首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 15 毫秒
1.
A new approach to the librational solution of the Ideal Resonance Problem has been devised--one in which a non-canonical transformation is applied to the classical Hamiltonian to bring it to the form of the simple harmonic oscillator. Although the traditional form of the canonical equations of motion no longer holds, a quasi-canonical form is retained in this single-degree-of-freedom system, with the customary equations being multiplied by a non-constant factor. While this makes the resulting system amenable to traditional transformation techniques, it must then be integrated directly. Singularities of the transformation in the circulation region limit application of the method to the librational region of motion.Computer-assisted algebra has been used in all three stages of the solution to fourth order of this problem: using a general-purpose FORTRAN program for the quadratic analytical solution of Hamiltonians in action-angle variables, the initial transformation is carried out by direct substitution and the resulting Hamiltonian transformed to eliminate angular variables. The resulting system of differential equations, requiring the expected elliptic functions as part of their solution, is currently in the process of being integrated using the LISP-based REDUCE software, by programming the required recursive rules for elliptic integration.Basic theory of this approach and the computer implementation of all these techniques is described. Extension to higher order of the solution is also discussed.  相似文献   

2.
We present our calculations of the spectrum and oscillator strengths for the 4f7?(4f65d+4f66s) Eu III transitions. The calculations were performed with Cowan's RCN-RCG-RCE codes in the single-configuration approximation. A comparison of computed level lifetimes with experimental data for three levels shows that the scale of theoretical oscillator strengths could be overestimated by a factor of 3. The theoretical oscillator strengths of red Eu III lines are two orders of magnitude smaller than their astrophysical oscillator strengths derived by Ryabchikova et al. (1999) from the condition of ionization balance. The new oscillator strengths were tested by analyzing the Eu abundance using Eu II and Eu III lines in the spectra of hot peculiar stars (α2 CVn is a typical representative) and cool peculiar stars (β CrB is a typical representative). First, we computed non-LTE corrections, which proved to be significant for α2 CVn. We also analyzed the Eu II λ6645.11-Å line as well as ultraviolet and optical Eu III lines. We show that the new oscillator strengths together with the non-LTE corrections allow the contradiction between the Eu abundances derived by Ryabchikova et al. (1999) separately from optical Eu II and Eu III lines in α2 CVn to be resolved. The new Eu abundance, log(Eu/N tot)=?6.5, also faithfully describes the blended near-ultraviolet resonance Eu III lines. Using the new Eu III oscillator strengths to analyze the spectrum of the cool Ap star β CrB, we found a significant deviation of the n(Eu II)/n(Eu III) ratio from its equilibrium value. For a chemically homogeneous model atmosphere, to obtain the observed intensity of the Eu III λ 6666.35-Å line, the Eu abundance must be increased by two orders of magnitude compared to that required to describe the Eu II λ 6645.11-Å line. We discuss the possibility of explaining the observed intensities of Eu II and Eu III lines in the spectrum of β CrB by the presence of an inhomogeneous atmosphere with Eu concentrated in its uppermost layers. In such atmospheres, the role of non-LTE effects becomes dominant.  相似文献   

3.
We obtained three-dimensional interpolated portraits for the radial and torsional oscillations of fragments of 12 sunspots in the form of deviations of their polar coordinates from drift as functions of the time and distance from the sunspot center. We performed a wavelet analysis of the two orthogonal components and determined the dominant oscillation modes; the period varies between 40 and 100 min for different sunspots. We revealed two types of dominant modes, one is associated with the sunspot and the other is associated with its surrounding pores: the central-mode frequency depends on the maximum field strength of the sunspot and decreases from its center toward the boundary, while the peripheral-mode frequency depends on the heliographic latitude and decreases toward the sunspot boundary from the far periphery. We revealed radial variations in frequency and amplitude with a spatial period of 0.8 sunspot radius. The types of dominant modes and the radial variations in oscillation parameters are linked with the subphotospheric structure of an active region—with two types of spiral waves and concentric magnetic-field waves. We estimated the mean pore oscillation energy to be ～1030 erg and found a singular oscillator with a mean energy of ～1031 erg in the penumbra at a distance of 0.8 sunspot radius. We argue that the singular penumbra oscillator is the source of solar flares.  相似文献   

4.
We propose a new method based on Lie transformations for simplifying perturbed Hamiltonians in one degree of freedom. The method is most useful when the unperturbed part has solutions in non-elementary functions. A non-canonical Lie transformation is used to eliminate terms from the perturbation that are not of the same form as those in the main part. The system is thus transformed into a modified version of the principal part. In conjunction with a time transformation, the procedure synchronizes the motions of the perturbed system onto those of the unperturbed part.A specific algorithm is given for systems whose principal part consists of a kinetic energy plus an arbitrary potential which is polynomial in the coordinate; the perturbation applied to the principal part is a polynomial in the coordinate and possibly the momentum.We demonstrate the strategy by applying it in detail to a perturbed Duffing system. Our procedure allow us to avoid treating the system as a perturbed harmonic oscillator. In contrast to a canonical simplification, our method involves only polynomial manipulations in two variables. Only after the change of time do we start manipulating elliptic functions in an exhaustive discussion of the flows.  相似文献   

