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.

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I: Stars, Planets, Satellites, Asteroids and Rings.- The Dynamics of Close Planetary Satellites and Rings.- The Motion of Saturn's Co-Orbiting Satellites 1980S1 and 1980S3.- A Qualitative Study of Stabilizing and Destabilizing Factors in Planetary and Asteroidal Orbits.- Perturbations in Stellar Paths.- Modern Lunar Theory.- 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.- The Stability of N-Body Hierarchical Dynamical Systems.- Reference Systems for Earth Dynamics.- II: Resonance.- Recent Progress in the Theory of the Trojan Asteroids.- The Adiabatic Invariants: Its Use in Celestial Mechanics.- III: Connection with Statistical Mechanics.- Modern and Old Views in the Dynamical Foundations of Classical Statistical Mechanics.- The KAM Invariant and Poincaré's Theorem.- IV: Regularization and Geodesics.- Regularization of the Singularities of the N-Body Problem.- Les Geodesiques de l'Ellipsoide a Trois Axes Inegaux, d'Apres Jacobi, Whittaker, Arnold.- Coordonnées Symetriques sur la Variété de Collision Triple du Problème Plan des Trois Corps.- V: Non-Linearity, Determinancy and Manifolds.- Ergodic Theory and Area Preserving Mappings.- Exploding Dynamical Systems.- On Some Invariant Manifold Results and Their Applications.- Is Celestial Mechanics Deterministic?.- VI: Abstracts of Seminar Contributions.- On a Family of Continuous Maps of the Circle into Itself Related to the Van der Pol Equation.- Review on Semiconvergent Series, Periodic Solutions and the Vanishing Hessian in Celestial Mechanics.- Perturbative Effects of Solar Radiation Pressure on the Orbital Motion of High Earth Satellites.- Quasi-Random Motions in a Perturbed Pendulum.- Small Bodies Captured by a Thin Annular Disk Orbiting Around a Primary Body.- Lie-Algebraic Methods in Dynamics and Celestial Mechanics.- Parabolic Escape and Capture in the Restricted Three-Body Problem for Larger Values of the Jacobi Constant.- Compatability Conditions for a Non-Quadratic Integral of Motion.- Contact Systems and Celestial Mechanics.- Dimensions of the Invariant Manifolds Associated with Equilibrium Points in the N-Body Problem.- On the Development of an Artificial Satellite Theory.- Motion at the Second Order Resonances, 3:1 and 5:3.- On the Applicability of the Transition Chains Mechanism.- Small Divisors in the Derivatives of Hansen's Coefficients.- Periodic Solutions of the Restricted Problem of Three Bodies with Small Values of the Mass Parameter.- Non-Universality for a Class of Bifurcations.- Application of Lie-Series to Numerical Integration in Celestial Mechanics.- Applications of Hamilton's Law of Varying Action.- Some Current Astrodynamics Developments at the North American Aerospace Defense Command (NORAD).- About the Triple Collision Manifold in the Planar Three-Body Problem.- Periodic Orbits Near Homoclinic Orbits.- Some Numerical Results of a Semi-Analytic Orbit Theory Using Observed Data.- Orbital Behaviour in the Vicinity of Unstable Periodic Orbits in Dynamical Systems with Three Degrees of Freedom.- On the Convergence of Formal Integrals in Finite Time.- A Numerical Study of the Asymptotic Solutions to the Family (C) of Periodic Orbits in the Restricted Problem of Three Bodies.- The Equivalence of the Generators of Deprit's and Giorgelli-Galgani's Change of Variables in Differential Systems.- Stabilization of Spiral Density Waves in Flat Galaxies for a Hydrodynamical Model.- Stability of Periodic Orbits Near a Homoclinic Orbit for Analytical Hamiltonians with Two Degrees of Freedom.- A Method for the Investigation of the Integrability of Dynamical Systems.- Reappearance of Ordered Motion in Classical Non-Integrable Hamiltonian Systems.- Hopf-Bifurcation in a Nearly Hamiltonian System.- A Realization of Dynamical Systems in Boolean Algebras.- Relativistic Astrodynamics: Problems in Interstellar Flight.- The Origin of the Kirkwood Gaps: A Mapping for Asteroidal Motion Near the 3/1 Commensurability.- Completely Integrable Systems and Singularity in the Complex t-Plane.- Index of Names.- Index of Subjects.