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History of Virtual Work Laws

A History of Mechanics Prospective

  • Danilo Capecchi

Part of the Science Networks. Historical Studies book series (SNHS, volume 42)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Danilo Capecchi
    Pages 1-13
  3. Danilo Capecchi
    Pages 15-32
  4. Danilo Capecchi
    Pages 33-61
  5. Danilo Capecchi
    Pages 63-89
  6. Danilo Capecchi
    Pages 91-133
  7. Danilo Capecchi
    Pages 135-155
  8. Danilo Capecchi
    Pages 195-215
  9. Danilo Capecchi
    Pages 217-236
  10. Danilo Capecchi
    Pages 237-279
  11. Danilo Capecchi
    Pages 281-297
  12. Danilo Capecchi
    Pages 299-315
  13. Danilo Capecchi
    Pages 317-334
  14. Danilo Capecchi
    Pages 335-351
  15. Danilo Capecchi
    Pages 353-360
  16. Danilo Capecchi
    Pages 361-373
  17. Danilo Capecchi
    Pages 375-393
  18. Danilo Capecchi
    Pages 395-403
  19. Back Matter
    Pages 405-492

About this book

Introduction

 The book presents a history of classical mechanics by focusing on issues of equilibrium. The historical point of view adopted here restricts attention to cases where the effectiveness of forces is assessed on the basis of the virtual motion of their points of application. For completeness, hints of the alternative approach are also referred, the Archimedean for ancient mechanics and the Newtonian for modern mechanics. The laws resulting from consideration of virtual motions are named laws of virtual work. The modern formulations of the principle of virtual work are only a particular form of them.

The book begins with the first documented formulations of laws of virtual work in the IV century BC in Greece and proceeds to the end of the XIX century AD in Europe. A significant space is devoted to Arabic and Latin mechanics of Middle Ages. With the Renaissance it began to appear slightly different wordings of the laws, which were often proposed as unique principles of statics. The process reached its apex with Bernoulli and Lagrange in the XVIII century. The book ends with some chapters dealing with the discussions that took place in the French school on the role of the Lagrangian version of the law of virtual work and its applications to continuum mechanics.

Keywords

Fundaments of mechanics History of mechanics Principle of virtual work

Authors and affiliations

  • Danilo Capecchi
    • 1
  1. 1.Università La SapienzaRomeItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-88-470-2056-6
  • Copyright Information Springer Milan 2012
  • Publisher Name Springer, Milano
  • eBook Packages Engineering
  • Print ISBN 978-88-470-2055-9
  • Online ISBN 978-88-470-2056-6
  • Buy this book on publisher's site
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