5.
In this investigation, a procedure is described for extending the application of canonical perturbation theories, which have been applied previously to the study of conservative systems only, to the study of non-conservative dynamical systems. The extension is obtained by imbedding then-dimensional non-conservative motion in a 2n-dimensional space can always be specified in canonical form, and, consequently, the motion can be studied by direct application of any canonical perturbation method. The disadvantage of determining a solution to the 2n-dimensional problem instead of the originaln-dimensional problem is minimized if the canonical transformation theory is used to develop the perturbation solution. As examples to illustrate the application of the method, Duffing's equation, the equation for a linear oscillator with cubic damping and the van der Pol equation are solved using the Lie-Hori perturbation algorithm.This research was supported by the Office of Naval Research under Contract N00014-67-a-0126-0013.  相似文献   

6.
A new analytic approach to the solution of the Sitnikov Problem is introduced. It is valid for bounded small amplitude solutions (z max = 0.20) (in dimensionless variables) and eccentricities of the primary bodies in the interval (–0.4 < e < 0.4). First solutions are searched for the limiting case of very small amplitudes for which it is possible to linearize the problem. The solution for this linear equation with a time dependent periodic coefficient is written up to the third order in the primaries eccentricity. After that the lowest order nonlinear amplitude contribution (being of order z 3) is dealt with as perturbation to the linear solution. We first introduce a transformation which reduces the linear part to a harmonic oscillator type equation. Then two near integrals for the nonlinear problem are derived in action angle notation and an analytic expression for the solution z(t) is derived from them. The so found analytic solution is compared to results obtained from numeric integration of the exact equation of motion and is found to be in very good agreement. CERN SL/AP  相似文献   

7.
A model oscillator for irregular stellar variability presented by Tanaka and Takeuti has only one singularity in the original form. We show it has three different types of singular points when damping terms are ignored. The nonlinear pulsation of Baker's one-zone stellar models is discussed in comparison with the properties of the Tanaka-Takeuti oscillator.  相似文献   

8.
The theoretical estimates of the oscillator strengths by Kirby, Saxon and Liu (1979) for theA II2 — XΣ2 system of the MgH molecule are compared with the solar photospheric results. It is found that the two results are in reasonable agreement.  相似文献   

9.
An analytical study of the elliptic Sitnikov restricted four-body problem when all the primaries as source of same radiation pressure is presented. We find a solution, which is valid for small bounded oscillations in case of moderate eccentricity of the primary. We have linearized the equation of motion to obtain the Hill’s type equation. Using the Courant and Snyder transformation, Hill’s equation transformed into harmonic oscillator type equation. We have used the Lindstedt-Poincare perturbation method and again we have applied the Courant and Snyder transformation to obtain the final result.  相似文献   

10.
The Newtonian differential equations of motion for the two-body problem can be transformed into four, linear, harmonic oscillator equations by simultaneously applying the regularizing time transformation dt/ds=r and the Kustaanheimo-Stiefel (KS) coordinate transformation. The time transformation changes the independent variable from time to a new variables, and the KS transformation transforms the position and velocity vectors from Cartesian space into a four-dimensional space. This paper presents the derivation of uniform, regular equations for the perturbed twobody problem in the four-dimensional space. The variation of parameters technique is used to develop expressions for the derivatives of ten elements (which are constants in the unperturbed motion) for the general case that includes both perturbations which can arise from a potential and perturbations which cannot be derived from a potential. These element differential equations are slightly modified by introducing two additional elements for the time to further improve long term stability of numerical integration.Originally presented at the AAS/AIAA Astrodynamics Specialists Conference, Vail, Colorado, July 1973  相似文献   

11.
Kustaanheimo–Stiefel (KS) transformation depends on the choice of some preferred direction in the Cartesian 3D space. This choice, seldom explicitly mentioned, amounts typically to the direction of the first or the third coordinate axis in Celestial Mechanics and atomic physics, respectively. The present work develops a canonical KS transformation with an arbitrary preferred direction, indicated by what we call a defining vector. Using a mix of vector and quaternion algebra, we formulate the transformation in a reference frame independent manner. The link between the oscillator and Keplerian first integrals is given. As an example of the present formulation, the Keplerian motion in a rotating frame is re-investigated.  相似文献   

