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Unformatted text preview: Î» 2 t 2 x 2 ) Ë™ x + 2 mÎ» 2 tx 3 . Equivalently, Ë™ x = p2 mÎ» 2 tx 3 m (1 + 4 Î» 2 t 2 x 2 ) . (1) 1 H = p Ë™ xL H = Â± m (1 + 4 Î» 2 t 2 x 2 ) Ë™ x + 2 mÎ» 2 tx 3 Â² Ë™ xÂ³ 1 2 m (1 + 4 Î» 2 t 2 x 2 ) Ë™ x 2 + 2 mÎ» 2 t Ë™ xx 3 Â´ + mgÎ»tx 21 2 mÎ» 2 x 4 H = 1 2 m (1 + 4 Î» 2 t 2 x 2 ) Ë™ x 2 + mgÎ»tx 21 2 mÎ» 2 x 4 Use Eqn. (1) to write H in terms of only p , x , and t . H = ( p2 mÎ» 2 tx 3 ) 2 2 m (1 + 4 Î» 2 t 2 x 2 ) + mgÎ»tx 21 2 mÎ» 2 x 4 (d) dH dt =âˆ‚L âˆ‚t Since L has an explicit timedependence, the Hamiltonian is not conserved. 2...
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 Spring '08
 Staff
 Physics, mechanics, Gravity, Mass, Hamiltonian mechanics, Coordinate system, 1 M, Lagrangian mechanics, Generalized coordinates, 2 1 1 L

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