9783527409778

Celestial Dynamics : Chaoticity and Dynamics of Celestial Systems

by ;
  • ISBN13:

    9783527409778

  • ISBN10:

    3527409777

  • Format: Hardcover
  • Copyright: 5/28/2013
  • Publisher: Vch Pub
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Summary

Written by an internationally renowned expert author and researcher, this monograph fills the need for a book conveying the sophisticated tools needed to calculate exo-planet motion and interplanetary space flight. It is unique in considering the critical problems of dynamics and stability, making use of the software Mathematica, including supplements for practical use of the formulae. A must-have for astronomers and applied mathematicians alike.

Author Biography

Rudolf Dvorak, now serving at the Institute of Astronomy in Vienna, has gained research experience in planet research at international institutions including the Bureau des Longitudes in Paris. More than 130 publications provide proof.
Dr. Christoph Lhotka is member of Rudolf Dvorak's workgroup, and an expert with the software Mathematica.

Table of Contents

1. INTRODUCTION
Dawn of Astronomy: Observations from Babylon
Three major steps: Computer-Chaos-Extrasolar planets
Outlook Interplanetary Space Flights
2. BASICS
The pendulum as dynamical model
Perturbed pendulum
Standard map
Chaos indicators
Correspondance mappings - dynamical systems
Resonances
3. NUMERICAL and ANALYTICAL TOOLS
Lie-operator and Lie-series
Lie-series as num. Integrators
Lie-transformation and Hamiltonian normal forms
Other applications of Lie-series
4. INTERMEZZO 1: THE SITNIKOV PROBLEM
5. The 2-BODY PROBLEM
Orbital Elements
Kepler?s laws
Kepler?s equation
Applications
6. THE 3-BODY PROBLEM
Newtonian vs. Hamiltonian formulation
Correspondance: resonant motion and the perturbed pendulum
Disturbing function
Mapping models
7. INTERMEZZO 2: EFFECTIVE STABILITY -
THE NEKHOROSHEV
THEOREM
8. THE PLANETARY PROBLEM
9. DYNAMICS OF EXO-PLANETARY SYSTEMS
10. Appendix: Interactive Demonstrations based on Mathematica

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