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Classical Mechanics and Relativity

This text provides a pedagogical tour through mechanics from Newton to Einstein with detailed explanations and a large number of worked examples. From the very beginning relativity is kept in mind, along with its relation to concepts of basic mechanics, such as inertia, escape velocity, Newton's potential, Kepler motion and curvature. The Lagrange and Hamilton formalisms are treated in detail, and extensive applications to central forces and rigid bodies are presented. After consideration of the motivation of relativity, the essential tensor calculus is developed, and thereafter Einstein's equation is solved for special cases with explicit presentation of calculational steps. The combined treatment of classical mechanics and relativity thus enables the reader to see the connection between Newton's gravitational potential, Kepler motion and Einstein's corrections, as well as diverse aspects of mechanics. The text addresses students and others pursuing a course in classical mechanics, as well as those interested in a detailed course on relativity.
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Table of Contents

Recapitulation of Newtonian Mechanics; The Lagrange Formalism; The Canonical or Hamilton Formalism; Symmetries and Transformations; Looking Beyond Classical Mechanics; Two-Body Central Forces; Rigid Body Dynamics; Small Oscillations and Stability; Motivation of the Theory of Relativity; A Simple Look at Phenomenological Consequences; Aspects of Special Relativity; Equation of Motion of a Particle in a Gravitational Field; Tensor Calculus for Riemann Spaces; Einstein's Equation of the Gravitational Field; The Schwarzschild Solution.

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