Recent Advances in Dynamical Astronomy: Proceedings of the NATO Advanced Study Institute in Dynamical Astronomy Held in Cortina d'Ampezzo, Italy, Augu

ISBN-13: 9789401026130 / Angielski / Miękka / 2011 / 470 str.

B.D. Tapley;Victor G. Szebehely

Opis

IX LIST OF PRINCIPAL SPEAKERS XI LIST OF PARTICIPANTS 1. REGULARIZATION E. STIEFEL / A Linear Theory of the Perturbed Two-Body Problem (Regul- ization) 3 J. WALDVOGEL / Collision Singularities in Gravitational Problems 21 D. C. HEGGIE / Regularization Using a Time-Transformation Only 34 J. BAUMGAR TE / Stabilization of the Differential Equations of Keplerian Motion 38 F. NAHON / The Particular Solutions of Levi-Civita 45 O. GODAR T / Example ofIntegration of Strongly Oscillating Systems 53 w. BLACK / The Application of Recurrence Relations to Special Perturbation Methods 61 D. G. BETTIS / Numerical Solution of Ordinary Differential Equations (Abstract) 71 II. THE THREE-BODY PROBLEM V. SZEBEHELY / Recent Advances in the Problem of Three Bodies 75 R. F. ARENSTORF / Periodic Elliptic Motion in the Problem of Three Bodies (Abstract) 107 G. KATSIARIS and c. L. GOUDAS / On a Conjecture by Poincare 109 G. KATSIARIS / The Three-Dimensional Elliptic Problem 118 P. G. KAZANTZIS / Second and Third Order Variations of the Three Dimensional Restricted Problem 135 c. G. ZAGOURAS / Planar Periodic Orbits Using Second and Third Variations 146 E. RABE / Elliptic Restricted Problem: Fourth-Order Stability Analysis of the Triangular Points 156 P. GUILLAUME / A Linear Description of the Second Species Solutions 161 III. THE N-BODY PROBLEM AND STELLAR DYNAMICS G. CONTOPOULOS / Problems of Stellar Dynamics 177 w. T. KYNER / Invariant Manifolds in Celestial Mechanics 192 s. J.

Spis treści

I. Regularization.- A Linear Theory of the Perturbed Two-Body Problem (Regularization).- Collision Singularities in Gravitational Problems.- Regularization Using a Time-Transformation Only.- Stabilization of the Differential Equations of Keplerian Motion.- The Particular Solutions of Levi-Civita.- Example of Integration of Strongly Oscillating Systems.- The Application of Recurrence Relations to Special Perturbation Methods.- Numerical Solution of Ordinary Differential Equations (Abstract).- II. The Three-Body Problem.- Recent Advances in the Problem of Three Bodies.- Periodic Elliptic Motion in the Problem of Three Bodies (Abstract).- On a Conjecture by Poincaré.- The Three-Dimensional Elliptic Problem.- Second and Third Order Variations of the Three Dimensional Restricted Problem.- Planar Periodic Orbits Using Second and Third Variations.- Elliptic Restricted Problem: Fourth-Order Stability Analysis of the Triangular Points.- A Linear Description of the Second Species Solutions.- III. The N-Body Problem and Stellar Dynamics.- Problems of Stellar Dynamics.- Invariant Manifolds in Celestial Mechanics.- Theoretical Aspects of N-Body Computer Simulations.- Integration Methods of the N-Body Problem (Abstract).- Numerical Studies of the Gravitational Problem of N-Bodies (Abstract).- Star Encounter Simulations.- Yukawa Potential and Stellar Encounter.- An Investigation of the Rôle of Turbulence in the Formation of Star Clusters by a Point-Mass Simulation.- IV. The Theory of General Perturbations.- Theory of General Perturbations.- The Algorithm of the Inverse for Lie Transform.- The Property of Covariance in Hori’s Non-Canonical Perturbation Theory (Abstract).- Subdynamics in Classical Mechanics.- V. The Solar System and Orbital Resonances.- Astronomical Systems of Units, Co-ordinates and Time-Scales.- Masses of the Planets and Satellites (Abstract).- Planetary Ephemerides.- Orbits of the Natural Satellites. Lectures on Some Types of Orbital Motion Amongst Them.- On the Origin of the Titan-Hyperion System.- Planetary Distances and the Missing Planet.- Change of Inclination in Passing Through Resonance.- VI. Trajectory Determination and the Motion of Rigid Bodies.- Review of Non-Numerical Uses of Computers.- Elementary Dynamical Astronomy.- Statistical Orbit Determination Theory.- Orbit Determination by Solving a Boundary Value Problem.- Long-Term Motion in a Restricted Problem of Rotational Motion.- Uniform Theory of a Rotating Rigid Body with Dynamical Symmetry.- Attitude Stability of a Satellite in the Restricted Three-Body Problem.- Analytic Treatment of Straight-Line Flights into the Sun after Planetary Fly-By.