cases A and B does the Yang-Mills Hamiltonian possess the Painlevé property. Therefore the Painlevé test does not take account of the integrability for the case C.  相似文献   

6.
A quiescent filament was observed near the center of the disk (N5, W5) with the MSDP spectrograph of the 50 cm refractor of the Pic-du-Midi Observatory on June 17, 1986. We focus our study on the statistical moments of the Dopplershift,V 1, and the intensity,I 1, at the center of a chord of the Hα profile (±0.256 Å), versus the minimum intensityI 0. We use a statistical model simulating a numbern max of threads (of optical thicknessτ 0 and source functionS 0), seen over the chromosphere. The threadsj along the same line-of-sighti are identical except for the velocityv j (gaussian distributionv 0,σ v). We search for the best fit between the observed and simulated quantities:V 1,σ (V 1),I 1,σ(I 1), and the histogram of theI 0 values over the field of view. A good fit is obtained with: (a) threads characterized byτ 0 = 0.2,S 0 = 0.06 (unit of the continuum at disk center), mean upward velocityv 0 = 1.7 km s−1 and gaussian-type velocity distributionσ v = 3.5 km s−1. Other possible values ofτ 0 andσ v are discussed; (b) underlying chromosphere deduced from observed quiet Sun (outside the filament) by modifying the chromospheric velocities: additional mean upward velocity 0.7 km s−1, standard deviation reduced by a factorF c ∼ 0.7. The results are discussed in connection with the values deduced from prominence observations.  相似文献   

7.
The supernova yields of r-process elements are obtained as a function of the mass of their progenitor stars from the abundance patterns of extremely metal-poor stars on the left-side [{Ba/Mg}]--[{Mg/H}] boundary with a procedure proposed by Tsujimoto and Shigeyama. The ejected masses of r-process elements associated with stars of progenitor mass M ms ≤ 18 M ⊙ are infertile sources and the SNe II with 20 M ⊙ ≤ M ms ≤ 40 M ⊙ are the dominant source of r-process nucleosynthesis in the Galaxy. The ratio of these stars 20 M ⊙ ≤ M ms ≤ 40 M ⊙ with compared to the all massive stars is about∼ 18%. In this paper, we present a simple model that describes a star's [r/Fe] in terms of the nucleosynthesis yields of r-process elements and the number of SN II explosions. Combined the r-process yields obtained by our procedure with the scatter model of the Galactic halo, the observed abundance patterns of the metal-poor stars can be well reproduced.  相似文献   

8.
A new prediction technique based on logarithmic values is proposed to predict the maximum amplitude (R m) of a solar cycle from the preceding minimum aa geomagnetic index (aa min). The correlation between lnR m and lnaa min (r=0.92) is slightly stronger than that between R m and aa min (r=0.90). From this method, cycle 24 is predicted to have a peak size of R m(24)=81.7(1±13.2%). If the suggested error in aa (3 nT) before 1957 is corrected, the correlation coefficient between R m and aa min (r=0.94) will be slightly higher, and the peak of cycle 24 is predicted much lower, R m(24)=52.5±13.1. Therefore, the prediction of R m based on the relationship between R m and aa min depends greatly on the accurate measurement of aa.  相似文献   

9.
Central configurations are critical points of the potential function of the n-body problem restricted to the topological sphere where the moment of inertia is equal to constant. For a given set of positive masses m 1,..., m n we denote by N(m 1, ..., m n, k) the number of central configurations' of the n-body problem in k modulus dilatations and rotations. If m n 1,..., m n, k) is finite, then we give a bound of N(m 1,..., m n, k) which only depends of n and k.  相似文献   

10.
It is shown that the equation of motion Du j/Ds = (e/mc 2)F ji u i , a natural generalization to the curved spacetime of the Heaviside-Lorentz law of ponderomotive force, is equivalent to the metric independent and covariant Van Dantzig's equations of motion dx j [jpi] = 0 or L v p i = 0, where p i is the conjugate momentum 4-vector and v a vector determined by the condition p i v i, only with respect to holonomic coordinates. With respect to an anholonomic system, the Heaviside-Lorentz equation is a particular case of the VD equations valid for a privileged class of anholonomic frames, those consisting of orthogonal unit vectors.  相似文献   

