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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.
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