The Experts below are selected from a list of 201 Experts worldwide ranked by ideXlab platform

V. A. Brumberg - One of the best experts on this subject based on the ideXlab platform.

  • Celestial Mechanics: Past, present, future
    Solar System Research, 2013
    Co-Authors: V. A. Brumberg
    Abstract:

    Over all steps of its development Celestial Mechanics has played a key role in solar system researches and verification of the physical theories of gravitation, space and time. This is particularly characteristic for Celestial Mechanics of the second half of the 20th century with its various physical applications and sophisticated mathematical techniques. This paper is attempted to analyze, in a simple form (without mathematical formulas), the Celestial Mechanics problems already solved, the problems that can be and should be solved more completely, and the problems still waiting to be solved.

  • Relativistic Celestial Mechanics on the verge of its 100 year anniversary
    Celestial Mechanics and Dynamical Astronomy, 2010
    Co-Authors: V. A. Brumberg
    Abstract:

    As we are now approaching 2015, both the General Relativity Theory (GRT) and the relativistic Celestial Mechanics based on it will soon arrive at their 100 year anniversaries. There is no border between Newtonian and relativistic Celestial Mechanics. The five-decade period of intensive development of Celestial Mechanics in the second half of the 20th century left many interesting techniques and problems uncompleted. This lecture reviews some problems of Newtonian and relativistic Celestial Mechanics worthy of further investigation. Concerning Newtonian Mechanics, these problems include general solution of the three-body problem by means of the series of polynomials, construction of the short-term and long-term theories of motion using the fast converging elliptic function expansions, and representation of the rotation of the planets in the form compatible with the General Planetary Theory reducing the problem to the combined secular system for translatory motion and rotation. Relativistic problems considered here include the determination of the main relativistic effects in the motion of a satellite, e.g. the Moon, and in the rotation of the primary planet using the Newtonian theories of motion and rotation combined with the relativistic transformation of the reference systems, the use of the linearized weak-field GRT metric as a basis of relativistic Celestial Mechanics in the post-Newtonian approximation, and the motion of the Solar System bodies at the cosmological background in the framework of the basic cosmological models. The exposition of the chosen relativistic problems is preceded by reminding the basic features of relativistic Celestial Mechanics with discussing some present tendencies concerning the Parametrized Post-Newtonian formalism, International Astronomical Union resolutions, and standardization of the GRT routines.

  • relativistic Celestial Mechanics on the verge of its 100 year anniversary brouwer award lecture
    Celestial Mechanics and Dynamical Astronomy, 2010
    Co-Authors: V. A. Brumberg
    Abstract:

    As we are now approaching 2015, both the General Relativity Theory (GRT) and the relativistic Celestial Mechanics based on it will soon arrive at their 100 year anniversaries. There is no border between Newtonian and relativistic Celestial Mechanics. The five-decade period of intensive development of Celestial Mechanics in the second half of the 20th century left many interesting techniques and problems uncompleted. This lecture reviews some problems of Newtonian and relativistic Celestial Mechanics worthy of further investigation. Concerning Newtonian Mechanics, these problems include general solution of the three-body problem by means of the series of polynomials, construction of the short-term and long-term theories of motion using the fast converging elliptic function expansions, and representation of the rotation of the planets in the form compatible with the General Planetary Theory reducing the problem to the combined secular system for translatory motion and rotation. Relativistic problems considered here include the determination of the main relativistic effects in the motion of a satellite, e.g. the Moon, and in the rotation of the primary planet using the Newtonian theories of motion and rotation combined with the relativistic transformation of the reference systems, the use of the linearized weak-field GRT metric as a basis of relativistic Celestial Mechanics in the post-Newtonian approximation, and the motion of the Solar System bodies at the cosmological background in the framework of the basic cosmological models. The exposition of the chosen relativistic problems is preceded by reminding the basic features of relativistic Celestial Mechanics with discussing some present tendencies concerning the Parametrized Post-Newtonian formalism, International Astronomical Union resolutions, and standardization of the GRT routines.

  • Analytical Techniques of Celestial Mechanics - Analytical Techniques of Celestial Mechanics
    1995
    Co-Authors: V. A. Brumberg
    Abstract:

    This text exposes contemporary analytical and semianalytical techniques for solving typical Celestial Mechanics problems by computer. It presents new algorithms of perturbation theory and helps to develop, on the basis of some general computer algebra systems, specialized software enabling one to construct analytical theories of the motion of Celestial objects. Particular attention is paid to applying the elliptic function expansions to economize on the number of terms in the resulting series in problems with large values of parameters. Even problems considered as intractable may now be treated efficiently. The author addresses not only astronomers but also amateurs interested in orbit calculations for Celestial objects or satellites. He also develops specialized computer systems and perturbation algorithms to construct a general planetary theory general relativistic lunar theory, for solving typical Celestial Mechanics problems.

