sol3 - MAE294B/SIO203B Methods in Applied Mechanics Winter...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
MAE294B/SIO203B: Methods in Applied Mechanics Winter Quarter 2010 http://maecourses.ucsd.edu/mae294b Solution III 1 Draw the loci where ˙ x vanishes and ˙ x is singular. The former are fixed points and correspond to μ = x 2 and x + μ 2 = 2. The latter correspond to x + μ 2 and are not fixed points. However they do latter separate regions where ˙ x has different signs. There are four intersection points of these loci. The points ( 1 , 1 ) and ( 1 . 8312 , - 1 . 3532 ) are standard transcritical bifurcations. The points ( 0 , 0 ) and ( 1 , - 1 ) are not normal bifurcations since they contain the singular curve. However they look like transcritical bifurcations since two “stable” and two “unstable” singularities/fixed points meet. Figure 1 shows the diagram. 2 The simplest way to do this is to use the iteration u n + 1 = nt - ε sin u n , u 0 = 0 . Then u 1 = nt , u 2 = nt - ε sin nt and u 3 = nt - ε sin [ nt - ε sin nt ] = nt - ε [ sin nt - ε sin nt cos nt + O ( ε 2 ) = nt - ε sin nt
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/16/2010 for the course MAE 294b taught by Professor Young,w during the Winter '08 term at UCSD.

Page1 / 3

sol3 - MAE294B/SIO203B Methods in Applied Mechanics Winter...

This preview shows document pages 1 - 2. Sign up to view the full document.

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