δScuti变量和相关天体

δScuti型变星是赫罗图上A3-F5区间的主序及其以上的一种周期短于0.3d的单周期或多周期小变幅脉动变星，与它们相关的变星有矮造父变星，γDol变星，蓝离散星，金属线星，A型特殊星，λBoo变星的δDel变星，有些赫比格Ae/Be星也存在类似的脉动，对自1964年起的研究工作进行了系统的总结，给出了1995年后新发现的相关变星数和最可靠的周期变化表，提出应当用双星轨道光时效应来解释实测得到的变星周期变化中的幅度很大的成分，统计表明自转越快变幅越小，因此年轻星团中不可能存在大变幅变星，变幅随周期的分布有3个极大值，最大变由是周期0.17d处的1.0mag，恒星系统内变星的平均周期越短系统的年龄越大，金属丰度也越低。     

On redundant variables in Lagrangian mechanics,with applications to perturbation theory and KS regularization

It is shown that it is possible to make a change of variables in a Lagrangian in such a way that the number of variables is increased. The Euler-Lagrange equations in the redundant variables are obtained in the standard way (without the use of Lagrange Multipliers!). These equations are not independent but they are all valid and consistent. In some cases they are simpler than if the minimum number of variables are used. The redundant variables are supposed to be related to each other by several constraints (not necessarily holonomic), but these constraints are not used in the derivation of the equations of motion. The method is illustrated with the well known Kustaanheimo-Stiefel Regularization. Some interesting applications to perturbation theory are also described.The present research was carried out partially at the University of California and partially at the Jet Propulsion Laboratory under contract NAS7-100 with NASA.Presently Visiting Associate Professor at the University of Texas.     

Andoyer construction for Hill and Delaunay variables

Andoyer variables are well known for the study of rotational dynamics. These variables were derived by Andoyer through a procedure that can be also used to obtain the Hill variables of the Kepler problem. Andoyer construction can also forecast the Delaunay variables which canonicity is then obtained without the use of a generating function.     

Discovery of Four Peculiar Variable Stars

Four stars, GSC 1258-0143, GSC 1986-1665, GSC 3045-0892 and GSC 2983-1597 were found to be new variables during a campaign of CCD photometric monitoring of short-period eclipsing binary stars. The variabilities of these new variables are reported. The main characteristics and probable classifications of the variables are discussed through a preliminary analysis on their light curves. Among these stars, GSC 1258-0143 is classified as a RR Lyr star of sub-type a. Its pulsation period is determined to be about 0.5206 days. The other three stars, are definite variables, but their periods and types of light variations remain unknown.     

New periodic variables from the Hipparcos epoch photometry

Two selection statistics are used to extract new candidate periodic variables from the epoch photometry of the Hipparcos catalogue. The primary selection criterion is a signal-to-noise ratio. The dependence of this statistic on the number of observations is calibrated using about 30 000 randomly permuted Hipparcos data sets. A significance level of 0.1 per cent is used to extract a first batch of candidate variables. The second criterion requires that the optimal frequency be unaffected if the data are de-trended by low-order polynomials. We find 2675 new candidate periodic variables, of which the majority (2082) are from the Hipparcos 'unsolved' variables. Potential problems with the interpretation of the data (e.g. aliasing) are discussed.     

A possible P-L relation for RR-Lyrae variables in globular clusters

A study of the mean photographic magnitudes of RR Lyrae variables in galactic globular clusters has shown that the luminosity of RR-ab variables decreases with period. It is found that RR-ab variables, in the cluster Centauri, whose distances are greater than 8 arc min from the centre of the cluster, are less luminous than such variables seen in the inner region. The possibility of two transition periods for RR-ab variables, one near 0 _. ^d 4 and the other near 0 _. ^d 9, is suggested to explain the sharp boundaries of the instability gap and of the periods of RR Lyrae variables. It is also shown that the inner RR Lyrae variables in Centauri are more massive than the outer ones.     

Polarimetric observations of pulsating variable stars

Results are presented for polarimetric observations of 17 red giants and supergiants, of which nine are long-period Mira variables, five are semiregular variables (SR), and three are slowly fluctuating variables (Lb). Light polarization is detected for eight stars, seven of them for the first time.Translated fromAstrofizika, Vol. 39, No. 3, pp. 385–391, July–September, 1996.     

The Lissajous transformation I. Basics

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.     

Population Synthesis for Mira Variables

By means of a population synthesis code, we investigate the Mira variables. Their birth rate (over 0.65 yr-1) and their number (-130000) in the Galaxy are estimated. For all possible Mira variables, ranges of their initial masses, pulsating periods, mass losses and lifetimes are given. We check our model with the observed Mira variables near the Sun and our results prove to be valid.     

On Pfaff's equations of motion in dynamics; Applications to satellite theory

In this article we study a form of equations of motion which is different from Lagrange's and Hamilton's equations: Pfaff's equations of motion. Pfaff's equations of motion were published in 1815 and are remarkably elegant as well as general, but still they are much less well known. Pfaff's equations can also be considered as the Euler-Lagrange equations derived from the linear Lagrangian rather than the usual Lagrangian which is quadratic in the velocity components. The article first treats the theory of changes of variables in Pfaff's equations and the connections with canonical equations as well as canonical transformations. Then the applications to the perturbed two-body problem are treated in detail. Finally, the Pfaffians are given in Hill variables and Scheifele variables. With these two sets of variables, the use of the true anomaly as independent variable is also considered.     

