Evaluation of Scientific Sources in Mechanics: Heiberg’s Prolegomena to the Works of Archimedes and Hellinger’s Encyclopedia Article on Continuum Mechanics (Advanced Structured Materials, 152)

This book evaluates the importance of various historical sources and discusses their role in the creation and transmission of scientific knowledge. It presents an annotated translation of the introductory words given by Johan Ludvig Heiberg to his translation of the works of Archimedes. Further, it offers English translations of and commentaries on selected fundamental works by Ernst Hellinger and Gabrio Piola, which lay the groundwork for the modern theory of advanced materials, and also examines the criteria used to evaluate scientific works. Preface 6 Contents 9 Chapter 1 The study of the genesis of novel mathematical and mechanical theories provides an inspiration for future original research 11 1.1 Introduction 11 1.2 The process of knowledge transmission: a sociological problem that needs to be studied by using the scientific method 12 1.3 An epistemological intermezzo: inductivism versus falsificationism 23 1.4 From the world reality to its mathematical model and from the model to the replacement of the world reality 32 1.5 Reconstruction, partly conjectural, of the birth and decline of the mathematical models for planetary motion 34 1.6 The postulations of Mechanics, forces and their materializations 50 1.7 Conclusive remarks 70 References 76 Chapter 2 Translation of Heiberg’s Prolegomena 84 2.1 Translators’ preface 84 2.2 Prolegomena. On the Archimedean codices 85 Chapter 3 Hellinger’s 1913 encyclopedia article on the fundamentals of the mechanics of continua 107 3.1 Translator’s preface 107 3.2 Die allgemeinen Ansätze der Mechanik der Kontinua 110 3.3 Translator’s commentaries 298 References 313 Chapter 4 The loss and recovery of the works by Piola and the Italian tradition of Mechanics 322 4.1 Orthodoxy in Continuum Mechanics: social phenomenology and its naive explanations 322 4.2 In other scientific groups Variational Principles remained the mainly used conceptual tool 325 4.3 How Piola’s works were transmitted and how they were – locally in space and time – lost in the Mechanics literature 327 4.4 Mathematical difficulties inherent to Variational Formulation 334 4.5 Conclusions 339 References 340 Chapter 5 A partial report on the controversies about the Principle of Virtual Work: from Archytas of Tarentum to Lagrange, Piola, Mindlin and Toupin. 348 5.1 Some «forgotten» – but not «lost» – sources in mechanical sciences. 349 5.2 An Italian secondary source: Vailati. While underestimating Hellenistic mechanics, he recognizes in it two different ways for studying Statics problems. 352 5.3 The Principle of Virtual Work as formulated by Archytas of Tarentum in the Mechanical Problems. 356 5.4 D’Alembert: the rediscovery of the Principle of Virtual Velocities (or Virtual Work) 359 5.5 The formulation of Continuum Mechanics by Lagrange 362 5.6 The controversy between Poisson and Piola about the deduction of the equation of the equilibrium of fluids: Piola’s contact interactions in continua 363 5.7 Navier, Cauchy, Poisson, and Saint-Venant versus Lagrange, Piola, and George Green or postulations based on Balance Laws versus postulations based on the Principle of Virtual Velocity. 367 5.8 Nationalistic Science or How Piola’s legacy has been blurred because of writing in Italian and counter-posing Italian science to French science. 369 5.9 The formulation of N-th Gradient Continuum Mechanics by Piola: an ignored result that is still topical after more than 150 years 371 5.10 Research perspectives as suggested by the lesson given by History of Mechanics 374 References 376