Long-Time Predictions in Dynamics

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 the Capture 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.