This book presents classical celestial mechanics and its interplay with dynamical systems in a way suitable for advance level undergraduate students as well as postgraduate students and researchers. First paradigmatic models are usedto introduce the reader to the concepts of order, chaos, invariant curves, cantori. Next the main numerical methods to investigate a dynamical system are presented. Then the author reviews the classical two-body problem and proceeds to explore the three-body model in order to investigate orbital resonances andLagrange solutions. In rotational dynamics the author details the derivation of the rigid body motion, and continues by discussing related topics, from spin-orbit resonances to dumbbell satellite dynamics. Perturbation theory is thenexplored in full detail including practical examples of its application to finding periodic orbits, computation of the libration in longitude of the Moon. The main ideas of KAM theory are provided including a presentation of long-term stability and converse KAM results. Celletti then explains the implementation of computer-assisted techniques, which allow the user to obtain rigorous results in good agreement with the astronomical expectations. Finally the study of collisions in the solar system is approached. 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 celestialmechanics and the modern tools of dynamical systems Gives useful examples forthe constructive implementation of perturbation theory Investigates the regular and chaotic behavior of the trajectories of planets, spacecraft orbits, androtation of satellites Will be used for teaching and research in space exploration INDICE: Preface.- Acknowledgements.- Chapter 1 Order and chaos.- Chapter 2Numerical dynamical methods.- Chapter 3 Kepler’s problem.- Chapter 4 The Three-body problem and the Lagrangian solutions.- Chapter 5 Rotational dynamics.- Chapter 6 Perturbation theory.- Chapter 7 Invariant tori.- Chapter 8 Long-timestability.- Chapter 9 Determination of periodic orbits.- Chapter 10 Regularization theory.- Appendices.- Bibliography.- Index.
- ISBN: 978-3-540-85145-5
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 264
- Fecha Publicación: 25/11/2009
- Nº Volúmenes: 1
- Idioma: Inglés