Unformatted text preview: function of ˙ x 1 , ˙ x 2 , x 1 and x 2 . Then, substitute normal coordinates as found in (B) and write down the Lagrangian in terms of ˙ Θ 1 , ˙ Θ 2 , Θ 1 and Θ 2 . Due November 7 before class (6 points). (D) Assume at time t = 0 the initial conditions Θ 1 (0) = 1, ˙ Θ 1 (0) = 0, Θ 2 (0) = 0 and ˙ Θ 2 (0) = 1. Plot the resulting solution ﬁrst in in the Θ 1Θ 2 plane and then in the x 1x 2 plane. Due November 9 before class (4 points). (28) The Lagrangian of a 2D oscillator is L = m 2 ´ ˙ x 2 + ˙ y 2ω 2 1 x 2ω 2 2 y 2 µ . Write down the general solution for the case that x = y = 0 at t = 0. Which condition applies to ω 1 and ω 2 , so that the mass point returns to x = y = 0 at some future time t ? How long will it take? Due November 14 before class (4 points). Read LandauLifshitz p.96 up to p.101 ( § 31 and § 32)....
View
Full Document
 Fall '11
 berg
 mechanics, Work, Normal mode, 50 L, Mik

Click to edit the document details