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Unformatted text preview: 1 = 2 = 3 = . Write down the Lagrangian of the system (6 pts). b. Approximate the Lagrangian in the small angle limit 1 , 2 , 3 <<1, to the leading order involving 1 , 2 , 3 (6 pts) c. Write down the EulerLagrange equations. (6 pts) d. Find the normal frequencies of the system. (6 pts) e. Find the normal modes of the system. You dont need to normalize the vectors, but please illustrate schematically what they look like (6 pts). f. Initially the system is at rest and 1 1 << = . Use the normal modes to solve the time evolution of 1 , 2 , 3 (6 pts). 2 1 1 l 2 l g 1 m 2 m 3 3 l 3 m...
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This note was uploaded on 02/01/2011 for the course MATH 171 taught by Professor R during the Spring '09 term at Stanford.
 Spring '09
 R

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