Long-Time Predictions in Dynamics: Proceedings of the NATO Advanced Study Institute held in Cortina d’Ampezzo, Italy, August 3–16, 1975

Front Matter....Pages I-XVIII
Front Matter....Pages 1-1
From the Theory of Numbers via Gyroscopes and Lie Algebras to Linear Celestial Mechanics....Pages 3-15
Lectures on Linearizing Transformations of Dynamical Systems....Pages 17-42
Strongly Perturbed Dynamical Systems....Pages 43-56
Catastrophes in Lagrangian Systems — A....Pages 57-65
Catastrophes in Lagrangian Systems: An Example — B....Pages 67-70
Statistical Behavior in Conservative Classical Systems....Pages 71-98
Global Stability of Area-Preserving Mappings....Pages 99-110
On the Method of Averaging....Pages 111-117
On the Theory of Averaging....Pages 119-140
Qualitative Investigation of Almost Separable Hamiltonian System of Two Degrees of Freedom....Pages 141-150
Front Matter....Pages 151-151
Stabilization, Manipulation and Analytic Step Adaption....Pages 153-163
On the Interpretation of Least Squares Collocation....Pages 165-172
A Note on Stabilization in Three-Body Regularization....Pages 173-177
Front Matter....Pages 179-179
Qualitative Methods and Results in Celestial Mechanics....Pages 181-208
On the Characteristic Exponents of the General Three-Body Problem....Pages 209-222
Families of Periodic Orbits in the General N-Body Problem....Pages 223-240
Triple Collision....Pages 241-258
An Invariant Measure for the Planar Restricted Three Body problem....Pages 259-266
Periodic Oscillations of the First Generation in the Stormer Problem....Pages 267-276
Front Matter....Pages 277-277
Formal Expressions for the Motion of N Planets in the Plane, with the Secular Variations Included, and An Extension to Poisson’s Theorem....Pages 279-293
Front Matter....Pages 277-277
The Principle of Least Interaction Action....Pages 295-305
Rotational Motions of the Terrestrial Planets....Pages 307-320
Long-Term Orbit Determination and Prediction for Geodynamic Investigations....Pages 321-326
Front Matter....Pages 327-327
Dynamical Systems Involving Uncertainty....Pages 329-329
Periodic Orbits around the Equilibrium Points of a Central Gravitational Potential Perturbed By the J 22 Term....Pages 330-330
Time Regularization and Stabilization of an Adams-Moulton-Cowell Algorithm....Pages 331-332
On The Theory of an Artificial Satellite....Pages 333-333
The Evolution of Planetary Orbits in the Capture Theory of the Origin of the Solar System....Pages 334-334
Geodynamic Investigations Using Very Long Term Observation of Near-Earth Satellites....Pages 335-335
A New Transformation for the Perturbed Problem of Two Bodies....Pages 336-336
Kozai’s Theory of an Artificial Satellite....Pages 337-337
Cassini’s Laws....Pages 338-338
Theory of the Rotation of the Rigid Earth....Pages 339-339
Periodic Oscillations of the Second Generation in the Störmer Problem....Pages 340-340
Three-Dimensional Branchings of Plane Periodic Solutions....Pages 341-341
On Stabilization Using the Energy Integral....Pages 342-343
Resonance Effects in Satellite Orbits....Pages 344-344
On the Resonance 1 – 1 for Hamiltonian Systems near an Equilibrium Point....Pages 345-345
Periodic Orbits near An Equilibrium Point: The Liapunov Center Theorem....Pages 346-346
Analytical and Numerical Study of a Perturbed Pendulum....Pages 347-348
Front Matter....Pages 327-327
Algebraical Aspects of Perturbation Theories....Pages 349-351
Stabilization and Time Elements for Kepler’s Problem....Pages 352-353
A Note on the Hénon-Heiles Problem....Pages 354-355
Newtonian Cosmology with Varying G....Pages 356-357
The Effects of Integrals on the Totality of Solutions of Dynamical Systems....Pages 358-358