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Unformatted text preview: ME 530.343: Design and Analysis of Dynamic Systems Spring 2009 Lecture 33 - Lagranges Equation with Damping & Example Friday, April 3, 2009 Todays Objectives Lagranges equations for systems with damping Double Pendulum Example Reminder: Modal analysis only applies to undamped systems. You can figure out modes with no damping, then add damping to see the actual response. Lagrange with Damping Note: this is a trick to get the damping correct, but technically this should just be thought of as an external force. We introduce a function R : Rayleighs dissipation function R = 1 2 x T B x B is the damping matrix Re-write Lagranges equation: d dt ( L x i )- L x i + R x i = Q i The third term is new. Substitute V = 1 2 x T K x T = 1 2 x T M x R = 1 2 x T B x L = T- V And you will get M x + B x + K x = Q 1 Double Pendulum Example Velocity of m 1 : v 1 = l 1 1 Velocity of m 2 : v 2 = ( v 2 2 x + v 2 2 y ) 1 2 v 2 x = l...
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This note was uploaded on 03/02/2010 for the course MECH 530.343 taught by Professor Sun during the Spring '08 term at Johns Hopkins.
- Spring '08