This preview shows page 1. Sign up to view the full content.
Unformatted text preview: connecting them are constrained to move in a circle, so that each atom has just one (angular) degree of freedom. Show that the 0frequency mode is a rotation about the center of mass. 2. A double pendulum (Fig. 1.4), consisting of masses m 1 and m 2 at the ends of rods of lengths l 1 and l 2 which are hinged at the location of m 1 , swings in the xzplane. a) Write down the full Lagrangian in terms of the coordinates in Fig. 1.4, and the Lagrangian for small displacements about equilibrium. b) Find a transformation of coordinates, as done in class, which diagonalizes both the kinetic and potential energy terms. c) Describe the normal modes of vibration and the general solution for θ 1 and 2 , in terms of the initial angular displacements and velocities....
View
Full
Document
This note was uploaded on 11/16/2010 for the course PHY 504 taught by Professor Staff during the Fall '08 term at Kentucky.
 Fall '08
 Staff
 mechanics

Click to edit the document details