Recent Advances in Dynamical Astronomy: Proceedings of the NATO Advanced Study Institute in Dynamical Astronomy Held in Cortina D’Ampezzo, Italy, August 9–21, 1972

Front Matter....Pages I-XIII
Front Matter....Pages 1-1
A Linear Theory of the Perturbed Two-Body Problem (Regularization)....Pages 3-20
Collision Singularities in Gravitational Problems....Pages 21-33
Regularization Using a Time-Transformation Only....Pages 34-37
Stabilization of the Differential Equations of Keplerian Motion....Pages 38-44
The Particular Solutions of Levi-Civita....Pages 45-52
Example of Integration of Strongly Oscillating Systems....Pages 53-60
The Application of Recurrence Relations to Special Perturbation Methods....Pages 61-70
Numerical Solution of Ordinary Differential Equations....Pages 71-71
Front Matter....Pages 73-73
Recent Advances in the Problem of Three Bodies....Pages 75-106
Periodic Elliptic Motion in the Problem of Trhee Bodies....Pages 107-108
On a Conjecture by Poincaré....Pages 109-117
The Three-Dimensional Elliptic Problem....Pages 118-134
Second and Third Order Variations of the Three Dimensional Restricted Problem....Pages 135-145
Planar Periodic Orbits Using Second and Third Variations....Pages 146-155
Elliptic Restricted Problem: Fourth-Order Stability Analysis of the Triangular Points....Pages 156-160
A Linear Description of the Second Species Solutions....Pages 161-174
Front Matter....Pages 175-175
Problems of Stellar Dynamics....Pages 177-191
Invariant Manifolds in Celestial Mechanics....Pages 192-196
Theoretical Aspects of N -Body Computer Simulations....Pages 197-207
Integration Methods of the N -Body Problem....Pages 208-208
Front Matter....Pages 175-175
Numerical Studies of the Gravitational Problem of N -Bodies....Pages 209-210
Star Encounter Simulations....Pages 211-215
Yukawa Potential and Stellar Encounter....Pages 216-221
An Investigation of the Rôle of Turbulence in the Formation of Star Clusters by a Point-Mass Simulation....Pages 222-228
Front Matter....Pages 229-229
Theory of General Perturbations....Pages 231-249
The Algorithm of the Inverse for Lie Transform....Pages 250-259
The Property of Covariance in Hori’s Noncanonical Perturbation Theory....Pages 260-261
Subdynamics in Classical Mechanics....Pages 262-269
Front Matter....Pages 271-271
Astronomical Systems of Units, Co-Ordinates and Time-Scales....Pages 273-286
Masses of the Planets and Satellites....Pages 287-288
Planetary Ephemerides....Pages 289-308
Orbits of the Natural Satellites Lectures on Some Types of Orbital Motion amongst them....Pages 309-311
On the Origin of the Titan-Hyperion System....Pages 312-318
Planetary Distances and the Missing Planet....Pages 319-332
Change of Inclination in Passing through Resonance....Pages 333-348
Front Matter....Pages 349-349
Review of Non-Numerical Uses of Computers....Pages 351-391
Elementary Dynamical Astronomy....Pages 392-395
Statistical Orbit Determination Theory....Pages 396-425
Orbit Determination by Solving a Boundary Value Problem....Pages 426-428
Long-Term Motion in a Restricted Problem of Rotational Motion....Pages 429-453
Front Matter....Pages 349-349
Uniform Theory of a Rotating Rigid Body with Dynamical Symmetry....Pages 454-456
Attitude Stability of a Satellite in the Restricted Three-Body Problem....Pages 457-460
Analytical Treatment of Straight-Line Flights into the Sun after Planetary Fly-By....Pages 461-468
Back Matter....Pages 469-470