Applications of Modern Dynamics to Celestial Mechanics and Astrodynamics : Proceedings of the NATO Advanced Study Institute Held at Cortina D’Ampezzo, Italy, August 2–14, 1981

This volume contains the detailed text of the major lectures and the abstracts of the lectures delivered during the seminar sessions. The subject of our NATO Advanced Study Institute in 1981 was the Application of Modern Dynamics to Celestial Mechanics and Astrodynamics. This Preface will first explain the terminology, then it will review shortly the content of the lectures and will outline how all this was made possible and, finally, it will disclose our future aspirations. Periodicity is an extremely important concept in our field, therefore, it should not be unexpected that our NATO Advanced Study Institute is enjoying a period of three years. Since 1972 we conducted four Institutes with increasing interest and en­ thusiasm displayed by the participants, lecturers and by this Director. Celestial Mechanics or Dynamical Astronomy is part of Astronomy dealing mostly with the motion of natural celestial bodies. Astrodynamics or Orbital Mechanics is the application of dynamics to problems of Space Engineering and it treats mostly the dynamical behavior of artificial satellites and space probes. The underlying mathematical and dynamical principles are, of course, the same for Celestial Mechanics and for Astrodynamics. This Director of the Institute and Editor of the Proceedings was extremely fortunate to have obtained the cooperation of out­ standing lecturers who were clear, thorough, understandable, patient to answer questions, but above all, had knowledge of the ix V. Szebehely (ed.). Applications of Modern Dynamics to Celestial Mechanics and Astrodynamics. ix-x. Front Matter....Pages i-xviii The Dynamics of Close Planetary Satellites and Rings....Pages 1-20 The Motion of Saturn’s Co-Orbiting Satellites 1980S1 and 1980S3....Pages 21-23 A Qualitative Study of Stabilizing and Destabilizing Factors in Planetary and Asteroidal Orbits....Pages 25-44 Perturbations in Stellar Paths....Pages 45-57 Modern Lunar Theory....Pages 59-76 Some Aspects of Motion in the General Planar Problem of Three Bodies; in Particular in the Vicinity of Periodic Solutions Associated with Near Small-Integer Commensurabilities of Orbital Period....Pages 77-101 The Stability of N-Body Hierarchical Dynamical Systems....Pages 103-130 Reference Systems for Earth Dynamics....Pages 131-144 Recent Progress in the Theory of the Trojan Asteroids....Pages 145-152 The Adiabatic Invariant: Its Use in Celestial Mechanics....Pages 153-171 Modern and Old Views in the Dynamical Foundations of Classical Statistical Mechanics....Pages 173-184 The Kam Invariant and Poincaré’s Theorem....Pages 185-199 Regularization of the Singularities of the N-Body Problem....Pages 201-236 Les Geodesiques de l’Ellipsoide a Trois Axes Inegaux, d’Apres Jacobi, Whittaker, Arnold....Pages 237-247 Coordonnées Symétriques sur la Variété de Collision Triple du Problème Plan des Trois Corps....Pages 249-266 Ergodic Theory and Area Preserving Mappings....Pages 267-276 Exploding Dynamical Systems....Pages 277-299 On Some Invariant Manifold Results and Their Applications....Pages 301-320 Is Celestial Mechanics Deterministic ?....Pages 321-324 On a Family of Continuous Maps of the Circle into Itself Related to the Van Der Pol Equation....Pages 325-325 A Review on Semiconvergent Series, Periodic Solutions and the Vanishing Hessian in Celestial Mechanics....Pages 326-326 Perturbative Effects of Solar Radiation Pressure on the Orbital Motion of High Earth Satellites....Pages 327-327 Quasi-Random Motions in a Perturbed Pendulum....Pages 328-328 Small Bodies Captured by a Thin Annular Disk Orbiting Around a Primary Body....Pages 329-330 Lie-Algebraic Methods in Dynamics and Celestial Mechanics....Pages 331-332 Parabolic Escape and Capture in the Restricted Three-Body Problem for Larger Values of the Jacobi Constant....Pages 333-333 Compatibility Conditions for a Non-Quadratic Integral of Motion....Pages 334-335 Contact Systems and Celestial Mechanics....Pages 336-336 Dimensions of the Invariant Manifolds Associated with Equilibrium Points in the N-Body Problem....Pages 337-337 On the Development of an Artificial Satellite Theory....Pages 338-338 Motion at the Second Order Resonances, 3:1 and 5:3....Pages 339-340 On the Applicability of the Transition Chains Mechanism....Pages 341-341 Small Divisors in the Derivatives of Hansen’s Coefficients....Pages 342-342 Periodic Solutions of the Restricted Problem of Three Bodies with Small Values of the Mass Parameter....Pages 343-343 Non-Universality for a Class of Bifurcations....Pages 344-344 Application of Lie-Series to Numerical Integration in Celestial Mechanics....Pages 345-345 Applications of Hamilton’s Law of Varying Action....Pages 346-346 Some Current Astrodynamics Developments at the North American Aerospace Defense Command (NORAD)....Pages 347-347 About the Triple Collision Manifold in the Planar Three-Body Problem....Pages 348-349 Periodic Orbits Near Homoclinic Orbits....Pages 350-350 Some Numerical Results of a Semi-Analytic Orbit Theory Using Observed Data....Pages 351-351 Orbital Behaviour in the Vicinity of Unstable Periodic Orbits in Dynamical Systems with Three Degrees of Freedom....Pages 352-352 On the Convergence of Formal Integrals in Finite Time....Pages 353-353 A Numerical Study of the Asymptotic Solutions to the Family (C) of Periodic Orbits in the Restricted Problem of Three Bodies....Pages 354-354 The Equivalence of the Generators of Deprit’s and Giorgelli-Galgani’s Change of Variables in Differential Systems....Pages 355-355 Stabilization of Spiral Density Waves in Flat Galaxies for a Hydrodynamical Model....Pages 356-356 Stability of Periodic Orbits Near a Homoclinic Orbit for Analytical Hamiltonians with Two Degrees of Freedom....Pages 357-357 A Method for the Investigation of the Integrability of Dynamical Systems....Pages 358-358 Reappearance of Ordered Motion in Classical Non-Integrable Hamiltonian Systems....Pages 359-359 HOPF-Bifurcation in a Nearly Hamiltonian System....Pages 360-361 A Realization of Dynamical Systems in Boolean Algebras....Pages 362-362 Relativistic Astrodynamics: Problems in Interstellar Flight....Pages 363-363 The Origin of the Kirkwood Gaps: A Mapping for Asteroidal Motion Near the 3/1 Commensurability....Pages 364-364 Completely Integrable Systems and Singularity in the Complex t — Plane....Pages 365-365 Back Matter....Pages 367-373 Proceedings of the NATO Advanced Study Institute, Cortina d'Ampezzo, Italy, August 2-14, 1981