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s1112 - ∂L ∂q j = d dt ∂L ∂ ˙ q j = ˙ p j and...

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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 find 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 definition of the
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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 o² Hamilton’s equations: ∂H ∂p j = ˙ q j and ∂H ∂q j =-˙ p j ....
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