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    Rational Mechanics: The Classic Notre Dame Course
    Rational Mechanics: The Classic Notre Dame Course
    Rational Mechanics: The Classic Notre Dame Course
    Ebook553 pages112 hours

    Rational Mechanics: The Classic Notre Dame Course

    By R. Catesby Taliaferro

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    About this ebook

    Developed from a classic undergraduate course on the study of the motion of bodies, this volume stresses the history of science as well as relevant physics and mathematics. R. Catesby Taliaferro developed a well-attended and much-revered course during his 20-year tenure at Notre Dame. He left among his papers the unfinished manuscript for this text, which has now been completed and prepared for publication by a group of his former students and colleagues.
    Suitable for undergraduates and beginning graduate students of physics and the history of science, this volume begins with an exploration of ancient Greek celestial mechanics and the seventeenth-century scientific revolution incited by Kepler's work. Subsequent chapters examine vector spaces and their applications, elementary differential geometry, particle dynamics, displacement and kinematics, theories of light, and the special theory of relativity.
    LanguageEnglish
    PublisherDover Publications
    Release dateSep 18, 2013
    ISBN9780486315737
    Rational Mechanics: The Classic Notre Dame Course

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      Book preview

      Rational Mechanics - R. Catesby Taliaferro

      Course

      Chapter 1

      Greek Celestial Mechanics

      The science of the motion of bodies began, for obvious reasons, with the science of the motion of celestial bodies: they could be observed at leisure in their movements without apparent interference since they pass slowly through the sky and they could be supposed to move in an unimpeded region without friction as we shall see. It is therefore proper to begin with celestial mechanics; the planets are intellectually the closest to us even if they appear to be farther away than the things we handle every day; and, indeed, it will turn out that the principles of the classical mechanics of Newton came more from the heavens than from the earth.

      We start with Greek systems of celestial mechanics because it is from them that the systems of Copernicus, Kepler, and Newton are derived, not from the Babylonian, however interesting it may be. Further the Greek systems of celestial mechanics are rigorously constructed, complete, and run the range of geocentric and heliocentric theories. By the end of the 4th century B.C. both the geocentric and heliocentric theories had been developed with several variations. If the geocentric hypothesis seems the most obvious to the common man, this is not so for the astronomer, and heliocentric theories probably appear just as early as geocentric ones. The first clear statements concerning the nature of the science of celestial mechanics are found in the dialogues of Plato, developing a long previous Pythagorean tradition. The burden of this Pythagorean-Platonic statement is that the motions of the heavenly bodies can be only understood in terms of mathematical models which it is up to the scientist to build. These mathematical models must satisfy at least two conditions: (1) they must fit the appearance as gotten by observations; (2) they must be interesting in themselves so as to reveal further appearances and to suggest further observations which could not have been seen without the suggestions of the structures of the mathematical models themselves or without the presence of an idea which generates these

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