s1112 - L q j = d dt L q j = p j and, therefore, dH = X j (...

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ADVANCED DYNAMICS — PHY 4241/5227 HOME AND CLASS WORK – SET 3 Solution for assignment 12: With H = X j ˙ q j ∂L ˙ q j - L we Fnd dH = X j " d ∂L ˙ q j ! ˙ q j + ∂L ˙ q j d ˙ q j - ∂L ˙ q j d ˙ q j - ∂L ∂q j dq j # . The two central terms cancel out. Using Euler-Lagrange and the deFnition of the generalized momentum, we have
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Unformatted text preview: L q j = d dt L q j = p j and, therefore, dH = X j ( q j dp j- p j dq j ) . rom this we read o Hamiltons equations: H p j = q j and H q j =- p j ....
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This note was uploaded on 11/10/2011 for the course PHY 4241 taught by Professor Berg during the Spring '11 term at University of Florida.

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