W UMa-type stars BV Dra conis and BW DRa conis: Photoelectric observations

Photoelectric UBV observations of two W UMa-type stars, BV Dra (ADS 9537A) and BW Dra (ADS 9537B), are presented. New periods and epochs of minima are given for both variables, and magnitudes at maximum light are determined from standard star observations. It is concluded that these variables are quite normal W UMa stars.The two variables are members of the visual binary star ADS 9537, for which the angular separation and the position angle are determined from the photographic observations.On leave of absence from Dept. of Earth Science and Astronomy, College of General Education University of Tokyo.     

A note on the averaging method

When time-averaged equations are used to discuss the secular behavior of dynamical systems, the action-angle variables conjugate to the action variables of the unperturbed motion of the system should be chosen as dependent variables; otherwise, the results are not correct.Presented at the Division of Dynamical Astronomy Meeting of the American Astronoming Society, Chapel Hill, N.C., U.S.A., December 4, 1976.     

Canonical Floquet theory

Classical Floquet theory is reviewed with careful attention to the case of repeated eigenvalues common in Hamiltonian systems. Floquet theory generates a canonical transformation to modal variables if the periodic matrix can be made symplectic at the initial time. It is shown that this symplectic normalization can always be carried out, again with careful attention to the degenerate case. The periodic modal vectors and canonical modal variables can always be chosen to be purely real. It is possible to introduce real valued action-angle variables for all modes. Physical interpretation of the canonical degenerate normal modal variables are offered. Finally, it is shown that this transformation enables canonical perturbation theory to be carried out using Floquet modal variables.     

Increased accuracy of computations in the main satellite problem through linearization methods

The set of canonical redundant variables previously introduced by the first author is derived from Cartesian coordinates in a simplified form which allows the reduction of the Kepler problem to four harmonic oscillators with unit frequency. The coordinates are defined to be the direction cosines of the position of the particle along with the inverse of its distance. True anomaly is the new independent variable. The behavior of this new transformation is studied when applied to the numerical integrations of the main problem in satellite theory. In particular, computation time and accuracy of orbits in the new variables are compared with those in K-S and Cartesian variables. It is noteworthy that for high eccentricities the new variables require the least computation time for comparable accuracy, regardless of the integration scheme.     

Satellite vibration-rotation motions studied via canonical transformations

Coupled vibration-rotation motion of a satellite is considered using a perturbation theory based on the Lie transformation method. Short-period oscillating terms are removed from the Hamiltonian function. The transformed damping forces directly affect rotational variables which were not directly influenced in the original variables. Motions and stability are more easily studied in the new variables. A dual-spin spacecraft model is used as an example; results for the usual nonresonant case are identical with the energy-sink method. Resonance cases produce a wealth of new dynamical phenomena. This canonical method extends and unifies various approximation methods in attitude dynamics.     

Pulsation mode and period-luminosity relation of Mira variables

Employing recent TP-AGB synthesis, we have carried out a detailed study on pulsation mode and period-luminosity relation of Mira variables by means of a population synthesis code. The theoretical criterion for selecting Mira variables has a great effect on the periods distribution. Compared with the observations, the distributions of the periods and the period-luminosity relations support that Mira variables are the fundamental mode pulsators.     

Remark on integrable Hamiltonian systems

An extension ton degrees of freedom of the fact is established that forn=1 the time and the energy constant are canonically conjugate variables. This extension is useful in some cases to get action-angle variables from the general solution of a given integrable Hamiltonian system. As an example the Delaunay variables are proved to be canonical.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

Long-term variations and periods of Mira stars from ROTSE-IIId

We have studied the long-term variations of Mira type variables observed with Robotic Optical Transient Search Experiment telescope (ROTSE-IIId) between 2004 and 2009 located at TÜB?TAK National Observatory (TUG) in Antalya, Turkey. The actual pulsation periods, variability amplitudes, epochs of maximums and light curves of selected 70 Mira type variables already defined in the SIMBAD database were investigated. In these variables, 17 periods are identified for the first time.     

Hipparcos parallaxes for Mira-like long-period variables

This paper concerns the calibration of the K period–luminosity relation for Mira variables using Hipparcos parallaxes. K magnitudes are available for 255 Mira-like variables which were observed by Hipparcos . Period–luminosity zero-points are evaluated for various subgroups of data. The best solution for oxygen-rich Miras, which uses 180 stars, omitting the short-period red group (which had different kinematics from the short-period blue stars) and the low-amplitude variables, provides a zero-point of     which implies a distance modulus for the Large Magellanic Cloud of     or perhaps slightly greater if a metallicity correction is required, in good agreement with the value derived from Cepheids. The zero-point of the period–luminosity relation for carbon stars is briefly discussed.
Linear diameters are derived for red variables with measured angular diameters and parallaxes, and are used to examine the long-standing question of the pulsation mode(s) of these stars. Evidence is presented to suggest that most of them are pulsating in the same mode and, if published model atmospheres are correct, this is probably the first overtone. Some discussion is given of sequences in the period–luminosity and period–colour diagrams and their bearing on the pulsation mode problem.     

Perturbations of the Kepler Problem in Global Coordinates

The usual action-angle variables for the Kepler Problem (the Delaunay variables) are not globally defined, leaving out some orbits (circular orbits or those lying on the xy-plane). Moreover they are trascendental functions of the physical variables, making it quite difficult to write the perturbed Hamiltonian. The way-out proposed here is to pass to a 8-dimensional rank-6 Poisson manifold, that is, to parametrize the state of the Kepler Problem with two 4-dimensional vectors mutually orthogonal and of equal norm. This revised version was published online in July 2006 with corrections to the Cover Date.