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This book discusses in detail all the relevant numerical methods for the classical N-body problem. It demonstrates how to develop clear and elegant algorithms for models of gravitational systems, and explains the fundamental mathematical tools needed to describe the dynamics of a large number of mutually attractive particles. Particular attention is given to the techniques needed to model astrophysical phenomena such as close encounters and the dynamics of black hole binaries. The author reviews relevant work in the field and covers applications to the problems of planetary formation and star cluster dynamics, both of Pleiades type and globular clusters. Self-contained and pedagogical, this book is suitable for graduate students and researchers in theoretical physics, astronomy and cosmology.
This book presents basic methods for numerical simulation of gravitational systems, demonstrating how to develop clear and elegant algorithms. It explains the fundamental mathematical tools needed to describe the dynamics of a large number of mutually attractive particles, and the techniques needed to model various known planetary and astrophysical phenomena.
This self-contained book presents basic methods of numerical simulation of gravitational systems, with applications in astronomy and cosmology. The first half of the book presents and explains the fundamental mathematical tools needed to describe the dynamics of a large number of mutually attractive particles. Particular attention is given to the techniques needed to model known planetary and astrophysical phenomena such as Hubble motion. The second half of the book demonstrates how to develop clear and elegant algorithms for models of gravitational systems.
This book discusses in detail all the relevant numerical methods for the classical N-body problem. It demonstrates how to develop clear and elegant algorithms for models of gravitational systems, and explains the fundamental mathematical tools needed to describe the dynamics of a large number of mutually attractive particles. Particular attention is given to the techniques needed to model astrophysical phenomena such as close encounters and the dynamics of black hole binaries. The author reviews relevant work in the field and covers applications to the problems of planetary formation and star cluster dynamics, both of Pleiades type and globular clusters. Self-contained and pedagogical, this book is suitable for graduate students and researchers in theoretical physics, astronomy and cosmology.
In this classic text, a Nobel Prize-winning astrophysicist presents the theory of stellar dynamics as a branch of classical dynamics--a discipline in the same general category as celestial mechanics. His method offers the advantages of clarifying the theory's fundamental issues and defining its underlying motivations. S. Chandrasekhar investigates two areas. The first concerns problems in which the time of relaxation of a stellar system is central. His method consists of analyzing the effects of stellar encounters in terms of the two-body problem of classical dynamics and applying this theory to the dynamics of star clusters. The second area investigates problems centering around Liouville's theorem and the solutions of the equation of continuity; here, the author discusses the dynamic implications of the existence of a field of differential motions, which appears to be the most striking kinematic feature of the galaxy and the extragalactic systems. This edition includes two papers by the author that were published after Principles of Stellar Dynamics and that have been studied and quoted extensively: "New Methods in Stellar Dynamics" (originally published in the Annals of the New York Academy of Sciences) and "Dynamical Friction" (originally published in The Astrophysical Journal).
Computer simulation of systems has become an important tool in scientific research and engineering design, including the simulation of systems through the motion of their constituent particles. Important examples of this are the motion of stars in galaxies, ions in hot gas plasmas, electrons in semiconductor devices, and atoms in solids and liquids. The behavior of the system is studied by programming into the computer a model of the system and then performing experiments with this model. New scientific insight is obtained by observing such computer experiments, often for controlled conditions that are not accessible in the laboratory. Computer Simulation using Particles deals with the simulation of systems by following the motion of their constituent particles. This book provides an introduction to simulation using particles based on the NGP, CIC, and P3M algorithms and the programming principles that assist with the preparations of large simulation programs based on the OLYMPUS methodology. It also includes case study examples in the fields of astrophysics, plasmas, semiconductors, and ionic solids as well as more detailed mathematical treatment of the models, such as their errors, dispersion, and optimization. This resource will help you understand how engineering design can be assisted by the ability to predict performance using the computer model before embarking on costly and time-consuming manufacture.
An introduction to the laws of celestial mechanics and a step-by-step guide to developing software for direct use in astrophysics research. This book offers both an introduction to the laws of celestial mechanics and a step-by-step guide to developing software for direct use in astrophysics research. It bridges the gap between conventional textbooks, which present a rigorous and exhaustive exposition of theoretical concepts, and applying the theory to tackle real experiments. The text is written engagingly in dialogue form, presenting the research journey of the fictional Alice, Bob, and Professor Starmover. Moving Planets Around not only educates students on the laws of Newtonian gravity, it also provides all that they need to start writing their own software, from scratch, for simulating the dynamical evolution of planets and exoplanets, stars, or other heavenly bodies.
Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.
Since it was first published in 1987, Galactic Dynamics has become the most widely used advanced textbook on the structure and dynamics of galaxies and one of the most cited references in astrophysics. Now, in this extensively revised and updated edition, James Binney and Scott Tremaine describe the dramatic recent advances in this subject, making Galactic Dynamics the most authoritative introduction to galactic astrophysics available to advanced undergraduate students, graduate students, and researchers. Every part of the book has been thoroughly overhauled, and many sections have been completely rewritten. Many new topics are covered, including N-body simulation methods, black holes in stellar systems, linear stability and response theory, and galaxy formation in the cosmological context. Binney and Tremaine, two of the world's leading astrophysicists, use the tools of theoretical physics to describe how galaxies and other stellar systems work, succinctly and lucidly explaining theoretical principles and their applications to observational phenomena. They provide readers with an understanding of stellar dynamics at the level needed to reach the frontiers of the subject. This new edition of the classic text is the definitive introduction to the field. ? A complete revision and update of one of the most cited references in astrophysics Provides a comprehensive description of the dynamical structure and evolution of galaxies and other stellar systems Serves as both a graduate textbook and a resource for researchers Includes 20 color illustrations, 205 figures, and more than 200 problems Covers the gravitational N-body problem, hierarchical galaxy formation, galaxy mergers, dark matter, spiral structure, numerical simulations, orbits and chaos, equilibrium and stability of stellar systems, evolution of binary stars and star clusters, and much more Companion volume to Galactic Astronomy, the definitive book on the phenomenology of galaxies and star clusters