Download or read book New Methods of Celestial Mechanics written by Henri Poincaré and published by . This book was released on 1967 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Century of Mathematics in America written by Peter L. Duren and published by Springer Science & Business. This book was released on 1988 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of the A Century of Mathematics in America collection, this book contains articles that describe the mathematics and the mathematical personalities in some of the nations' prominent departments: Johns Hopkins, Clark, Columbia, MIT, Michigan, Texas, and the Institute for Advanced Study.

Download or read book Dynamical Systems III written by Vladimir I. Arnol'd and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work describes the fundamental principles, problems, and methods of elassical mechanics focussing on its mathematical aspects. The authors have striven to give an exposition stressing the working apparatus of elassical mechanics, rather than its physical foundations or applications. This appara tus is basically contained in Chapters 1, 3,4 and 5. Chapter 1 is devoted to the fundamental mathematical models which are usually employed to describe the motion of real mechanical systems. Special consideration is given to the study of motion under constraints, and also to problems concerned with the realization of constraints in dynamics. Chapter 3 is concerned with the symmetry groups of mechanical systems and the corresponding conservation laws. Also discussed are various aspects of the theory of the reduction of order for systems with symmetry, often used in applications. Chapter 4 contains abrief survey of various approaches to the problem of the integrability of the equations of motion, and discusses some of the most general and effective methods of integrating these equations. Various elassical examples of integrated problems are outlined. The material pre sen ted in this chapter is used in Chapter 5, which is devoted to one of the most fruitful branches of mechanics - perturbation theory. The main task of perturbation theory is the investigation of problems of mechanics which are" elose" to exact1y integrable problems.

Download or read book The Three Body Problem and the Equations of Dynamics written by Henri Poincaré and published by Springer. This book was released on 2017-05-11 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations’ solutions, such as orbital resonances and horseshoe orbits. Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating.

Download or read book Poincare and the Three Body Problem written by June Barrow-Green and published by American Mathematical Soc.. This book was released on 1997 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Poincare's famous memoir on the three body problem arose from his entry in the competition celebrating the 60th birthday of King Oscar of Sweden and Norway. His essay won the prize and was set up in print as a paper in Acta Mathematica when it was found to contain a deep and critical error. In correcting this error Poincare discovered mathematical chaos, as is now clear from June Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincare himself, recently discovered in the Institut Mittag-Leffler in Stockholm. Poincare and the Three Body Problem opens with a discussion of the development of the three body problem itself and Poincare's related earlier work. The book also contains intriguing insights into the contemporary European mathematical community revealed by the workings of the competition. After an account of the discovery of the error and a detailed comparative study of both the original memoir and its rewritten version, the book concludes with an account of the final memoir's reception, influence and impact, and an examination of Poincare's subsequent highly influential work in celestial mechanics.

Download or read book Stable and Random Motions in Dynamical Systems written by Jurgen Moser and published by Princeton University Press. This book was released on 2016-03-02 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.

Download or read book A Russian Childhood written by S. Kovalevskaya and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the year 1889 Sofya Vasilievna Kovalevskaya, Profes sor of Mathematics at the University of Stockholm, pub lished her recollections of growing up in mid-nineteenth century Russia. Professor Kovalevskaya was already an international celebrity, and partly for the wrong reasons: less as the distinguished mathematician she actually was than as a "mathematical lady"--A bizarre but fascinating phenomenon.* Her book was an immediate success. She had written it in Russian, but its first publication was a translation into Swedish, the language of her adopted homeland, where it appeared thinly disguised as a novel under the title From Russian Ltfe: the Rajevski Sisters (Sonja Kovalevsky. Ur ryska lifvet. Systrarna Rajevski. Heggstrom, 1889). In the following year the book came out in Russia in two *"My gifted Mathematical Assistant Mr. Hammond exclaimed ... 'Why, this is the first handsome mathematical lady I have ever seen!'" Letter to S.V. Kovalevskaya from].]. Sylvester, Professor of Mathe matics, New College, Oxford, Dec. 25, 1886

Download or read book The Calculus of Variations in the Large written by Marston Morse and published by American Mathematical Soc.. This book was released on 1934-12-31 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. Calculus of Variations in the Large is certainly one of the essential references on Morse theory.