  • analytical techniques of Celestial Mechanics
    Analytical Techniques of Celestial Mechanics, 1995
    Co-Authors: V. A. Brumberg
    Abstract:

    This text exposes contemporary analytical and semianalytical techniques for solving typical Celestial Mechanics problems by computer. It presents new algorithms of perturbation theory and helps to develop, on the basis of some general computer algebra systems, specialized software enabling one to construct analytical theories of the motion of Celestial objects. Particular attention is paid to applying the elliptic function expansions to economize on the number of terms in the resulting series in problems with large values of parameters. Even problems considered as intractable may now be treated efficiently. The author addresses not only astronomers but also amateurs interested in orbit calculations for Celestial objects or satellites. He also develops specialized computer systems and perturbation algorithms to construct a general planetary theory general relativistic lunar theory, for solving typical Celestial Mechanics problems.

Alessandra Celletti - One of the best experts on this subject based on the ideXlab platform.

  • Nearly-integrable dissipative systems and Celestial Mechanics
    The European Physical Journal Special Topics, 2010
    Co-Authors: Alessandra Celletti, S. Di Ruzza, Christoph Lhotka, L. Stefanelli
    Abstract:

    The influence of dissipative effects on classical dynamical models of Celestial Mechanics is of basic importance. We introduce the reader to the subject, giving classical examples found in the literature, like the standard map, the Henon map, the logistic mapping. In the framework of the dissipative standard map, we investigate the existence of periodic orbits as a function of the parameters. We also provide some techniques to compute the breakdown threshold of quasi-periodic attractors. Next, we review a simple model of Celestial Mechanics, known as the spin-orbit problem which is closely linked to the dissipative standard map. In this context we present the conservative and dissipative KAM theorems to prove the existence of quasi-periodic tori and invariant attractors. We conclude by reviewing some dissipative models of Celestial Mechanics. Among the rotational dynamics we consider the Yarkovsky and YORP effects; within the three-body problem we introduce the so-called Stokes and Poynting-Robertson effects.

  • Cosmic Visions in Celestial Mechanics
    Celestial Mechanics and Dynamical Astronomy, 2010
    Co-Authors: Alessandra Celletti, Antonio Giorgilli, Ettore Perozzi, Sylvio Ferraz-mello
    Abstract:

    Modern Celestial Mechanics gains new momentum as its methods and results enter more and more into different academic fields and are, in turn, influenced by them. This is exactly what happens now: perturbation theories are a continuous source of inspiration for novel applications in spaceflight dynamics, while planetary dynamics must keep pace with the rapidly expanding field of exoplanets as well as with more traditional yet unresolved problems concerning the Solar System. In the short time span of a few years, significant results have been obtained on the subject of the long-standing questions on the stability of the inner planets. New and classical problems related to periodic orbits and chaotic diffusion have been investigated under a new light, as mission design is increasingly entering the realm of the three-body problem for computing station keeping strategies and transfer trajectories. This exciting situation of cross-breeding among different communities is likely to further increase in the future, fostered by the ambitious plans of the major space agencies. The newly announced NASA plans call for a robust scientific program of robotic solar system exploration and of space observatories/probes, where the recent advances of Celestial Mechanics can play a crucial role. The European Space Agency has just approved a suite of new scientific missions and started the Space Situational Awareness program, whose aim is to monitor the

  • Some KAM applications to Celestial Mechanics
    Discrete & Continuous Dynamical Systems - S, 2010
    Co-Authors: Alessandra Celletti
    Abstract:

    The existence of invariant tori in Celestial Mechanics has been widely investigated through implementations of the Kolmogorov-Arnold-Moser (KAM) theory. We provide an introduction to some results on the existence of maximal and low-dimensional, rotational and librational tori for models of Celestial Mechanics: from the spin--orbit problem to the three-body and planetary models. We also briefly review a result on dissipative invariant attractors for the spin-orbit problem, whose existence is proven through a dissipative KAM theorem.

  • Quasi-periodic attractors in Celestial Mechanics
    Archive for Rational Mechanics and Analysis, 2008
    Co-Authors: Alessandra Celletti, Luigi Chierchia
    Abstract:

    We prove that KAM tori smoothly bifurcate into quasi-periodic attractors in dissipative mechanical models, provided external parameters are tuned with the frequency of the motion. An application to the dissipative spin–orbit model of Celestial Mechanics (which actually motivated the analysis in this paper) is presented.

