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1.
《天文和天体物理学研究(英文版)》2016,(9)
Celestial mechanics has been a classical field of astronomy. Only a few astronomers were in this field and not so many papers on this subject had been published during the first half of the 20 thcentury.However, as the beauty of classical dynamics and celestial mechanics attracted me very much, I decided to take celestial mechanics as my research subject and entered university, where a very famous professor of celestial mechanics was a member of the faculty. Then as artificial satellites were launched starting from October 1958, new topics were investigated in the field of celestial mechanics. Moreover, planetary rings,asteroids with moderate values of eccentricity, inclination and so on have become new fields of celestial mechanics. In fact I have tried to solve such problems in an analytical way. Finally, to understand what gravitation is I joined the TAMA300 gravitational wave detector group. 相似文献
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One of the main problems in celestial mechanics is the management of long developments in Fourier or Poisson series used to describe the perturbed motion in the planetary system.In this work we shall develop a software package that is suitable for managing these objects. This package includes algorithms to obtain the inverse of the distance based on an iterative method, a set of integration algorithms according to several sets of temporal variables.This paper contains a comparative study on the use of the true, eccentric, and elliptic anomalies in semi-analytical methods on celestial mechanics. 相似文献
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In different problems of celestial mechanics it is often necessary to estimate the effect of the truncated higher harmonics of the gravity potential on the motion of a test particle. As a rule the magnitude of this effect is strictly connected with the gravitational acceleration, i.e. partials of the potential. But the mathematical theory of attraction gives the estimations for the potential itself. However, as far as the general term of development (spherical harmonic) possesses a definite reserve of the smoothness, we have succeeded in passing from potential estimations to its partials estimations. The mathematical method based on a multidimensional generalization (obtained here) of an inequality by BERNSTEIN is used. By the way several inequalities connecting different norms of spherical harmonics are proved. 相似文献
5.
Franz Spirig 《Celestial Mechanics and Dynamical Astronomy》1980,21(2):199-201
The topic presented here is not really a topic of celestial mechanics, because a dissipative system is considered, and dissipative systems do not occur in celestial mechanics at least if drag is not taken into account. Only in the theoretical background of Baumgarte-Stiefel stabilization dissipative systems become important. The only justification is that, in order to establish the result, a tool, namely the method of averaging, is used here which is a good tool for many problems of celestial mechanics too.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978. 相似文献
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A. S. Baranov 《Celestial Mechanics and Dynamical Astronomy》2003,87(3):241-256
For the complete system of biharmonic functions a suitable representation in spheroidal coordinates is found. It is used for expanding the distance between two arbitrary gravitating points and its inverse quantity in appropriate series. Such expansions can be of interest and useful in a number of problems of celestial mechanics and stellar dynamics. 相似文献
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V. A. Brumberg S. V. Tarasevich N. N. Vasiliev 《Celestial Mechanics and Dynamical Astronomy》1988,45(1-3):149-162
Construction and application of the current high accuracy analytical theories of motion of celestial bodies necessitates the development of specialized software for the implementation of analytical algorithms of celestial mechanics. This paper describes a typical software package of this kind. This package includes a universal Poisson processor for the rational functions of many variables, a tensorial processor for purposes of relativistic celestial mechanics, a Keplerian processor valid for the solutions of the two body problem in the form of a Poisson series, Taylor expansions in powers of time and closed expressions, and an analytical generator of celestial mechanics functions, facilitating the immediate implementation of the present analytical methods of celestial mechanics. The package is completed with a numerical-analytical interface designed, in particular, for the fast evaluation of the long Poisson series. 相似文献
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We present an algorithm to compute the incomplete elliptic integral of a general form. The algorithm efficiently evaluates some linear combinations of incomplete elliptic integrals of all kinds to a high precision. Some numerical examples are given as illustrations. This enables us to numerically calculate the values and the partial derivatives of incomplete elliptic integrals of all kinds, which are essential when dealing with many problems in celestial mechanics, including the analytic solution of the torque-free rotational motion of a rigid body around its barycenter. 相似文献
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With a new theory on the 1PN celestial mechanics recently developed by Damour, Soffel and Xu (1991,1992,1993,1994), definitions
and expressions of the 1PN spin angular momentum are investigated and analysed. The total spin angular momentum of a system
of extended bodies such as the solar system is calculated and expressed as the function of local parameters and observables
under reasonable assumptions, which would find its application in the evolution and dynamics of systems of celestial bodies.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
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P. Moore 《Celestial Mechanics and Dynamical Astronomy》1978,17(3):281-297
Lambert and Watson (1976) examine the family of symmetric linear multistep methods for the special second-order initial value problem, and connect the property of symmetry with a property of periodicity. The problems of celestial mechanics may be formulated as second-order initial value problems, but these frequently incorporate the first derivative explicity. It is common for such equations to be reduced to a system of first-order equations. Thus motivated, we utilize ideas from the aforementioned paper to determine the family of linear multistep methods for first-order initial value problems that possess an analogous property of periodicity. This family of orbitally stable methods is illustrated by examining the regularized equations of motion of an artificial earth satellite in an oblate atmosphere. 相似文献
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Liam M. Healy 《Celestial Mechanics and Dynamical Astronomy》2003,85(2):175-207
The Lie transfer map method may be applied to orbit propagation problems in celestial mechanics. This method, described in another paper, is a perturbation method applicable to Hamiltonian systems. In this paper, it is used to calculate orbits for zonal perturbations to the Kepler (two-body) problem, in both expansion in the eccentricity and closed form. In contrast with a normal form method like that of Deprit, the Lie transformations here are used to effect a propagation of phase space in time, and not to transform one Hamiltonian into another. 相似文献
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Cl. Froeschlé 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):95-115
After a presentation of Lyapunov characteristic exponents (LCE) we recall their basic properties and numerical methods of computation. We review some numerical computations which are concerned with LCEs and mainly related to celestial mechanics problems. 相似文献
15.