11.
Ma  Zhenguo 《Solar physics》2002,211(1-2):189-198
The evolution dH R/dt of relative helicity H R provides a gauge-invariant measure of the helicity flow across the open surface S o of an active region. With the incompressible approximation, reformulation of the evolution reveals that it is determined not only by the widely used cross-helicity h mvp=A pv contributed by the vector potential A p of a reference potential field B p, where v is the fluid velocity, but by another cross-helicity h mvo=A ov contributed by the vector potential A o of the open field B o in the region as well. Only under two conditions, (1) A p=A (A is the transverse component of A o), (2) v z=0 (v z is the longitudinal component of v) or A z=0 (A z is the longitudinal component of A o), can h mvo be merged into h mvp to give the pioneering dH R/dt equation shown in Equation (4) of Berger (1984). Results show that h mvo originates from vh o (h o=A oB o is the helicity density of the open field) and should also be considered in dealing with the development of relative helicity in active regions. Finally, the equation to calculate dH R/dt in active regions is synthesized and presented.  相似文献   

12.
In this paper we present a method for computing the equilibrium structures and various physical parameters of a primary component of the binary system assuming that the primary is more massive than the secondary and is rotating differentially according to the law of the w2 = b0 + b1 × s2 + b2 × s4, w being the angular velocity of rotation of a fluid element distant s from the axis of rotation and b0, b1, b2 suitably chosen numerical constants. This method utilizes the averaging approach of Kippenhahn and Thomas (1997) and the concept of Roche equipotentials in a manner earlier used by Mohan et al. (1997) to incorporate the effects of rotation and tidal distortions on the equilibrium structures of certain rotationally and tidally distorted stellar models. The use of the method has been illustrated by applying it to obtain the structures and some observable parameters of certain differentially rotating and tidally distorted binary systems whose primary component is assumed to be a white dwarf star.  相似文献   

13.
The degree of polarization of light from stars in 44 O B associations as a function of interstellar absorption is investigated. It is shown that the character of the dependence of P on A V for stars in associations and stars not in associations depends on the value of A V: for A V 2 m .5 it has a linear character and is the same for both groups of stars. For A V > 2 m .5 the dependence of P on A V for stars in and not in associations departs from linearity and for A V = 4 m .5 it reaches P ass = 1.8% and P nonass = 1%, respectively. Such a difference is explained by the additional depolarization in stellar associations. Such strong depolarization in associations may be due to the overall magnetic field of the Galaxy and to physical peculiarities in the association itself.  相似文献   

14.
A simple, semi-analytic method is developed for obtaining the orbits of galaxies undergoing fast collisions in which the galaxies are represented by Plummer models. The results are found to agree fairly well with those of N-body simulations.A simple formula for obtaining the angle of deflection is deduced. The maximum angle of deflection is 180° forV p/V esc(p)=1.00, about 36° forV p/V esc(p)=1.50, and about 18° forV p/V esc(p)=2.00, whereV p is the velocity at closest approachp, andV esc(p) is the parabolic velocity of escape atp. The angle of deflection of a pair of colliding elliptical galaxies without halos is about twice that for a pair of galaxies with halos for the same relative velocity at infinite separation.  相似文献   

15.
The stellar equilibrium equations for given surface pressureP * and temperatureT *, and in the absence of convection, are translated into a nonlinear integral equation, in which the radiusR of the star enters as an eigenvalue. We show that under broad mathematical assumptions on the constitutive equations (equation of state, opacity and energy generation) a global existence and uniqueness property can be formulated. If a valueP M is selected, which restricts the allowed pressure and temperature range |P(r)–P *|+E|T(r)–T *P M (E, arbitrary constant of dimensions of a pressure over temperature), thenat least one solutionP(r),T(r) exists in the pressure-temperature range chosen, for anyR<R E . This solution isunique forR<R c .R E andR c are expressed in terms of the constitutive equations, and of the pressure-temperature range adopted. A physical argument in favour of the stability of this solution is presented.  相似文献   

16.
We investigate numerically the chemodynamical evolution of major disc–disc galaxy mergers in order to explore the origin of the mass-dependent chemical, photometric and spectroscopic properties observed in elliptical galaxies. We investigate especially the dependence of the fundamental properties on merger progenitor disc mass (M d). Three main results are obtained in this study:– More massive (luminous) ellipticals formed by galaxy mergers between more massive spirals have higher metallicity (Z) and thus show redder colours; the typical metallicity ranges from ∼ 1.0 solar abundance (Z∼ 0.02) for ellipticals formed by mergers with M d = 1010 M ⊙to ∼ 2.0 solar (Z∼ 0.04) for those with M d= 1012 M ⊙.– Both the Mg2 line index in the central part of ellipticals (R ≤ 0.1 R e) and the radial gradient of Mg2 (δ Mg2 / δ log R) are more likely to be larger for massive ellipticals. δ Mg2 / δ log R correlates reasonably well with the central Mg2 in ellipticals. For most of the present merger models, ellipticals show a positive radial gradient of the Hβ line index. – Both M/L B and M/L K (where M, L B, and L K are the total stellar mass of galaxy mergers, the B-band and the K-band luminosities, respectively) depend on galactic mass in such a way that more massive ellipticals have larger M/L B and smaller M/L K. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

