Foundations Of Mechanics

Foundations Of Mechanics
Author: Ralph Abraham
Publisher: CRC Press
Total Pages: 849
Release: 2019-04-24
Genre: Science
ISBN: 0429689047

Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.

A History of Mechanics

A History of Mechanics
Author: René Dugas
Publisher: Courier Corporation
Total Pages: 672
Release: 2012-11-07
Genre: Science
ISBN: 0486173372

"A remarkable work which will remain a document of the first rank for the historian of mechanics." — Louis de Broglie In this masterful synthesis and summation of the science of mechanics, Rene Dugas, a leading scholar and educator at the famed Ecole Polytechnique in Paris, deals with the evolution of the principles of general mechanics chronologically from their earliest roots in antiquity through the Middle Ages to the revolutionary developments in relativistic mechanics, wave and quantum mechanics of the early 20th century. The present volume is divided into five parts: The first treats of the pioneers in the study of mechanics, from its beginnings up to and including the sixteenth century; the second section discusses the formation of classical mechanics, including the tremendously creative and influential work of Galileo, Huygens and Newton. The third part is devoted to the eighteenth century, in which the organization of mechanics finds its climax in the achievements of Euler, d'Alembert and Lagrange. The fourth part is devoted to classical mechanics after Lagrange. In Part Five, the author undertakes the relativistic revolutions in quantum and wave mechanics. Writing with great clarity and sweep of vision, M. Dugas follows closely the ideas of the great innovators and the texts of their writings. The result is an exceptionally accurate and objective account, especially thorough in its accounts of mechanics in antiquity and the Middle Ages, and the important contributions of Jordanus of Nemore, Jean Buridan, Albert of Saxony, Nicole Oresme, Leonardo da Vinci, and many other key figures. Erudite, comprehensive, replete with penetrating insights, AHistory of Mechanics is an unusually skillful and wide-ranging study that belongs in the library of anyone interested in the history of science.

Advances in Mechanics and Mathematics

Advances in Mechanics and Mathematics
Author: David Yang Gao
Publisher: Springer Science & Business Media
Total Pages: 329
Release: 2013-12-01
Genre: Science
ISBN: 1461302471

As any human activity needs goals, mathematical research needs problems -David Hilbert Mechanics is the paradise of mathematical sciences -Leonardo da Vinci Mechanics and mathematics have been complementary partners since Newton's time and the history of science shows much evidence of the ben eficial influence of these disciplines on each other. Driven by increasingly elaborate modern technological applications the symbiotic relationship between mathematics and mechanics is continually growing. However, the increasingly large number of specialist journals has generated a du ality gap between the two partners, and this gap is growing wider. Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications which fall into the two following complementary categories: 1. An annual book dedicated to the latest developments in mechanics and mathematics; 2. Monographs, advanced textbooks, handbooks, edited vol umes and selected conference proceedings. The AMMA annual book publishes invited and contributed compre hensive reviews, research and survey articles within the broad area of modern mechanics and applied mathematics. Mechanics is understood here in the most general sense of the word, and is taken to embrace relevant physical and biological phenomena involving electromagnetic, thermal and quantum effects and biomechanics, as well as general dy namical systems. Especially encouraged are articles on mathematical and computational models and methods based on mechanics and their interactions with other fields. All contributions will be reviewed so as to guarantee the highest possible scientific standards.

Quantum Mechanics for Mathematicians

Quantum Mechanics for Mathematicians
Author: Leon Armenovich Takhtadzhi͡an
Publisher: American Mathematical Soc.
Total Pages: 410
Release: 2008
Genre: Mathematics
ISBN: 0821846302

Presents a comprehensive treatment of quantum mechanics from a mathematics perspective. Including traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin.

Mechanics

Mechanics
Author: J. P. Den Hartog
Publisher: Courier Corporation
Total Pages: 484
Release: 2013-03-13
Genre: Science
ISBN: 0486158691

This classic introductory text features hundreds of applications and design problems that illuminate fundamentals of trusses, loaded beams and cables, and related areas. Includes 334 answered problems.