Victor Szebehely 《Celestial Mechanics and Dynamical Astronomy》1987,43(1-4):139-145
The concept of finite predictability of gravitational many-body systems is related to the non-deterministic nature of celestial mechanics and of dynamics, in general. The basic, fundamental reasons for the uncertainty of predictions are as follows: (1) the initial conditions are known only approximately since they are obtained either from observations or from approximate computations; (2) the equations of motion given by a selected model describe the actual system only approximately; (3) the physical constants of the dynamical system have error limits; (4) the differential equations of motion are non-integrable and numerical integration methods must be used for solution, generating errors in the final result at every integration step.In addition to these reasons, mostly depending on our techniques, there are some more fundamental reasons depending on the nature of the dynamical system investigated. These are the appearance of regions of instability, non-integrability and chaotic motion.Details, effects and controls of these regions for finite predictability are discussed for various dynamical systems of importance in celestial mechanics with special emphasis on planetary systems. 相似文献
16.
Ivan R. King 《Celestial Mechanics and Dynamical Astronomy》1974,9(3):349-357
This review attempts to place stellar dynamics in relation to other dynamical fields and to describe some of its important techniques and present-day problems. Stellar dynamics has some parallels, in increasing order of closeness, with celestial mechanics, statistical mechanics, kinetic theory, and plasma theory; but even in the last case the parallels are not very close. Stellar dynamics describes, usually through distribution functions, the motions of a large number of bodies as they all act on each other gravitationally. To a good approximation each star can be considered to move in the smoothed-out field of all the others, with random encounters between pairs of stars adding a slow statistical change to these smooth motions. Smooth-field dynamics has a well-developed theory, and the state of smooth stellar systems can be described in some detail. The ‘third integral’ presents an outstanding problem, however. Stellar encounters also have a well-developed theory, but close encounters and encounters of a single star with a binary pose serious problems for the statistical treatment. Star-cluster dynamics can be approached through a theory of smooth-field dynamics plus changes due to encounters, or alternatively through numerical simulations. The relation between the two methods is not yet close enough. The dynamical evolution of star clusters is still not fully understood. 相似文献
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A study has been made of a dynamical system composed of a pendulum and a harmonic oscillator, in order to show the remarkable resemblance with many classical celestial mechanics problems, in particular the restricted three-body problem. It is shown that the well-known investigations of periodic orbits can be applied to the present dynamics problem.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 27–September 2, 1972. 相似文献
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Arnold Rom 《Celestial Mechanics and Dynamical Astronomy》1970,1(3-4):301-319
A software package for Mechanized Algebraic Operations (MAO) is described. With MAO one is able to manipulate on the computer Poisson series in literal form. The system is operational; it has application in the fields of celestial mechanics, astrodynamics, and nonlinear mechanics. Besides describing the system, the present paper suggests various techniques to prepare problems such that they lend themselves for an automated treatment with MAO. Optimized implementation of the general subroutines is discussed. 相似文献
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The three-body problem is the most celebrated problem of classical celestial mechanics that is not soluble in finite terms by means of any of the functions at present known to mathematical analysis.In the modern celestial mechanics is known as the main problem of the theory of the satellites and it too is not soluble in finite terms.The low-altitude satellites, which move along close orbits, are encountered. They may be done case in which the centers of masses of the bodies form an isosceles or nearly equilaterial triangle with the center of the oblate planet, and another one in which they are always located in the straight line.We study the planar problem, in which the satellites move along close orbits in a plane which forms an angle with the equatorial plane of the planet; the oblateness of which exercises a great effect. The practical importance of this problem arises from its applications.Differential equations of motion are given and particular solutions are shown to exist when the centers of masses are at the vertices of a nearly equilateral triangle or are collinear. Of course, if we take the first two terms of the Legendre series with =0, we shall obtain the same results as Aksenov (1988). 相似文献
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叙述了与Astrod工程有关的相对论天体力学基础内容。包括相对论天体力学、广义相对论基本原理、PPN方法体系、PPN多体问题、PPN二体问题。高阶PN二体问题等 相似文献