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Astronomy | Stability and Chaos in Celestial Mechanics

Stability and Chaos in Celestial Mechanics

Celletti, Alessandra

Jointly published with Praxis Publishing, UK

2010

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  • Provides a comprehensive survey of the tools of celestial mechanics from classical theories to modern methods
  • Presents a variety of useful computer-assisted techniques with practical examples of applications
  • Demonstrates the interplay between classical celestial mechanics and the modern tools of dynamical systems
  • Gives useful examples for the constructive implementation of perturbation theory
  • Investigates the regular and chaotic behavior of the trajectories of planets, spacecraft orbits, and rotation of satellites
  • Will be used for teaching and research in space exploration
The last decades have marked the beginning of a new era in Celestial Mech- ics. The challenges came from several di?erent directions. The stability theory of nearly–integrable systems (a class of problems which includes many models of - lestial Mechanics) pro?ted from the breakthrough represented by the Kolmogorov– Arnold–Moser theory, which also provides tools for determining explicitly the - rameter values allowing for stability. A con?nement of the actions for exponential times was guaranteed by Nekhoroshev’s theorem, which gives much information about the geography of the resonances. Performing ever-faster computer simu- tionsallowedustohavedeeperinsightsintomanyquestionsofDynamicalSystems, most notably chaos theory. In this context several techniques have been developed to distinguish between ordered and chaotic behaviors. Modern tools for computing spacecraft trajectories made possible the realization of many space missions, es- cially the interplanetary tours, which gave a new shape to the solar system with a lot of new satellites and small bodies. Finally, the improvement of observational techniques allowed us to make two revolutions in the sky: the solar system does not end with Pluto, but it extends to the Kuiper belt, and the solar system is not unique, but the universe has plenty of extrasolar planetary systems. Cookingalltheseingredientstogetherwiththeclassicaltheoriesdevelopedfrom the 17th to the 19th centuries, one obtains themodern Celestial Mechanics.

Content Level » Research

Keywords » Celestial Mechanics - Computational methods - Dynamical Systems - KAM theory - Solar System - Three-body problem - Two-body problem - solar

Related subjects » Astronomy - Astrophysics and Astroparticles - Classical Continuum Physics - Complexity - Theoretical, Mathematical & Computational Physics

Table of contents 

Order and chaos.- Numerical dynamical methods.- Kepler’s problem.- The three-body problem and the Lagrangian solutions.- Rotational dynamics.- Perturbation theory.- Invariant tori.- Long-time stability.- Determination of periodic orbits.- Regularization theory.

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