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From Newton to Chaos : Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems - Archie E. Roy

From Newton to Chaos

Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems

By: Archie E. Roy (Editor), B.A. Steves (Editor)

Hardcover Published: 30th April 1995
ISBN: 9780306449048
Number Of Pages: 584

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The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d' Ampezzo, Italy, between July 25 and August 6, 1993, under the title From Newton to Chaos: Modem Techniques for Understanding and Coping With Chaos inN-Body Dynamical Systems. This institute was the latest in a series of meetings held every three years from 1972 to 1990 in dynamical astronomy, theoretical mechanics and celestial mechanics. The proceedings from these institutes have been well-received in the international community of research workers in these disciplines. The present institute was well attended with 15 series of lectures being given by invited speakers: in addition some 40 presentations were made by the other participants. The majority of these contributions are included in these proceedings. The all-pervading influence of chaos in dynamical systems (of even a few variables) has now been universally recognised by researchers, a recognition forced on us by our ability, using powerful computer hardware and software, to tackle dynamical problems that until twenty-five years ago were intractable. Doubtless it was felt by many that these new techniques provided a break-through in celestial mechanics and its related disciplines. And so they were.

Prelude: Poincare's Contribution to Chance and Chaosp. 1
Perturbation Theory: Techniques and Limitationsp. 5
Quantitative Methods in Classical Perturbation Theoryp. 21
Jacobi Geometry and Chaos in N-Body Systemsp. 39
Proper Elements and Stable Chaosp. 47
Mechanisms of Generation of Chaos in the Solar Systemp. 79
On the Convergence of the Disturbing Functionp. 97
Improving the Classical Expansion of the Disturbing Functionp. 99
The Great Inequality in a Hamiltonian Planetary Theoryp. 103
Stability Over Exponentially Long Times in the Planetary Problemp. 109
Interlude: Remarkable and Spectacular Cometsp. 119
From Order to Chaos: Clustering and Diffusion Processes for Small Bodies in the Solar Systemp. 129
Depletion of the Asteroid Belt at Resonancesp. 157
On the Depletion of the Outer Asteroid Beltp. 171
The Chaotic Zone Connected With the 5/2 Mean Motion Resonancep. 177
The Influence of Chaos on the Evolution of the Minor Bodies of the Solar Systemp. 183
Project Criss-Cross: A Preliminary Analysisp. 193
Meteoroid Stream Dynamicsp. 199
Interlude: From Newton's Adjustable Clock to Poincare's Chaosp. 209
Chaotic Motion in Hill's Lunar Problemp. 217
Hunting for Periodic Orbits Close to that of the Moon in the Restricted Circular Three Body Problemp. 231
Orbital Elements of a Satellite Moving in the Potential of an Oblate Spheroidp. 235
Integrability and Chaos in the Classical 2-Centre Field J[subscript 2]-Approximationp. 241
Analytic Non-integrability and the J[subscript 2]-Problemp. 247
Guidelines for a General Treatment of the J[subscript 2] Problem in DS Variables with True Anomaly Type Fictitious Timep. 253
Second Order Perturbations Due to the Gravity Potential of a Planetp. 259
Perturbation Expansions Around Elliptic Fixed Points in the Spin-Orbit Problemp. 269
Moment Formalism for the Radiative Force Evaluationp. 279
Optimization of Spacecraft Trajectories Using Nonlinear Programmingp. 287
Order Out of Chaos in the Three Body Problem: Regions of Escapep. 299
Chaos in the Hyperbolic Restricted Three Body Problemp. 315
Types of Motion and Stability of Hierarchical Triple Star Systemsp. 319
On the Role of the Moment of Inertia in Three Body Scatteringp. 327
The Bicircular Model Near the Triangular Libration Points of the RTBPp. 343
Nonlinear Stability Zones Around the Triangular Lagrangian Pointsp. 371
An Investigation of Orbits Around the Triangular Lagrangian Points of Saturnp. 379
Collision Orbits in the Isosceles Rectilinear Restricted Problemp. 387
Asymptotic Orbits as Terminations of Families of Periodic Orbits in the Copenhagen Problem with and without Radiation Pressurep. 395
A Typical Family FII of Symmetric and Periodic Orbits of Charged Particles Moving in the Plane of Motion of Two Parallel Rotating Magnetic Dipolesp. 407
Interlude: Fractals, Chaos and Quaternionsp. 417
Order in Chaosp. 425
Chaos as the True Source of the Irreversibility of Timep. 451
Representation and Classification of Dynamical Systemsp. 461
Analytic Hamiltonian Systems, the Vicinity of a Periodic Solutionp. 471
Complex Instabilityp. 485
Inverse Problems Leading to Integrable Systemsp. 495
The Observer - New Method for Numerical Integration of Differential Equations in the Presence of First Integralsp. 503
Analytical Approximations for Sitnikov's Problemp. 513
Elementary Derivation of Hopf Type Bifurcation Formulasp. 525
Chaotic Scattering in the Gaussian Potentialp. 531
Stochastic Motion in a Central Field with a Weak Non-Rotating Bar Perturbationp. 537
A Note on the Canonical Character of the Stiefel-Scheifele Time Elementp. 545
Fractal Structures in Self-Gravitating Cosmological Flowsp. 551
Quaternionic Generalisation of the Mandelbrot Setp. 557
Participants and Speakersp. 563
Author Indexp. 573
Subject Indexp. 581
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780306449048
ISBN-10: 0306449048
Series: NATO Science Series B:
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 584
Published: 30th April 1995
Country of Publication: US
Dimensions (cm): 25.4 x 17.78  x 3.33
Weight (kg): 1.26

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