Gravitational Few-Body Dynamics

A Numerical Approach

Seppo Mikkola (University of Turku, Finland)

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English

Cambridge University Press
16 April 2020

Differential calculus & equations; Integral calculus & equations; Mathematical modelling; Astrophysics

Using numerical integration, it is possible to predict the individual motions of a group of a few celestial objects interacting with each other gravitationally. In this introduction to the few-body problem, a key figure in developing more efficient methods over the past few decades summarizes and explains them, covering both basic analytical formulations and numerical methods. The mathematics required for celestial mechanics and stellar dynamics is explained, starting with two-body motion and progressing through classical methods for planetary system dynamics. This first part of the book can be used as a short course on celestial mechanics. The second part develops the contemporary methods for which the author is renowned - symplectic integration and various methods of regularization. This volume explains the methodology of the subject for graduate students and researchers in celestial mechanics and astronomical dynamics with an interest in few-body dynamics and the regularization of the equations of motion.

By: Seppo Mikkola (University of Turku Finland)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 250mm, Width: 174mm, Spine: 17mm
Weight: 630g
ISBN: 9781108491297
ISBN 10: 1108491294
Pages: 252
Publication Date: 16 April 2020
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Preface; Introduction; 1. The problems; 2. Two-body motion; 3. Analytical tools; 4. Variation of parameters; 5. Numerical integration; 6. Symplectic integration; 7. KS-regularization; 8. Algorithmic regularization; 9. Motion in the field of a black hole; 10. Artificial satellite orbits; References; Index.

Seppo Mikkola is a senior lecturer at the University of Turku, Finland, and staff member at Tuorla Observatory. He has made important contributions to the regularization of equations of N-body motion. Since he invented 'algorithmic regularization' of few-body system dynamics, it has become the foundation of many simulations worldwide.