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"Originally published as Absolute or relative motion? volume 1, The discovery of dynamics, Cambridge University Press, 1989".
Ever since Newton created dynamics, there has been controversy about its foundations. Are space and time absolute? Do they form a rigid but invisible framework and container of the universe? Or are space, time, and motion relative? If so, does Newton's 'framework' arise through the influence of the universe at large, as Ernst Mach suggested? Einstein's aim when creating his general theory of relativity was to demonstrate this and thereby implement 'Mach's Principle'. However, it is widely believed that he achieved only partial success. This question of whether motion is absolute or relative has been a central issues in philosophy; the nature of time has perennial interest. Current attempts to create a quantum description of the whole universe keep these issues at the cutting edge of modern research. Written by the world's leading expert on Mach's Principle, The Discovery of Dynamics is a highly original account of the development of notions about space, time, and motion. Widely praised in its hardback version, it is one of the fullest and most readable accounts of the astronomical studies that culminated in Kepler's laws of planetary motion and of the creation of dynamics by Galileo, Descartes, Huygens, and Newton. Originally published as Absolute or Relative Motion?, Vol. 1: The Discovery of Dynamics (Cambridge), The Discovery of Dynamics provides the technical background to Barbour's recently published The End of Time, in which he argues that time disappears from the description of the quantum universe.
This book aims to develop models and modeling techniques that are useful when applied to all complex systems. It adopts both analytic tools and computer simulation. The book is intended for students and researchers with a variety of backgrounds.
This book, first published in 2000, is a comprehensive introduction to holomorphic dynamics, that is the dynamics induced by the iteration of various analytic maps in complex number spaces. This has been the focus of much attention in recent years, with, for example, the discovery of the Mandelbrot set, and work on chaotic behaviour of quadratic maps. The treatment is mathematically unified, emphasizing the substantial role played by classical complex analysis in understanding holomorphic dynamics as well as giving an up-to-date coverage of the modern theory. The authors cover entire functions, Kleinian groups and polynomial automorphisms of several complex variables such as complex Henon maps, as well as the case of rational functions. The book will be welcomed by graduate students and professionals in pure mathematics and science who seek a reasonably self-contained introduction to this exciting area.
Discovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Mandelbrot sets in the complex plane, and symbolic dynamics. Topics have been carefully chosen as a means for developing student persistence and skill in exploration, conjecture, and generalization while at the same time providing a coherent introduction to the fundamentals of discrete dynamical systems. This book is written for undergraduate students with the prerequisites for a first analysis course, and it can easily be used by any faculty member in a mathematics department, regardless of area of expertise. Each module starts with an exploration in which the students are asked an open-ended question. This allows the students to make discoveries which lead them to formulate the questions that will be addressed in the exposition and exercises of the module. The exposition is brief and has been written with the intent that a student who has taken, or is ready to take, a course in analysis can read the material independently. The exposition concludes with exercises which have been designed to both illustrate and explore in more depth the ideas covered in the exposition. Each module concludes with a project in which students bring the ideas from the module to bear on a more challenging or in-depth problem. A section entitled "To the Instructor" includes suggestions on how to structure a course in order to realize the inquiry-based intent of the book. The book has also been used successfully as the basis for an independent study course and as a supplementary text for an analysis course with traditional content.
This volume is a collection of scholarly articles on the Mach Principle, the impact that this theory has had since the end of the 19th century, and its role in helping Einstein formulate the doctrine of general relativity. 20th-century physics is concerned with the concepts of time, space, motion, inertia and gravity. The documentation on all of these makes this book a reference for those who are interested in the history of science and the theory of general relativity
Vortex dynamics is a natural paradigm for the field of chaotic motion and modern dynamical system theory. However, this volume focuses on those aspects of fluid motion that are primarily controlled by the vorticity and are such that the effects of the other fluid properties are secondary.
A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.