hwk03_soln - kx c x kR kR f f ME 563 Fall 2011 SOLUTION...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: kx c x kR kR f f ME 563 Fall 2011 SOLUTION Homework Prob. 3.1 For the two-DOF system shown below, the springs are unstretched when x = = . a) Use the Newton-Euler equations to develop the EOMs for this system using the generalized coordinates of x and . b) Use Lagranges equations to develop the EOMs for this system using the generalized coordinates of x and . c) Compare the mass, damping and stiffness matrices found in a) and b) above. Are they the same? Which formulation, if either, produces symmetric matrices? Newton-Euler Kinematics: a Gx = x + R Wheel: (1) F x = f kR = ma Gx f = kR m x + R ( ) (2) M G = fR = I G = 1 2 mR 2 f = 1 2 mR L-shaped block: (3) F x = f + kR kx c x = m x f = m x + c x + kx kR Combining (2) and (3): m x 1 2 mR + c x + kx kR = Combining (1) and (2): m x + 3 2 mR + kR = In matrix form: k x smooth no slip R k G A c m mR 2 m 3 mR 2 x + c x + k kR kR x = The mass and stiffness matrices are not symmetric, whereas the damping matrix is symmetric. NOTE : Depending on how you eliminated the friction constraint force f, you can get a set of EOMs with different symmetry properties than those found above. can get a set of EOMs with different symmetry properties than those found above....
View Full Document

This document was uploaded on 12/23/2011.

Page1 / 6

hwk03_soln - kx c x kR kR f f ME 563 Fall 2011 SOLUTION...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online