1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Lyapunov Stability

  1. Nov 22, 2013 #1
    A question I am doing hints that the solution (y,[itex]\dot{y}[/itex]) = (0,0) of [itex]\ddot{y}[/itex] - [itex]\frac{2}{t}[/itex][itex]\dot{y}[/itex] + y = 0 is unstable. I believe (although I am not 100% sure) that is true however I am struggling to prove it.

    I can rewrite the equation as a system of equations in matrix form to get

    [itex]\dot{x}[/itex] = Ax + B(t)x,

    where A = [{0,1},{-1,0}], B(t) = [{0,0},{0,[itex]\frac{2}{t}[/itex]}].

    This the form of all the theorems I appear to have. But all my theorems require me to find an eigenvalue of A with positive real part - which I can't here.

    So basically have I made a mistake already or is there another theorem anybody knows of that can tell me the trivial solution is unstable?
  2. jcsd
  3. Nov 23, 2013 #2
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted