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Unformatted text preview: ! q i However, since we know how to express the kinetic energy of the system in terms of the generalized coordinates we conclude that ! T ! q i = ! ! q i 1 2 m jk ! q j ! q k j , k " # $ % & ( = where m jk = m ! " x , i " q j " x , i " q k # $ % & ( i ) ) For the potential energy U we conclude that ! U ! q i = ! T ! q i = The potential energy can be expanded around the equilibrium position using a Taylor series and we find that U q 1 , q 2 ,... ( ) = U + ! U ! q k " # $ % & q k k ( + 1 2 ! 2 U ! q j ! q k " # $ % & q j q k j , k ( + .. ) 1 2 ! 2 U ! q j ! q k " # $ % & q j q k j , k ( = 1 2 A jk q j q k j , k ( where...
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 Spring '09
 MORGAN
 Physics

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