Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems

Front Matter....Pages i-xvii
Front Matter....Pages 1-1
Dynamical Evolution of Planetary Systems and the Significance of Bode’s Law....Pages 3-12
Further Numerical Investigations into the Significance of Bode’s Law....Pages 13-20
Where are the Saturnian Trojans?....Pages 21-26
Orbital Evolution....Pages 27-46
Planetary Perturbation Theory from Lie Series, including Resonance and Critical Arguments....Pages 47-72
Secular Perturbations of Planetary Orbits and their Representation as Series....Pages 73-108
The Accumulation of Integration Error....Pages 109-116
Numerical Regularization of the Lagrange Planetary Equations....Pages 117-122
Front Matter....Pages 123-123
General Formulas for Three-Body Resonances....Pages 125-139
Analytical Methods for the Radial Intermediaries....Pages 141-147
Analytical Theory of the Rotation of an Artificial Satellite....Pages 149-154
Some Models for the Motion of the Co-orbital Satellites of Saturn....Pages 155-169
Long-Period Changes in the Semimajor Axis of Lageos....Pages 171-172
Effects of a Non-Circular Shepherd upon a Planetary Ring....Pages 173-180
General Motion of a Triaxial Rigid Body in a Newtonian Force Field....Pages 181-187
The Motion of the Orbit Plane of Iapetus....Pages 189-192
Astrodynamics in the Real-World Environment (The Whole Truth and Nothing but the Truth)....Pages 193-196
A Finite-Time Stability Criterion for Sun-Perturbed Planetary Satellites....Pages 197-215
A New Radial Intermediary and its Numerical Integration....Pages 217-222
Co-orbital Satellites and Hill’s Lunar Problem....Pages 223-234
Front Matter....Pages 235-235
The Puzzle of Asteroid Families....Pages 237-244
High Eccentricity Libration....Pages 245-250
Evolution of Asteroidal Orbits Located in the Main Secular Resonances v 5 ,v 6 and v 16 ....Pages 251-256
Algebraic Mappings near a Resonance with an Application to Asteroid Motion....Pages 257-276
The Hierarchical Restricted Problem with Applications....Pages 277-288
The Motions of Asteroids in the Secular Resonance v 6 : An Analytical Model and Numerical Calculations....Pages 289-293
Front Matter....Pages 295-295
Families of Periodic Orbits in a Model of Interacting Galaxies....Pages 297-300
Qualitative Characteristics of Dynamical Systems....Pages 301-315
On the Galactic Motion....Pages 317-327
The N-Body Problem in Stellar Dynamics....Pages 329-347
Rotationally and Tidally Perturbed Orbital Elements of Close Binary Stars....Pages 349-353
Front Matter....Pages 355-355
Escape and Capture in the RTBP....Pages 357-362
A Formulation of the N-Body Problem where the Velocities are Bounded....Pages 363-369
A Report on Some New KAM Estimates....Pages 371-375
Extended Canonical Transformations Increasing the Number of Variables....Pages 377-383
Non Local Spiraling Characteristic Curves....Pages 385-391
Connectance and Stability of Linear Differential Systems....Pages 393-403
Resonances in the Planar Elliptic Restricted Problem....Pages 405-425
The Near-Resonance Theorem: Analysis of the Vicinity of Periodic Solutions of Analytic Differential Systems....Pages 427-448
Homoclinic and Heteroclinic Solutions of the RTBP Joining the Triangular Equilibrium Points....Pages 449-455
Front Matter....Pages 355-355
Double Collision Orbits and Second Species Solutions in the Restricted Three-Body Problem....Pages 457-464
Bifurcations and Instabilities in the Restricted Three-Body Problem....Pages 465-469
Three Dimensional Equations of Szebehely of the Inverse Problem and Frenet Reference Frame....Pages 471-475
Fourier Transform in Astrodynamics....Pages 477-479
Estimates of the Error in Normal Forms of Hamiltonian Systems. Applications to Effective Stability and Examples....Pages 481-503
Passages near Triple Collision....Pages 505-512
Non-Integrability of Hamiltonian Systems Based on Ziglin’s Theorem....Pages 513-513
Back Matter....Pages 515-526