  • Modern Celestial Mechanics: From Theory to Applications - Modern Celestial Mechanics: From Theory to Applications
    2002
    Co-Authors: Alessandra Celletti, Sylvio Ferraz-mello, Jacques Henrard
    Abstract:

    t the opening of the "Third Meeting on Celestial Mechanics - CELMEC III", strong sensations hit our minds. The conference (18-22 June 2001) was being held in Villa Mondragone, a beautiful complex of buildings and gardens located within the township of Monte Porzio Catone, on the hills surrounding Rome. A former papal residence, the building has been recently restored by the University of Rome "Tor Vergata" to host academic activities and events

Yu. N. Chelnokov - One of the best experts on this subject based on the ideXlab platform.

  • Quaternion regularization and trajectory motion control in Celestial Mechanics and astrodynamics: II
    Cosmic Research, 2014
    Co-Authors: Yu. N. Chelnokov
    Abstract:

    Problems of regularization in Celestial Mechanics and astrodynamics are considered, and basic regular quaternion models for Celestial Mechanics and astrodynamics are presented. It is shown that the effectiveness of analytical studies and numerical solutions to boundary value problems of controlling the trajectory motion of spacecraft can be improved by using quaternion models of astrodynamics. In this second part of the paper, specific singularity-type features (division by zero) are considered. They result from using classical equations in angular variables (particularly in Euler variables) in Celestial Mechanics and astrodynamics and can be eliminated by using Euler (Rodrigues-Hamilton) parameters and Hamilton quaternions. Basic regular (in the above sense) quaternion models of Celestial Mechanics and astrodynamics are considered; these include equations of trajectory motion written in nonholonomic, orbital, and ideal moving trihedrals whose rotational motions are described by Euler parameters and quaternions of turn; and quaternion equations of instantaneous orbit orientation of a Celestial body (spacecraft). New quaternion regular equations are derived for the perturbed three-dimensional two-body problem (spacecraft trajectory motion). These equations are constructed using ideal rectangular Hansen coordinates and quaternion variables, and they have additional advantages over those known for regular Kustaanheimo-Stiefel equations.

  • Quaternion regularization in Celestial Mechanics and astrodynamics and trajectory motion control. I
    Cosmic Research, 2013
    Co-Authors: Yu. N. Chelnokov
    Abstract:

    Regularization problems in Celestial Mechanics and astrodynamics are considered. The fundamental regular quaternion models of Celestial Mechanics and astrodynamics are presented. It is shown that the efficiency of analytical investigation and numerical solution of boundary problems of optimal trajectory motion control of spacecraft may be increased using quaternion astrodynamics models. The regularization problem of Celestial Mechanics and astrodynamics that implies eliminating the feature, which arises in the equations of the two-body problem in case of impact of the second body with the central body, is considered in the first section of the paper. The quaternion method for regularizing the equations of the perturbed spatial two-body problem suggested by the author is presented; the method is compared with Kustaanheimo-Stiefel (KS) regularization. Demonstrative geometric and kinematic interpretations of regularizing transformations are provided. Regular quaternion equations for the two-body problem, which generalize the regular Kustaanheimo-Stiefel equations, as well as regular equations in quaternion osculating elements and quaternion regular equations for perturbed central motion of a material point, are considered. The papers on quaternion regularization in Celestial Mechanics and astrodynamics are briefly analyzed.

Nikolai N. Gorkavyi - One of the best experts on this subject based on the ideXlab platform.

  • Celestial Mechanics Minimum
    Astronomy and Astrophysics Library, 1999
    Co-Authors: Alexei M. Fridman, Nikolai N. Gorkavyi
    Abstract:

    In the present chapter we shall give those results from Celestial Mechanics which we shall use in the present book. This makes our exposition more self-contained and makes it unnecessary for the reader to turn to textbooks on Celestial Mechanics.

J. Klačka - One of the best experts on this subject based on the ideXlab platform.

  • Generalized perturbation equations of Celestial Mechanics
    Earth Moon and Planets, 1993
    Co-Authors: J. Klačka
    Abstract:

    Generalized perturbation equations of Celestial Mechanics in terms of orbital elements are derived. The most general case is considered: Keplerian motion of two bodies caused by gravitational forces between them is disturbed by disturbing acceleration acting on each of the bodies separately and by changes of masses of these bodies. It is also pointed out why derivation presented in Klacka (1992a) is completely physically correct only for constant masses.

  • PERTURBATION EQUATIONS OF Celestial Mechanics
    Earth Moon and Planets, 1992
    Co-Authors: J. Klačka
    Abstract:

    Perturbation equations of Celestial Mechanics in terms of orbital elements are completely derived in application to the motion of interplanetary dust particle in the gravational field of the Sun and under the action of disturbing forces. Consideration of change of mass of interplanetary dust particle is the most important feature of this derivation. The results obtained are completely general in the case of constant masses.