Download or read book The Birth of the Orchestra written by John Spitzer and published by Oxford University Press. This book was released on 2004-04-29 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book traces the emergence of the orchestra from 16th-century string bands to the 'classical' orchestra of Haydn, Mozart, Beethoven, and their contemporaries. Ensembles of bowed stringed instruments, several players per part plus continuo and wind instruments, were organized in France in the mid-17th century and then in Rome at the end of the century. The prestige of these ensembles and of the music and performing styles of their leaders, Jean-Baptiste Lully and ArcangeloCorelli, caused them to be imitated elsewhere, until by the late 18th century, the orchestra had become a pan-European phenomenon.Spitzer and Zaslaw review previous accounts of these developments, then proceed to a thoroughgoing documentation and discussion of orchestral organization, instrumentation, and social roles in France, Italy, Germany, England, and the American colonies. They also examine the emergence of orchestra musicians, idiomatic music for orchestras, orchestral performance practices, and the awareness of the orchestra as a central institution in European life.

Download or read book Helmholtz and the Conservation of Energy written by Kenneth L. Caneva and published by MIT Press. This book was released on 2021-08-03 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: An examination of the sources Helmholtz drew upon for his formulation of the conservation of energy and the impact of his work on nineteenth-century physics. In 1847, Herman Helmholtz, arguably the most important German physicist of the nineteenth century, published his formulation of what became known as the conservation of energy--unarguably the most important single development in physics of that century, transforming what had been a conglomeration of separate topics into a coherent field unified by the concept of energy. In Helmholtz and the Conservation of Energy, Kenneth Caneva offers a detailed account of Helmholtz's work on the subject, the sources that he drew upon, the varying responses to his work from scientists of the era, and the impact on physics as a discipline. Caneva describes the set of abiding concerns that prompted Helmholtz's work, including his rejection of the idea of a work-performing vital force, and investigates Helmholtz's relationship to both an older generation of physicists and an emerging community of reformist physiologists. He analyzes Helmholtz's indebtedness to Johannes Müller and Justus Liebig and discusses Helmholtz's tense and ambivalent relationship to the work of Robert Mayer, who had earlier proposed the uncreatability, indestructibility, and transformability of "force." Caneva examines Helmholtz's continued engagement with the subject, his role in the acceptance of the conservation of energy as the central principle of physics, and the eventual incorporation of the principle in textbooks as established science.

Download or read book The Rise of Musical Classics in Eighteenth century England written by William Weber and published by Oxford University Press, USA. This book was released on 1996 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to explore the formation of musical 'classics' in regard to repertory and social context. It examines the performance of old music in eighteenth-century England, from the interest in music of the Elizabethan period at the beginning of the century, through the performance of works by Henry Purcell, Arcangelo Corelli, and other English and Italian composers, and the development of festivals that featured choral-orchestral works of Purcell and Handel. It concludes with the establishment of the Concert of Antient Music in 1776, where the traditions of performing old works came together as a self-conscious canon focused upon the work of Handel. The book examines closely the political and social reasons for these developments. In addition, it shows how they laid the groundwork for the classical-music tradition of the nineteenth century.

Download or read book Collected Mathematical Papers written by George David Birkhoff and published by . This book was released on 1968 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Creative Evolution written by Henri Bergson and published by . This book was released on 1911 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Matter and Memory written by Henri Bergson and published by e-artnow. This book was released on 2018-11-01 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matter and Memory presents an analysis of the classical philosophical problems concerning this relation. Within that frame the analysis of memory serves the purpose of clarifying the problem. Matter and Memory was written in reaction to the book The Maladies of Memory by Théodule Ribot, which appeared in 1881. Ribot claimed that the findings of brain science proved that memory is lodged within a particular part of the nervous system; localized within the brain and thus being of a material nature. Bergson was opposed to this reduction of spirit to matter. Defending a clear anti-reductionist position, he considered memory to be of a deeply spiritual nature, the brain serving the need of orienting present action by inserting relevant memories. The brain thus being of a practical nature, certain lesions tend to perturb this practical function, but without erasing memory as such. The memories are, instead, simply not 'incarnated', and cannot serve their purpose.

Download or read book Stability by Liapunov s Direct Method with Applications by Joseph L Salle and Solomon Lefschetz written by and published by Elsevier. This book was released on 2012-01-25 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, Non-Lagrange interpolation, Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Download or read book The Collected Mathematical Works of George William Hill written by George William Hill and published by Franklin Classics Trade Press. This book was released on 2018-10-22 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Download or read book A Thematic Catalogue of the Works of Michel Richard de Lalande 1657 1726 written by Lionel Sawkins and published by Oxford University Press, USA. This book was released on 2005 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: As chief court musician to Louis XIV and Louis XV, Michel-Richard de Lalande is chiefly remembered for his sumptuous orchestral motets and much attractive instrumental music. In this thematic catalogue of his music, Lionel Sawkins illustrates the composer's music with over 3,000 music examples, details of performing requirements and of all source materials, as well as with comprehensive indexes and thematic locators.