Transcription of Chapter 4. Lagrangian Dynamics
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Chapter 4. Lagrangian Dynamics
56 Chapter 4. Lagrangian Dynamics (Most of the material presented in this Chapter is taken from Thornton and Marion, Chap. 7) Important Notes on Notation In this Chapter , unless otherwise stated, the following notation conventions will be used: 1. Einstein s summation convention. Whenever an index appears twice (an only twice), then a summation over this index is implied. For example, xixi xixii =xi2i . ( ) 2. The index i is reserved for Cartesian coordinates. For example, xi, for i=1,2,3, represents either x,y, or z depending on the value of i.
Hamilton’s Principle, from which the equations of motion will be derived. These equations are called Lagrange’s equations. Although the method based on Hamilton’s Principle does not constitute in itself a new physical theory, it is probably justified to say that it is more fundamental that Newton’s equations.
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