Math 485 8 Feb 11 Page 1 of 6 Feb 8 2011 soln curves tangent to v f x y g x y for all t 1 what kind of solution curve is allowed by v x y vector 2 How do solution curves t together in phase space phase portrait Analysis Jacobian J x0 y0 1 f x y 0 g x y 0 to nd x0 y0 2 determine local phase portrait around x0 y0 determined by the phase portrait local is determined by the eigenvalues of the Jacobian Math 485 8 Feb 11 Page 2 of 6 Feb 8 2011 Math 485 8 Feb 11 Page 3 of 6 Feb 8 2011 Math 485 8 Feb 11 Page 4 of 6 Feb 8 2011 Conservative Systems How to sketch phase portrait Local Max corresponds to a saddle and Local Min corresponds to a center Math 485 8 Feb 11 Page 5 of 6 Feb 8 2011 Classical Pendulum Problem Math 485 8 Feb 11 Page 6 of 6 Feb 8 2011
View Full Document
Unlocking...