Unformatted text preview: p we obtain the Hamiltonian H = T + V = p 2 2 m + 1 2 kx 2 (3) Hamilton’s equations are ∂H ∂p = p m = ˙ x and ∂H ∂x = kx =˙ p (4) Newton’s force law follows kx =˙ p =m ¨ x or m ¨ x =kx PROBLEM 3 The given Lagrangian is independent of t and φ . Thus, ∂L ∂t = 0 ⇒ E = T + V conserved . and 0 = ∂L ∂φ = d dt ∂L ∂ ˙ φ = mr 2 sin 2 ( θ ) ˙ φ = p φ conserved ....
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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.
 Spring '11
 Berg

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