Long-Time Predictions in Dynamics

This volume contains lectures given at the NATO Advanced Study Institute on Long-Time Predictions in Dynamics conducted in Cortina d'Ampezzo, Italy during August 3-16, 1975. The lectures were presented in groups, according to the original structure of the Institute. Under "Fundamentals" the general concepts were treated by Contopoulos, DeWitt, Reichl, Stiefel, Szebehely, Bartlett, Kirchgraber, Verhults and Sigrist. This was followed by the series of lectures on "Numerical and Statistical Analysis" offered by Aarseth, Baumgarte and Tapley. The third principal subject was "Three and Many-Body Problems" with Garfinkel, Broucke, Hadjidemetriou, Marchal, Nahon, Waldvogel, Lasco, and Markellos as the major speakers. The last group of lectures treated "Dynamics in Astronomy" by Colombo, Message, Ovenden, Vicente, and Douglas. Some of the outstanding lectures were rather didactic in nature or were published elsewhere or could not meet the deadline for publication. The Editors will be delighted to furnish leads to those interested in these lectures. Some of the lectures were presented in form of seminar-contributions. These are published as Summaries at the end of this Volume. The Institute was dedicated to the conceptual, analytical, numerical and applied aspects of the problem of long-time predic tion in dynamics. This fundamental problem emerged in all lectures: linearization, regularization, stabilization, averaging, estimation, periodic orbits, qualitative aspects, secular variations, resonance, invariants, etc. were some of the subjects treated in depth. Some conclusions are offered here with the utmost humility and with the advance acknowledgement of the fact that we all hear what we want to hear.

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Proceedings of the NATO Advanced Study Institute, Cortina D'Ampezzo, Italy, August 3-16, 1975

Contenu
I. Fundamentals.- From the Theory of Numbers via Gyroscopes and Lie Algebras to Linear Celestial Mechanics.- Lectures on Linearizing Transformations of Dynamical Systems.- Strongly Perturbed Dynamical Systems.- Catastrophes in Lagrangian Systems - A.- An Example - B.- Statistical Behavior in Conservative Classical Systems.- G1obal Stability of Area-Preserving Mappings.- On the Method of Averaging.- On the Theory of Averaging.- Qualitative Investigation of Almost Separable Hamiltonian System of Two Degrees of Freedom.- II. Numerical and Statistical Analysis.- Stabilization, Manipulation, and Analytic Step Adaption.- On the Interpretation of Least Squares Collocation.- A Note on Stabilization in Three-Body Regularization.- III. Three and Many-Body Problems.- Qualitative Methods and Results in Celestial Mechanics.- On the Characteristic Exponents of the General Three-Body Problem.- Families of Periodic Orbits in the General N-Body Problem.- Triple Collision.- An Invariant Measure for the Planar Restricted Three Body Problem.- Periodic Oscillations of the First Generation in the Stormer Problem.- IV. Dynamics in Astronomy.- Formal Expressions for the Motion of NPlanets in the Plane, with the Secular Variations Included, and an Extension to Poisson's Theorem.- The Principle of Least Interaction Action.- Rotational Motions of the Terrestrial Planets.- Long-Term Orbit Determination and Prediction for Geodynamic Investigations.- V. Abstracts of Seminar-Contributions.- Dynamical Systems Involving Uncertainty.- Periodic Orbits Around the Equilibrium Points of a Central Gravitational Potential Perturbed by the J22 Term.- Time Regularization and Stabilization of an Adams-Moulton-Cowel1 Algorithm.- On the Theory of an Artificial Satellite.- The Evolution of Planetary Orbits in theCapture Theory of the Origin of the Solar System.- Geodynamic Investigations Using Very Long Term Observation of Near-Earth Satellites.- A New Transformation for the Perturbed Problem of Two Bodies.- Kozai's Theory of an Artificial Satellite.- Cassini's Laws.- Theory of the Rotation of the Riged Earth.- Periodic Oscillations of the Second Generation in the Störmer Problem.- Three-Dimensional Branchings of Plane Periodic Solutions.- On Stabilization Using the Energy Integral.- Resonance Effects in Satellite Orbits.- On the Resonance 1:1 for Hamiltonian Systems Near an Equilibrium Point.- Periodic Orbits Near an Equilibrium Pgint: The Liapunov Center Theorem.- Analytical and Numerical Study of a Perturbed Pendulum.- Algebraical Aspects of Perturbation Theories.- Stabilization and Time Elements for Kepler's Problem.- A Note on the Hénon-Heiles Problem.- Newtonian Cosmology with Varying G.- The Effects of Integrals on the Totality of Solutions of Dynamical Systems.