Download or read book Leonhard Euler and the Foundations of Celestial Mechanics written by Dora Musielak and published by Springer Nature. This book was released on 2022-11-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of this book is to shine a bright light on the intellectual context of Euler’s contributions to physics and mathematical astronomy. Leonhard Euler is one of the most important figures in the history of science, a blind genius who introduced mathematical concepts and many analytical tools to help us understand and describe the universe. Euler also made a monumental contribution to astronomy and orbital mechanics, developing what he called astronomia mechanica. Orbital mechanics of artificial satellites and spacecraft is based on Euler’s analysis of astromechanics. However, previous books have often neglected many of his discoveries in this field. For example, orbital mechanics texts refer to the five equilibrium points in the Sun-Earth-Moon system as Lagrange points, failing to credit Euler who first derived the differential equations for the general n-body problem and who discovered the three collinear points in the three-body problem of celestial mechanics. These equilibrium points are essential today in space exploration; the James Webb Space Telescope (successor to the Hubble), for example, now orbits the Sun near L2, one of the collinear points of the Sun-Earth-Moon system, while future missions to study the universe will place observatories in orbit around Sun-Earth and Earth-Moon equilibrium points that should be properly called Euler-Lagrange points. In this book, the author uses Euler’s memoirs, correspondence, and other scholarly sources to explore how he established the mathematical groundwork for the rigorous study of motion in our Solar System. The reader will learn how he studied comets and eclipses, derived planetary orbits, and pioneered the study of planetary perturbations, and how, old and blind, Euler put forward the most advanced lunar theory of his time.
Download or read book Euler Celestial Analysis written by Dora Musielak and published by . This book was released on 2018-03-20 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leonhard Euler stood at the center of mathematical development in the eighteenth century. Euler Celestial Analysis shines a dazzling light on the intellectual context of Eulers contributions to mathematical astronomy. Offering an elegant and unbiased portrait of this remarkable mathematician, Dora Musielak uses Eulers works to explore how he built the foundation for the rigorous study of motion in our Solar System. With his exquisite flair for analysis, Euler stated the three-body problem of celestial mechanics, and he derived the differential equations for the general n-body problem, identifying all the integrals of motion. He studied comets, eclipses, derived planetary orbits, and pioneered the study of planetary perturbations. Old and blind, Euler put forward the most advanced lunar theory of his time. Euler Celestial Analysis also provides an introduction to spacecraft orbit mechanics, a branch of celestial mechanics that studies spaceflight and that has revolutionized the direct exploration of the heavens.
Download or read book Foundations of Celestial Mechanics written by Elena Bannikova and published by Springer Nature. This book was released on 2022-12-02 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to classical celestial mechanics. It is based on lectures delivered by the authors over many years at both Padua University (MC) and V.N. Karazin Kharkiv National University (EB). The book aims to provide a mathematical description of the gravitational interaction of celestial bodies. The approach to the problem is purely formal. It allows the authors to write equations of motion and solve them to the greatest degree possible, either exactly or by approximate techniques, when there is no other way. The results obtained provide predictions that can be compared with the observations. Five chapters are supplemented by appendices that review certain mathematical tools, deepen some questions (so as not to interrupt the logic of the mainframe with heavy technicalities), give some examples, and provide an overview of special functions useful here, as well as in many other fields of physics. The authors also present the original investigation of torus potential. This book is aimed at senior undergraduate students of physics or astrophysics, as well as graduate students undertaking a master’s degree or Ph.D.
Download or read book The Foundations of Celestial Mechanics written by George William Collins and published by . This book was released on 1989 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Analytical Foundations of Celestial Mechanics written by Aurel Wintner and published by Courier Corporation. This book was released on 2014-06-18 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this 1941 monograph, Aurel Wintner joined Poincaré, Birkhoff, and others in placing celestial mechanics on a sound mathematical basis. The product of many years of work by the author, it remains an extremely valuable contribution to the literature of this field. Starting with a review of dynamical operations, the treatment advances to local and non-local questions, dynamical systems, the problem of two bodies and the problem of several bodies, and an introduction to the restricted problem. Suitable for advanced undergraduates and graduate students of physics, the text is amply supplemented by a substantial section of notes and references in which a great deal of the historical literature from which it derives is discussed.