New Foundations for Classical Mechanics

New Foundations for Classical Mechanics
Author: D. Hestenes
Publisher: Springer Science & Business Media
Total Pages: 655
Release: 2012-12-06
Genre: Science
ISBN: 9400948026

This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applica tions matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.

How Mechanics Shaped the Modern World

How Mechanics Shaped the Modern World
Author: David Allen
Publisher: Springer Science & Business Media
Total Pages: 425
Release: 2013-09-24
Genre: Technology & Engineering
ISBN: 3319017012

This unique book presents a nontechnical view of the history of mechanics, from the Big Bang to present day. The impact of mechanics on the evolution of a variety of subjects is vividly illustrated, including astronomy, geology, astrophysics, anthropology, archeology, ancient history, Renaissance art, music, meteorology, modern structural engineering, mathematics, medicine, warfare, and sports. While enormous in scope, the subject matter is covered (with ample photographic support) at a level designed to capture the interest of both the learned and the curious. The book concludes with a creative and thoughtful examination of the current state of mechanics and possibilities for the future of mechanics.

The Development of the Mechanics’ Institute Movement in Britain and Beyond

The Development of the Mechanics’ Institute Movement in Britain and Beyond
Author: Martyn Walker
Publisher: Taylor & Francis
Total Pages: 195
Release: 2016-08-12
Genre: Education
ISBN: 1317410920

The Development of the Mechanics’ Institute Movement in Britain and Beyond questions the prevailing view that mechanics’ institutes made little contribution to adult working-class education from their foundation in the 1820s to 1890. The book traces the historical development of several mechanics’ institutes across Britain and reveals that many institutes supported both male and female working-class membership before state intervention at the end of the nineteenth century resulted in the development of further education for all. This book presents evidence to suggest that the movement remained active and continued to expand until the end of the nineteenth century. Drawing on historical accounts, Walker describes the developments which shaped the movement and emphasises the institutes’ provision for scientific and technical education. He also considers the impact that the British movement had on the overseas development of mechanics’ institutes – particularly in Canada, America, Australia and New Zealand. The book concludes with a discussion of the legacy of the movement and its contribution to twentieth-century adult education. The Development of the Mechanics’ Institute Movement advances the argument that the movement made a substantial contribution to adult education for the working classes and provided a firm foundation for further education in Britain and beyond. It will appeal to academics, researchers and postgraduate students in the areas of education, history and sociology, as well as the philosophy of education, technical and vocational education, and post-compulsory education.

Mathematical Foundations of Quantum Mechanics

Mathematical Foundations of Quantum Mechanics
Author: John von Neumann
Publisher: Princeton University Press
Total Pages: 462
Release: 1955
Genre: Mathematics
ISBN: 9780691028934

A revolutionary book that for the first time provided a rigorous mathematical framework for quantum mechanics. -- Google books

Introduction to Unified Mechanics Theory with Applications

Introduction to Unified Mechanics Theory with Applications
Author: Cemal Basaran
Publisher: Springer Nature
Total Pages: 452
Release: 2021-02-02
Genre: Science
ISBN: 3030577724

This text describes the mathematical formulation and proof of the unified mechanics theory (UMT) which is based on the unification of Newton’s laws and the laws of thermodynamics. It also presents formulations and experimental verifications of the theory for thermal, mechanical, electrical, corrosion, chemical and fatigue loads, and it discusses why the original universal laws of motion proposed by Isaac Newton in 1687 are incomplete. The author provides concrete examples, such as how Newton’s second law, F = ma, gives the initial acceleration of a soccer ball kicked by a player, but does not tell us how and when the ball would come to a stop. Over the course of Introduction to Unified Mechanics Theory, Dr. Basaran illustrates that Newtonian mechanics does not account for the thermodynamic changes happening in a system over its usable lifetime. And in this context, this book explains how to design a system to perform its intended functions safely over its usable life time and predicts the expected lifetime of the system without using empirical models, a process currently done using Newtonian mechanics and empirical degradation/failure/fatigue models which are curve-fit to test data. Written as a textbook suitable for upper-level undergraduate mechanics courses, as well as first year graduate level courses, this book is the result of over 25 years of scientific activity with the contribution of dozens of scientists from around the world including USA, Russia, Ukraine, Belarus, Spain, China, India and U.K.