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Unformatted text preview: p we obtain the Hamiltonian H = T + V = p 2 2 m + 1 2 kx 2 (3) Hamiltons equations are H p = p m = x and H x = kx =- p (4) Newtons force law follows kx =- p =-m x or m x =-kx PROBLEM 3 The given Lagrangian is independent of t and . Thus, L t = 0 E = T + V conserved . and 0 = L = d dt L = mr 2 sin 2 ( ) = p conserved ....
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- Spring '11