Instabilities in Dynamical Systems: Applications to Celestial Mechanics

ISBN-13: 9789400994256 / Angielski / Miękka / 2011 / 338 str.

V. G. Szebehely

Opis

ix List of Speakers and Participants xi Group Photograph xviii Greetings by B. Garfinkel, A. E. Roy and P. J. Message xix Introduction xxiii PART I: FUNDAMENTAL CONSIDERATIONS OF STABILITY R. BROUCKE/Simple Non-Integrable Systems with Two Degrees of Freedom 3 G. CONTOPOULOS/lnstabilities in Systems of Three Degrees of Freedom 25 R. W. EASTON/Perturbed Twist Maps, Homoclinic Points and Ergodic Zones 41 O. GUREL/Bifurcation Theory and its Applications V. SZEBEHELY/General Considerations of Stability in 49 61 Celestial Mechanics PART II: ASPECTS OF NUMERICAL ANALYSIS AND STATISTICAL MECHANICS S. J. AARSETH/An N-Body Integration Method in Co-Moving Coordinates 69 J. BAUMGARTE/The General Theory of Conservative Stabilization of the Keplerian Problem 81 C. DEWITT-MORETTE /Celestial Mechanics, Quantum Mechanics, and Path Integration 95 G. C. STEY/Statistical Viewpoint in Classical Mechanics 103 PART III: STABILITY OF PLANETARY SYSTEMS ~ C. FROESCHLE and H. SCHOLL/Evolution of Orbits in the Outer Part of the Asteroidal Belt and in the Kirkwood Gaps as Influenced by the Mass Effects of Saturn and Jupiter 115 v TABLE OF CONTENTS vi B. GARFINKEL/On the Stability of Resonant Motion in 121 the Light of the Regularizing Function 129 P. GOLDREICH/The Rings of Saturn and Uranus J. D. HADJIDEMETRIOU/Instabilities in Periodic 135 Planetary-Type Orbits P. J. MESSAGE/Bounds on Secular Terms in Celestial 165 Mechanics A. E. ROY/Empirical Stability Criteria in the 177 Many-Body Problem R. O. VICENTE/Instabilities in Planetary Systems 211 PART IV: THE PROBLEM OF THREE BODIES H.

Spis treści

I: Fundamental Considerations of Stability.- Simple Non-Integrable Systems with Two Degrees of Freedom.- Instabilities in Systems of Three Degrees of Freedom.- Perturbed Twist Maps, Homoclinic Points and Ergodic Zones.- Bifurcation Theory and its Applications.- General Considerations of Stability in Celestial Mechanics.- II: Aspects of Numerical Analysis and Statistical Mechanics.- An N-Body Integration Method in Co-Moving Coordinates.- The General Theory of Conservative Stabilization of the Keplerian Problem.- Celestial Mechanics, Quantum Mechanics, and Path Integration.- Statistical Viewpoint in Classical Mechanics.- III: Stability of Planetary Systems.- Evolution of Orbits in the Outer Part of the Asteroidal Belt and in the Kirkwood Gaps as Influenced by the Mass Effects of Saturn and Jupiter.- On the Stability of Resonant Motion in the Light of the Regularizing function.- The Rings of Saturn and Uranus.- Instabilities in Periodic Planetary-Type Orbits.- Bounds on Secular Terms in Celestial Mechanics.- Empirical Stability Criteria in the Many-Body Problem.- Instabilities in Planetary Systems.- IV: The Problem of Three Bodies.- Note on the Triangular Lagrangian Points in the Elliptic Restricted Problem of Three Bodies.- Periodic Orbits with and without Symmetry in the Three-Dimensional General Three-Body Problem.- The Vicinity of the Primary of Small Mass in the Restricted Problem.- Stab1e and Unstable Manifolds in Planar Triple Collision.- V: Abstracts of Seminar-Contributions.- Cluster Formation and Gravitational Instabilities.- Application of a New Numerical Method for the Integration of the Equations of Motion for an N-Body System.- Evolution of a Mission Concept from a Solar Probe to a Solar Orbiter.- Simulation of Dynamical and Thermal Behaviour of Skyhook System.- The Jacobian Integral in the Elliptic Restricted Three-Body Problem.- Effect of Mass-Parameter on the Periodic Orbits of the Restricted Problem of Three Bodies.- Semi-Analytical Lunar Ephemeris.- On the Origin of the Kirkwood Gaps.- Generating Orbits for Stable Close Encounter Periodic Solutions of the Restricted Problem.- Optimal Continuous Torque Attitude Maneuvers.- Final Evolutions of Parabolic-Hyperbolic Type in the Restricted Three-Body Problem.- Asymptotic Orbits and Instability Zones in the Simplest Model of a Galactic Potential.- Generation of Periodic Orbits in the Three-Body Problem.- Measurement of the Gravitational Constant in Space.- Hill’s Stability Applied to the Asteroidal Belt.- Numerical Study of the Rectilinear Isosceles Restricted Problem.- Analytical Construction of Unstable Periodic Orbits about the Collinear Points.- On the Stability of an Equilibrium Solution in Hamiltonian Systems of Two Degrees of Freedom.- Regularization of Triple Collisions in the General Three-Body Problem.- Index of Names.- Index of Subjects.