Essential Physics 1 - F. Firk

Essential Physics 1 - F. Firk - ESSENT IAL P H Y SICS Par t...

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E S S E N T I A L P H Y S I C S P a r t 1 R EL AT I V IT Y , P A R T I CL E D Y NA MI CS , G R A V IT A T I O N, A ND W A V E M O T I ON F R A N K W . K . F I R K P r o f e s s o r E m e r i t u s o f P h y s i c s Y a l e U n i v e r s i t y 2 0 0 0
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PREFACE Throughout the decade of the 1990’s, I taught a one-year course of a specialized nature to students who entered Yale College with excellent preparation in Mathematics and the Physical Sciences, and who expressed an interest in Physics or a closely related field. The level of the course was that typified by the Feynman Lectures on Physics . My one-year course was necessarily more restricted in content than the two-year Feynman Lectures. The depth of treatment of each topic was limited by the fact that the course consisted of a total of fifty-two lectures, each lasting one-and-a-quarter hours. The key role played by invariants in the Physical Universe was constantly emphasized . The material that I covered each Fall Semester is presented, almost verbatim, in this book. The first chapter contains key mathematical ideas, including some invariants of geometry and algebra, generalized coordinates, and the algebra and geometry of vectors. The importance of linear operators and their matrix representations is stressed in the early lectures. These mathematical concepts are required in the presentation of a unified treatment of both Classical and Special Relativity. Students are encouraged to develop a “relativistic outlook” at an early stage . The fundamental Lorentz transformation is developed using arguments based on symmetrizing the classical Galilean transformation. Key 4-vectors, such as the 4-velocity and 4-momentum, and their invariant norms, are shown to evolve in a natural way from their classical forms. A basic change in the subject matter occurs at this point in the book. It is necessary to introduce the Newtonian concepts of mass, momentum, and energy, and to discuss the conservation laws of linear and angular momentum, and mechanical energy, and their associated invariants. The
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iv discovery of these laws, and their applications to everyday problems, represents the high point in the scientific endeavor of the 17th and 18th centuries. An introduction to the general dynamical methods of Lagrange and Hamilton is delayed until Chapter 9 , where they are included in a discussion of the Calculus of Variations. The key subject of Einsteinian dynamics is treated at a level not usually met in at the introductory level. The 4-momentum invariant and its uses in relativistic collisions, both elastic and inelastic, is discussed in detail in Chapter 6 . Further developments in the use of relativistic invariants are given in the discussion of the Mandelstam variables, and their application to the study of high-energy collisions. Following an overview of Newtonian Gravitation, the general problem of central orbits is discussed using the powerful method of [p, r] coordinates.
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