Unformatted text preview: Â¶ 1 = Â¶ 2 = Â¶ 3 = Â¶ . Write down the Lagrangian of the system (6 pts). b. Approximate the Lagrangian in the small angle limit Â´ 1 , Â´ 2 , Â´ 3 <<1, to the leading order involving Â´ 1 , Â´ 2 , Â´ 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 donâ€™t 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 << = Î³ Ï† . Use the normal modes to solve the time evolution of Â´ 1 , Â´ 2 , Â´ 3 (6 pts). 2 1 1 l 2 l g 1 m 2 m 3 3 l 3 m...
View
Full Document
 Spring '09
 R
 Lagrangian mechanics, Celestial mechanics

Click to edit the document details