s11f1036

s11f1036 - Solution for assignment 36: With H= qj ˙ j ∂L...

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Unformatted text preview: Solution for assignment 36: With H= qj ˙ j ∂L − L ∂ qj ˙ we find dH = d j ∂L ∂ qj ˙ qj + ˙ ∂L ∂L ∂L dqj − ˙ dqj − ˙ dqj ∂ qj ˙ ∂ qj ˙ ∂qj . The two central terms cancel out. Using Euler-Lagrange and the definition of the generalized momentum, we have d ∂L ∂L = = pj ˙ ∂qj dt ∂ qj ˙ and, therefore, (qj dpj − pj dqj ) . ˙ ˙ dH = j From this we read off Hamilton’s equations: ∂H = qj ˙ ∂pj and ∂H = −pj . ˙ ∂qj ...
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