Download or read book Integrable Systems in Celestial Mechanics written by Diarmuid Ó'Mathúna and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shows that exact solutions to the Kepler (two-body), the Euler (two-fixed center), and the Vinti (earth-satellite) problems can all be put in a form that admits the general representation of the orbits and follows a definite shared pattern Includes a full analysis of the planar Euler problem via a clear generalization of the form of the solution in the Kepler case Original insights that have hithertofore not appeared in book form
Download or read book Mathematical Aspects of Classical and Celestial Mechanics written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2007-07-05 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.
Download or read book The Legacy of Leonhard Euler written by Lokenath Debnath and published by World Scientific. This book was released on 2010 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily serves as a historical research monograph on the biographical sketch and career of Leonhard Euler and his major contributions to numerous areas in the mathematical and physical sciences. It contains fourteen chapters describing Euler?s works on number theory, algebra, geometry, trigonometry, differential and integral calculus, analysis, infinite series and infinite products, ordinary and elliptic integrals and special functions, ordinary and partial differential equations, calculus of variations, graph theory and topology, mechanics and ballistic research, elasticity and fluid mechanics, physics and astronomy, probability and statistics. The book is written to provide a definitive impression of Euler?s personal and professional life as well as of the range, power, and depth of his unique contributions. This tricentennial tribute commemorates Euler the great man and Euler the universal mathematician of all time. Based on the author's historically motivated method of teaching, special attention is given to demonstrate that Euler?s work had served as the basis of research and developments of mathematical and physical sciences for the last 300 years. An attempt is also made to examine his research and its relation to current mathematics and science. Based on a series of Euler?s extraordinary contributions, the historical development of many different subjects of mathematical sciences is traced with a linking commentary so that it puts the reader at the forefront of current research.
Download or read book An Introduction to Celestial Mechanics written by Forest Ray Moulton and published by . This book was released on 1914 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Celestial Encounters written by Florin Diacu and published by Princeton University Press. This book was released on 2020-12-08 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincaré found a serious mistake in his work. While correcting it, he discovered the phenomenon of chaos. Starting with the story of Poincaré's work, Florin Diacu and Philip Holmes trace the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's Principia in 1686. In describing how mathematical rigor was brought to bear on one of our oldest fascinations--the motions of the heavens--they introduce the people whose ideas led to the flourishing field now called nonlinear dynamics. In presenting the modern theory of dynamical systems, the models underlying much of modern science are described pictorially, using the geometrical language invented by Poincaré. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it.
Download or read book Lectures on Celestial Mechanics written by Carl L. Siegel and published by Springer Science & Business Media. This book was released on 1995-02-15 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book represents to a large extent the translation of the German "Vorlesungen über Himmelsmechanik" by C. L. Siegel. The demand for a new edition and for an English translation gave rise to the present volume which, however, goes beyond a mere translation. To take account of recent work in this field a number of sections have been added, especially in the third chapter which deals with the stability theory. Still, it has not been attempted to give a complete presentation of the subject, and the basic prganization of Siegel's original book has not been altered. The emphasis lies in the development of results and analytic methods which are based on the ideas of H. Poincare, G. D. Birkhoff, A. Liapunov and, as far as Chapter I is concerned, on the work of K. F. Sundman and C. L. Siegel. In recent years the measure-theoretical aspects of mechanics have been revitalized and have led to new results which will not be discussed here. In this connection we refer, in particular, to the interesting book by V. I. Arnold and A. Avez on "Problemes Ergodiques de la Mecanique Classique", which stresses the interaction of ergodic theory and mechanics. We list the points in which the present book differs from the German text. In the first chapter two sections on the tri pie collision in the three body problem have been added by C. L. Siegel.
