# assn4 - 1.685J/2.0345/18.377J Nonlinear Dynamics and Waves...

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

1.685J/2.0345/18.377J Nonlinear Dynamics and Waves Spring 2007 Problem Set No. 4 Out: 12, 2007 Due: 26, 2007 in class Problem 1 Consider the system and t) = = 1 for - oo < x < oo, t 2 0 = ii - u = ii+ul with normal modes of the form where 4 = + l)rx}, s = a) = a (1 - a2) - + + a2)/~ for n = 0, I,. .. and any real wavenumber a. Deduce that the mode is stable if and only if R 5 (a) = + + (1 - a2). Hence show that the flow is stable if and only if R 5 R, = Ro(a,) = 41.5 where = + rP2)'l2 - 1) = 0.488.

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

View Full Document
Show that the Landau equation for the amplitude A(t) of the most unstable mode for R 3 Rc7 where Problem 2 A particle of mass ml is attached to a light rigid rod of length
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

assn4 - 1.685J/2.0345/18.377J Nonlinear Dynamics and Waves...

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

View Full Document
Ask a homework question - tutors are online