Stability of the Solar System and Its Minor Natural and Artificial Bodies

Front Matter....Pages i-xxiv
Front Matter....Pages 1-1
The Tiny Satellites of Jupiter and Saturn and their Interactions with the Rings....Pages 3-16
Motion of a Geo-Centric Synchronous Satellite....Pages 17-32
On the Brown Conjecture....Pages 33-37
On the Evolution of the Lunar Orbit....Pages 39-51
The Three-Body Problem with Two Small Masses: A Singular-Perturbation Approach to the Problem of Saturn’s Coorbiting Satellites....Pages 53-63
Stability and Origin of the Minor Bodies of the Solar System....Pages 65-79
Front Matter....Pages 81-81
Existence and Stability of Circular Orbits in Axially-Symmetric Gravitational Fields....Pages 83-95
Bifurcations and Stability in Three-Dimensional Systems....Pages 97-113
Three-Body Problem Some Applications of the Tests of Escape....Pages 115-138
Methods of Stability Analysis in the Solar System....Pages 139-150
Studies in the Stability of Hierarchical Dynamical Systems....Pages 151-174
Stability in Celestial Mechanics....Pages 175-180
Front Matter....Pages 181-181
Resonance Sweeping in the Solar System....Pages 183-192
Some Results of Resonance and Periodic Motions....Pages 193-199
Sur Une Equation de Hill Singuliere....Pages 201-210
Front Matter....Pages 211-211
Hamiltonian Perturbations in Dynamical Systems and Applications in Planetary Systems....Pages 213-225
Recent Extensions of Hamilton’s Law of Varying Action with Applications — The Integral Variation Method....Pages 227-232
Recent Extensions of Hamilton’s Law of Varying Action — Mathematical Insights....Pages 233-240
KAM Theory and Dynamical Astronomy....Pages 241-252
Stability of Hamiltonian Systems of Two Degrees of Freedom and of Formally Conservative Mappings Near a Singular Point....Pages 253-262
Front Matter....Pages 263-263
The Lyapunov Characteristic Exponents and Applications to the Dimension of the Invariant Manifolds and Chaotic Attractors....Pages 265-282
Dynamics of Multi-Parameter Systems with Interacting Oscillations....Pages 283-304
Homoclinic Phenomena and Quasi-Integrability....Pages 305-316
Front Matter....Pages 317-317
Geodesic Flows....Pages 319-331
Extragalactic Celestial Mechanics: An Introduction....Pages 333-347
Motions in the Magnetic Field of Two Revolving Dipoles....Pages 349-364
Front Matter....Pages 365-365
Types of Motion in the Oblate Planet Problem....Pages 367-367
Future Orbital Evolution of Satellite Phobos....Pages 368-368
Precession Dynamics in Spin-Orbit Coupling: A Unified Theory....Pages 369-369
A Singularity Analysis of Dynamical Systems with Applications to Astronomy....Pages 370-370
Resonant Periodic Orbits in a Rotating Galaxy....Pages 371-371
Earth Deformations from Lageos Orbit....Pages 372-373
The Puzzle of Lageos’ Semimajor Axis Decay....Pages 374-375
On the Hill Variables and the Radial Intermediaries in Artificial Satellite Theory....Pages 376-376
Applications of the Method of Averaging to Predict Dual-Spin Spacecraft Attitude Motion....Pages 377-377
Orbit Determination: Preliminary Orbits....Pages 378-378
Quasiresonant Canonical Forms for Hamiltonian Systems....Pages 379-379
On the Equilibrium Solutions in the Circular Planar Restricted Problem of Three Rigid Bodies....Pages 380-380
Linearization in Special Cases of the Perturbed Two-Body Problem....Pages 381-381
Generalized Elliptic Anomalies....Pages 382-382
Front Matter....Pages 365-365
Invariant Manifolds and Homoclinic Opbits for L 3 in the R.T.R.P.....Pages 383-383
Models for the Splitting of Separatrices....Pages 384-385
Kolmogorov Entropy as a Measure of Disorder in Some Non-Integrable Hamiltonian Systems....Pages 386-386
Orbital Reversal of Particle Streams in Resonance with Jupiter....Pages 387-387
Approximate Solutions to the Restricted Problem of Three Bodies for Small Mass Parameter....Pages 388-389
A Perturbation Technique Based on the Integral Variation Method....Pages 390-390
Regularization of the Triple Collision Manifold in the Planar Three-Body Problem....Pages 391-391
A Restricted Problem of Four Bodies....Pages 392-392
Escape of a Subsystem in a N-Body Problem. Application to the Three Body Problem....Pages 393-393
The Orbits of Titan, Hyperion and Iapetus....Pages 394-394
Motion about the Stable Libration Points in the Linearized, Restricted Three-Body Problem....Pages 395-395
Stability in the Restricted Three Body Problem with Drag....Pages 396-396
Structure of the 3:1 Jovian Resonance....Pages 397-397
The Restricted Elliptic Three-Body Problem for the Mass Parameter Equal to Zero....Pages 398-398
Final Tidal Evolution of Orbit-Orbit Resonances....Pages 399-400
Two Applications of Joukowsky’s Formula in the Inverse Problem of Dynamics....Pages 401-401
A Canonical Approach to a Second-Order Solution for the Secular Motion of the Planets....Pages 402-402
Translatory-Rotatory Motion of a Gyrostat in a Newtonian Force Field....Pages 403-403
Analytical Expressions for Some Spatial Periodic Orbits of the Restricted Three-Body Problem and Their Invariant Manifolds....Pages 404-404
On the Integrability and Non-Integrability in Boolean Dynamics....Pages 405-406
Front Matter....Pages 365-365
Stability of Binary Asteroids....Pages 407-407
Back Matter....Pages 409-424