Download or read book Leonhard Euler written by Robert E. Bradley and published by Elsevier. This book was released on 2007-03-20 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment’s most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world’s best Eulerian scholars from seven different countries about Euler, his life and his work. Some of the essays are historical, including much previously unknown information about Euler’s life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler’s philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Euler’s innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science. - Over 20 essays by some of the best historians of mathematics and science, including Ronald Calinger, Peter Hoffmann, Curtis Wilson, Kim Plofker, Victor Katz, Ruediger Thiele, David Richeson, Robin Wilson, Ivor Grattan-Guinness and Karin Reich- New details of Euler's life in two essays, one by Ronald Calinger and one he co-authored with Elena Polyakhova- New information on Euler's work in differential geometry, series, mechanics, and other important topics including his influence in the early 19th century
Download or read book The Geometry of Celestial Mechanics written by Hansjörg Geiges and published by Cambridge University Press. This book was released on 2016-03-24 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.
Download or read book Leonhard Euler s Letters to a German Princess written by Ronald S. Calinger and published by Iop Concise Physics. This book was released on 2019-06-28 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leonhard Euler's Letters to a German Princess on Various Subjects in Physics and Philosophy is a milestone in the history of physics textbooks and the instruction of women in the sciences. It also covers views of its author on epistemology, religion, and innovations in scientific equipment, including telescopes and microscopes. Today, 250 years later, we study this work of Euler's as a foundation for the history of physics teaching and analyze the letters from an historical and pedagogical point of view.
Download or read book Encyclopedia of Nonlinear Science written by Alwyn Scott and published by Routledge. This book was released on 2006-05-17 with total page 1107 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.
Download or read book Celestial Mechanics written by Harry Pollard and published by American Mathematical Soc.. This book was released on 1976-12-31 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the basic mathematics underlying the subject of celestial mechanics. Chapter 1 formulates the central force problem and then deals with Kepler's first and second laws, orbits under non-Newtonian attraction, elements of an orbit, the two-body system, the solar system, and disturbed motion. Chapter 2 introduces the n-body problem. Included in Chapter 2 are the Lagrange—Jacobi formula, Sundman's theorem on total collapse, the three-body problem, and Lagrange's and Euler's solutions to the three-body problem. Chapter 3 is an introduction to Hamilton-Jacobi Theory.
Download or read book Encyclopedia of Early Modern Philosophy and the Sciences written by Dana Jalobeanu and published by Springer Nature. This book was released on 2022-08-27 with total page 2267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Encyclopedia offers a fresh, integrated and creative perspective on the formation and foundations of philosophy and science in European modernity. Combining careful contextual reconstruction with arguments from traditional philosophy, the book examines methodological dimensions, breaks down traditional oppositions such as rationalism vs. empiricism, calls attention to gender issues, to ‘insiders and outsiders’, minor figures in philosophy, and underground movements, among many other topics. In addition, and in line with important recent transformations in the fields of history of science and early modern philosophy, the volume recognizes the specificity and significance of early modern science and discusses important developments including issues of historiography (such as historical epistemology), the interplay between the material culture and modes of knowledge, expert knowledge and craft knowledge. This book stands at the crossroads of different disciplines and combines their approaches – particularly the history of science, the history of philosophy, contemporary philosophy of science, and intellectual and cultural history. It brings together over 100 philosophers, historians of science, historians of mathematics, and medicine offering a comprehensive view of early modern philosophy and the sciences. It combines and discusses recent results from two very active fields: early modern philosophy and the history of (early modern) science. Editorial Board EDITORS-IN-CHIEF Dana Jalobeanu University of Bucharest, Romania Charles T. Wolfe Ghent University, Belgium ASSOCIATE EDITORS Delphine Bellis University Nijmegen, The Netherlands Zvi Biener University of Cincinnati, OH, USA Angus Gowland University College London, UK Ruth Hagengruber University of Paderborn, Germany Hiro Hirai Radboud University Nijmegen, The Netherlands Martin Lenz University of Groningen, The Netherlands Gideon Manning CalTech, Pasadena, CA, USA Silvia Manzo University of La Plata, Argentina Enrico Pasini University of Turin, Italy Cesare Pastorino TU Berlin, Germany Lucian Petrescu Université Libre de Bruxelles, Belgium Justin E. H. Smith University de Paris Diderot, France Marius Stan Boston College, Chestnut Hill, MA, USA Koen Vermeir CNRS-SPHERE + Université de Paris, France Kirsten Walsh University of Calgary, Alberta, Canada
