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  • 1
    Electronic Resource
    Electronic Resource
    Construction of a general planetary theory of the first order (1973)
    Springer
    Celestial mechanics and dynamical astronomy 8 (1973), S. 335-355 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract All the necessary formulae for constructing a general solution for the motion of a planet, in rectangular coordinates, at the first order of the disturbing masses, in purely literal form in eccentricities and inclinations, are given. The authors present the transformation formulae in the two-body problem which give the correspondence between the constants of integration introduced in the theory and the classical keplerian elements. The practical elaboration of the algorithm and some partial results for the couple of planets Jupiter and Saturn are described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01227805
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  • 2
    Electronic Resource
    Electronic Resource
    Perturbation theory in rectangular coordinates (1978)
    Springer
    Celestial mechanics and dynamical astronomy 18 (1978), S. 319-336 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract For treating the perturbed two-body problem in rectangular coordinates a new method is developed. The method is based on the reduction of the variational equations of the two-body problem with arbitrary elements to the Jordan system. The equations of perturbed motion rewritten in the quasi-Jordan form are subjected to a transformation excluding fast variables and leading to a system governing the long term evolution of motion. The method may be easily extended to the problem of the heliocentric motion of the major planets. For performing this method on computer it is suitable to use facilities of Poissonian and Keplerian processors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230346
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  • 3
    Electronic Resource
    Electronic Resource
    Astronomical measurements and coordinate conditions in relativistic celestial mechanics (1979)
    Springer
    Celestial mechanics and dynamical astronomy 20 (1979), S. 329-342 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Determination of dynamical effects from the equations of motion and calculation of ephemerides in terms of measurable quantities on the basis of the equations of light should be performed in one and the same coordinate system. The choice of coordinate system is arbitrary. For illustration we consider coplanar circular motions of the Earth and one of the inner planets in the solar gravitational field described by the generalized three-parametric Schwarzschild metric. Specific values of the metric parameters characterize the adopted gravitational theory, as well as a definite coordinate system (for example, isotropic or ‘standard’ coordinates). Coordinates of the planets and radii of the orbits are coordinate-dependent quantities and cannot be directly reconciled with measurable quantities such as the round-trip transit times of radar signals or the angular distance between the planet and the distant fixed source (quasar). These ephemeris data may be calculated in terms of the initial measured values independently of the employed coordinate system. Relativistic ephemeris corrections should be taken into account both in radar reflection measurements and astrometric observations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230402
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  • 4
    Electronic Resource
    Electronic Resource
    New approach to determining planetary perturbations in lunar theory (1982)
    Springer
    Celestial mechanics and dynamical astronomy 26 (1982), S. 77-81 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The technique of the general planetary theory has been proposed for constructing a theory of motion of the Moon. This method enables us to elaborate the consistent theory of motion of the principal planets and the Moon, which is of particular importance for determining planetary perturbations in lunar motion. As an initial approximation for lunar motion, an intermediate orbit generalizing the Hill's variational curve has been built. This orbit includes all solar and planetary inequalities independent of eccentricities and inclinations of the Moon, Sun and planets. In calculating this orbit, the motion of the principal planets in quasi-periodic intermediate orbits has been taken into account. This solution was produced with the aid of the Universal Poissonian Processor (UPP) elaborated in the Institute for Theoretical Astronomy (Leningrad).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01233186
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  • 5
    Electronic Resource
    Electronic Resource
    G. N. Duboshin (1986)
    Springer
    Celestial mechanics and dynamical astronomy 39 (1986), S. 114-115 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230843
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  • 6
    Electronic Resource
    Electronic Resource
    Secular perturbations in general planetary theory (1975)
    Springer
    Celestial mechanics and dynamical astronomy 11 (1975), S. 131-138 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Description / Table of Contents: qAбстракт На основе общей планетной теории определены в полиномиальной форме вековые возмущения в движении восьми болших планет (за исключением Плутона). Результаты приведены в таблицах. В правой части вековой системы учитывались линейные члены второго порядка относительно масс и нелинейные члены первого порядка с точностью до пятой (и частично седьмой) степени включительно относительно эксцентриситетов и наклонов. Вычисления проводились с помошью системы аналитических оперчций на ЭВМ над степенными рядами с комплексными коэффициентами.
    Notes: Abstract Based on a general planetary theory, the secular perturbations in the motion of the eight major planets (excluding Pluto) have been derived in polynomial form. The results are presented in the tables. The linear terms of second order with respect to the planetary masses and the nonlinear terms of first order up to the fifth (and partly seventh) degree with respect to eccentricities and inclinations were taken into account in the right-hand members of the secular system. Calculations were carried out by computer with the use of a system that performed analytic operations on power series with complex coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01228740
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  • 7
    Electronic Resource
    Electronic Resource
    Gleb Alexandrovich Chebotarev (1913–1975) (1975)
    Springer
    Celestial mechanics and dynamical astronomy 12 (1975), S. ii 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01595386
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  • 8
    Electronic Resource
    Electronic Resource
    Analytical methods for the orbits of artificial satellites of the Moon (1971)
    Springer
    Celestial mechanics and dynamical astronomy 3 (1971), S. 197-221 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The motion of a close artificial satellite of the Moon is considered. The principal perturbations taken into account are caused by the nonsphericity of the Moon and the attraction of the Earth and the Sun. To begin with, the expansions of the disturbing functions due to the nonsphericity of the primary body and the action of the disturbing mass-point body have been derived. The second expansion is produced in terms of the Keplerian elements of a satellite and the spherical coordinates of the disturbing body. Both expansions are valid for an arbitrary reference plane. The motion of a satellite of the Moon is studied in the selenocentric coordinate system referred to the Lunar equator and rotating with respect to the fixed ecliptic system. However, the coordinate exes in the equatorial plane are chosen so that the angular speed of rotation of the system is small. The motion of the satellite is described by means of the contact elements which enable one to utilize the conventional Lagrange's planetary equations and may be regarded as the generalization of the notion of the osculating elements to the case of the disturbing function depending not only o the coordinates and the time but on the velocities as well. Two methods are proposed to represent the motion of Lunar satellites over long intervals of time: the von Zeipel method and the Euler method of analytical integration with application of the variation-of-elements technique at every step of integration. The second method is exposed in great detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01228033
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  • 9
    Electronic Resource
    Electronic Resource
    Encounter in the keplerian field: Analytical treatment (1990)
    Springer
    Celestial mechanics and dynamical astronomy 49 (1990), S. 133-144 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In extending the results of Henon and Petit (1986) an algorithm is suggested for constructing the series representing the general encounter-type solution of the spatial eccentric Hill's problem. The series are arranged in powers of the eccentricity E of Hill's problem and two integration constants e and k characterizing eccentricity and inclination of the relative motion. A particular non-periodic solution of Henon and Petit corresponding to E = e = k = 0 is taken as an intermediary. The perturbations to this solution are constructed similar to the lunar theory of Hill and Brown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00050710
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  • 10
    Electronic Resource
    Electronic Resource
    Specialized celestial mechanics systems for symbolic manipulation (1988)
    Springer
    Celestial mechanics and dynamical astronomy 45 (1988), S. 149-162 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01228996
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