12.
Using configuration interaction wavefunctions, the excitation thresholds for the twelve lowest terms arising from the configurations 1s 22s 22p 2, 1s 22s2p 3, and 1s 22p 4 of Mgvii have been calculated. The same wavefunctions have been used to calculate the oscillator strengths for the optically allowed transitions in Mgvii. Combining these results with earlier published values for Oiii, Nev, Siix, Caxv, and Fexxi, oscillator strengths for other ions in the carbon isoelectronic sequence (F through Ni) have been predicted. The predicted values are found to be slightly lower when compared with the available published results.  相似文献   

13.
Energy levels and oscillator strengths among the 27 fine-structure levels belonging to the (ls22s2)2p6, 2p53s, 2p53p and 2p53d configurations of the neon-like iron ion have been calculated using three atomic structure codes RCN/RCG, AUTOSTRUCTURE (AS) and GRASP. Relativistic corrections of the wave functions are taken into account in the RCN/RCG calculation. The results agree well with the available experimental and theoretical data. The accuracy of the three codes is analysed.  相似文献   

14.
R. Glass 《Solar physics》1982,78(1):29-38
We have used configuration interaction wavefunctions to calculate energy levels, wavelengths, oscillator strengths and transition probabilities for spin-orbit electric dipole transitions between the 2s 2, 2s2p, and 2p 2 states in beryllium-like ions (Z = 6–10). Some significant differences with previous calculations are obtained. A common set of radial functions is used.  相似文献   

15.
The production of discrete line and broad-band extinction by small interstellar oxide and silicate particles is discussed quantitatively. Restrictions on particle size and refractive index that are required to produce ‘pure’ absorption features are reviewed. The relationship between optical depth in interstellar extinction and absorption coefficients for bulk materials is used to reach some general conclusions concerning the diffuse interstellar features, VUV extinction and the composition of interstellar dust. It is noted that charge transfer bands of ions such as Fe3+ may be detectable in the VUV spectrum of dust. Several effects that lead to the enhancement of oscillator strength by 103–104 in small particles are discussed.  相似文献   

16.
When the perturbation affecting a Keplerian motion is proportional tor –n (n3), a canonical transformation of Lie type will convert the system into one in which the perturbation is proportional tor –2. Because it removes parallactic factors, the transformation is called the elimination of the parallax.In the main problem for the theory of artificial satellites, the elimination of the parallax has been conducted by computer to order 4. The first order in the reduced system may now be integrated in closed form, thereby revealing the fundamental property of the first-order intermediary orbits in line with Newton's Propositio XLIV.Extension beyond order 1 leads to identify a new class of intermediaries for the main problem in nodal coordinates, namely the radial intermediaries.The technique of smoothing a perturbation prior to normalizing the perturbed Keplerian system, of which the elimination of the parallax is an instance, is applied to derive the intermediaries in nodal coordinates proposed by Sterne, Garfinkel, Cid-Palacios and Aksnes, and to find the canonical diffeomorphisms which relate them to one another and to the radial intermediaries.  相似文献   

17.
The 1s 2-1s6p H– auto-ionization resonance has been observed as a diffuse interstellar line in several highly reddened O and B stars. The identification based on its wavelength has been confirmed by its equivalent width in HD 183143. The addition of the 1s 2-1snp diffuse-line series raises the total H– oscillator strength of absorption to a value close to 2.  相似文献   

18.
A new canonical transformation is proposed to handle elliptic oscillators, that is, Hamiltonian systems made of two harmonic oscillators in a 1-1 resonance. Lissajous elements pertain to the ellipse drawn with a light pen whose coordinates oscillate at the same frequency, hence their name. They consist of two pairs of angle-action variables of which the actions and one angle refer to basic integrals admitted by an elliptic oscillator, namely, its energy, its angular momentum and its Runge-Lenz vector. The Lissajous transformation is defined in two ways: explicitly in terms of Cartesian variables, and implicitly by resolution of a partial differential equation separable in polar variables. Relations between the Lissajous variables, the common harmonic variables, and other sets of variables are discussed in detail.  相似文献   

19.
We demonstrate, using a sample of high quality spectra, that the average equivalent width ratio of the unsaturated R(0) and R(1) lines of the CN B2Σ+ – X2Σ+ (0, 0) band near 3875 Å equals π instead of 3.73 – calculated for the CMBR temperature T = 2.725 K and the already published oscillator strengths of both transitions, i.e. the excitation temperature of CN is slightly higher than it should be expected if CMBR is the only excitation mechanism. Taking into account the saturation effects by means of profile fitting during the column density calculations does not remove the revealed temperature excess. Possible interpretations of the effect are discussed (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

20.
The dipole moment of the A2Πu?x2Πg transition of O+2 is calculated as a function of internuclear distance using ab initio methods. The band absorption oscillator strengths and band transition probabilities of the second negative system are derived and the resulting lifetimes are compared with experimental data. The high-lying v″ levels of the ground state may decay into low-lying v′ levels of the excited state. The corresponding radiative lifetimes are calculated.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号