Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems

Abstract

I: Planetary Dynamics.- Dynamical Evolution of Planetary Systems and the Significance of Bode's Law.- Further Numerical Investigations into the Significance of Bode's Law.- Where are the Saturnian Trojans?.- Orbital Evolution.- Planetary Perturbation Theory from Lie Series, including Resonance and Critical Arguments.- Secular Perturbations of Planetary Orbits and their Representation as Series.- The Accumulation of Integration Error.- Numerical Regularization of the Lagrange Planetary Equations.- II: Dynamics of Natural and Artificial Satellites.- General Formulas for Three-Body Resonances.- Analytical Methods for the Radial Intermediaries.- Analytical Theory of the Rotation of an Artificial Satellite.- Some Models for the Motion of the Co-orbital Satellites of Saturn.- Long-period Changes in the Semimajor Axis of Lageos.- Effects of a Non-circular Shepherd upon a Planetary Ring.- General Motion of a Triaxial Rigid Body in a Newtonian Force Field.- The Motion of the Orbit Plane of Iapetus.- Astrodynamics in the Real-World Environment (The Whole Truth and Nothing but the Truth).- A Finite-Time Stability Criterion for Sun-perturbed Planetary Satellites.- A New Radial Intermediary and its Numerical Integration.- Co-orbital Satellites and Hill's Lunar Problem.- III: Dynamics of Asteroids.- The Puzzle of Asteroid Families.- High Eccentricity Libration.- Evolution of Asteroidal Orbits Located in the Main Secular Resonances ?5,?6 and ?16.- Algebraic Mappings Near a Resonance with an Application to Asteroid Motion.- The Hierarchical Restricted Problem with Applications.- The Motions of Asteroids in the Secular Resonance ?6: an Analytical Model and Numerical Calculations.- IV: Dynamics of Stars and Galaxies.- Families of Periodic Orbits in a Model of Interacting Galaxies.- Qualitative Characteristics of Dynamical Systems.- On the Galactic Motion.- The N-Body Problem in Stellar Dynamics.- Rotationally and Tidally Perturbed Orbital Elements of Close Binary Stars.- V: Other Specific Topics in Dynamics.- Escape and Capture in the Restricted Three Body Problem (RTBP).- A Formulation of the N-body Problem where the Velocities are Bounded.- A Report on Some New KAM Estimates.- Extended Canonical Transformations Increasing the Number of Variables.- Non Local Spiraling Characteristic Curves.- Connectance and Stability of Linear Differential Systems.- Resonances in the Planar Elliptic Restricted Problem.- The Near-Resonance Theorem: Analysis of the Vicinity of Periodic Solutions of Analytic Differential Systems.- Homoclinic and Heteroclinic Solutions of the RTBP Joining the Triangular Equilibrium Points.- Double Collision Orbits and Second Species Solutions in the Restricted Three-Body Problem.- Bifurcations and Instabilities in the Restricted Three-Body Problem.- Three Dimensional Equations of Szebehely of the Inverse Problem and Frenet Reference Frame.- Fourier Transform in Astrodynamics.- Estimates of the Error in Normal Forms of Hamiltonian Systems. Applications to Effective Stability and Examples.- Passages Near Triple Collision.- Non-Integrability of Hamiltonian Systems Based on Ziglin's Theorem.- Index of Names.- Index of Subjects.