Published under the auspices of the Royal Astronomical Society, this volume contains a set of extensive school tested lectures, with the aim to give a coherent and thorough background knowledge of the subject and to introduce the latest developments in N-body computational astrophysics. The topics cover a wide range from the classical few-body problem with discussions of resonance, chaos and stability to realistic modelling of star clusters as well as descriptions of codes, algorithms and special hardware for N-body simulations. This collection of topics, related to the gravitational N-body problem, will prove useful to both students and researchers in years to come.

Complex systems modeling and simulation approaches are being adopted in a growing number of sectors, including finance, economics, biology, astronomy, and many more. Technologies ranging from distributed computing to specialized hardware are explored and developed to address the computational requirements arising in complex systems simulations. The aim of this book is to present a representative overview of contemporary large-scale computing technologies in the context of complex systems simulations applications. The intention is to identify new research directions in this field and to provide a communications platform facilitating an exchange of concepts, ideas and needs between the scientists and technologist and complex system modelers. On the application side, the book focuses on modeling and simulation of natural and man-made complex systems. On the computing technology side, emphasis is placed on the distributed computing approaches, but supercomputing and other novel technologies are also considered.

This is the first monograph dedicated entirely to problems of stability and chaotic behaviour in planetary systems and its subsystems. The author explores the three rapidly developing interplaying fields of resonant and chaotic dynamics of Hamiltonian systems, the dynamics of Solar system bodies, and the dynamics of exoplanetary systems. The necessary concepts, methods and tools used to study dynamical chaos (such as symplectic maps, Lyapunov exponents and timescales, chaotic diffusion rates, stability diagrams and charts) are described and then used to show in detail how the observed dynamical architectures arise in the Solar system (and its subsystems) and in exoplanetary systems. The book concentrates, in particular, on chaotic diffusion and clearing effects. The potential readership of this book includes scientists and students working in astrophysics, planetary science, celestial mechanics, and nonlinear dynamics.

The development of the orbits theory lags behind the development of satellite technology. This book provides, for the first time in the history of human satellite development, the complete third order solution of the orbits under all possible disturbances. It describes the theory of satellite orbits, derives the complete solutions of the orbital disturbances, describes the algorithms of orbits determination based on the theory, describes the applications of the theory to the phenomenon of the satellite formation physically. The subjects include: Orbits Motion Equations, Disturbance theory, Solutions of the differential Equations, Algorithms of Orbits determinations, Applications of the theory to the satellite formation.

Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot’s notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions. R. Montgomery’s notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in order to motivate the McGehee transformation. A. Pedroza’s notes provide a brief introduction to Lagrangian Floer homology and its relation to the solution of the Arnol’d conjecture on the minimal number of non-degenerate fixed points of a Hamiltonian diffeomorphism.

Vladislav Golyanik proposes several new methods for dense non-rigid structure from motion (NRSfM) as well as alignment of point clouds. The introduced methods improve the state of the art in various aspects, i.e. in the ability to handle inaccurate point tracks and 3D data with contaminations. NRSfM with shape priors obtained on-the-fly from several unoccluded frames of the sequence and the new gravitational class of methods for point set alignment represent the primary contributions of this book. About the Author: Vladislav Golyanik is currently a postdoctoral researcher at the Max Planck Institute for Informatics in Saarbrücken, Germany. The current focus of his research lies on 3D reconstruction and analysis of general deformable scenes, 3D reconstruction of human body and matching problems on point sets and graphs. He is interested in machine learning (both supervised and unsupervised), physics-based methods as well as new hardware and sensors for computer vision and graphics (e.g., quantum computers and event cameras).

Unifying work by a broad range of experts in the field, this is the most complete textbook on observational astrometry.