17.
The aim of the present paper will be to evaluate numerically Jacobian and other functions which have been discussed in more detail in a previous paper of this series (Edalati, 1978b, Paper XXII), and also choose the most convenient moments to obtain a good determination for the unknown eclipse parametersa andc 0. More than 12 different pairs ofg-functions for real values ofm have been investigated numerically and diagrammatically. The behaviour ofg-functions depends but very little on different combination of the moments, and related diagrams are approximately the same asg 2 andg 4 (Kopal and Demircan, 1978, Paper XIV).The behaviour of the vanishing Jacobian, arising from different pairs ofg-functions for real values ofm1 has been shown diagrammatically in terms ofa andc 0. Accordingly, we obtain the optimum combination of the moments (i.e.,A 6,A 7,A 8 andA 9) ing-functionsg 7 andg 8. It has been noted that the behaviour of theg-functions which depend on the combinations of the higher order moments (i.e.,m5) have been ruled out, because the proportional error of the momentsA 2m increases with increasing values of realm. The automated method has been tested successfully on the light curve of RT Per (Mancusoet al., 1977; Edalati, 1978a). Finally, a comparison is given of the elements of RT Per arising from two different pairs ofg-functions, i.e.,g 2,g 4 (Edalati, 1978a) andg 7,g 8 for the light curves analysis.  相似文献   

18.
An analytically tractable method of transforming the problem of light curve analysis of eclipsing binaries from the time domain into the frequency domain was introduced by Kopal (1975, 1979, 1990). This method uses a new general formulation of eclipse functions α, the so-called moments A 2m , and their combinations as g 2m = A 2m+2/(A 2m A 2m+4) functions for the basic spherical model. In this paper, I will review the use of these functions in the light curve analysis of eclipsing binaries.  相似文献   

19.
This is a study of the stability of strange dwarfs, superdense stars with a small quark core (M 0core /M ⨀ < 0.017) and an extended crust consisting of atomic nuclei and a degenerate electron gas where the density may be two orders of magnitude greater than the maximum density for white dwarfs. For a given equation of state, the mass, total number of baryons, and radius of strange dwarfs are uniquely determined by the central energy density ρ c and the energy density ρ tr of the crust at the surface of the quark core. Thus, the entire range of variation of ρ c and ρ tr must be taken into account in studying the stability of these configurations. This can be done by examining a series of configurations with a fixed rest mass M 0 (total baryon number) of the quark core and different masses of the crust. In each series, ρ tr ranges from the value for white dwarfs to ρ drip = 4.3∙1011 g/cm3, at which free neutrons are created in the crust. According to the static criterion for stability, stability is lost in an individual series when the mass of the strange dwarf reaches a maximum as a function of ρ tr . Translated from Astrofizika, Vol. 52, No. 2, pp. 325–332 (May 2009).  相似文献   

20.
Kakad  B. 《Solar physics》2011,270(1):393-406
The purpose of the present study is to develop an empirical model based on precursors in the preceding solar cycle that can be used to forecast the peak sunspot number and ascent time of the next solar cycle. Statistical parameters are derived for each solar cycle using “Monthly” and “Monthly smoothed” (SSN) data of international sunspot number (R i). Primarily the variability in monthly sunspot number during different phases of the solar cycle is considered along with other statistical parameters that are computed using solar cycle characteristics, like ascent time, peak sunspot number and the length of the solar cycle. Using these statistical parameters, two mathematical formulae are developed to compute the quantities [Q C] n and [L] n for each nth solar cycle. It is found that the peak sunspot number and ascent time of the n+1th solar cycle correlates well with the parameters [Q C] n and [L] n /[S Max] n+1 and gives a correlation coefficient of 0.97 and 0.92, respectively. Empirical relations are obtained using least square fitting, which relates [S Max] n+1 with [Q C] n and [T a] n+1 with [L] n /[S Max] n+1. These relations predict a peak of 74±10 in monthly smoothed sunspot number and an ascent time of 4.9±0.4 years for Solar Cycle 24, when November 2008 is considered as the start time for this cycle. Three different methods, which are commonly used to define solar cycle characteristics are used and mathematical relations developed for forecasting peak sunspot number and ascent time of the upcoming solar cycle, are examined separately.  相似文献   

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