1. Not finding help here? Sign up for a free 30min 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!

Stability equibrilium solution

  1. Dec 21, 2008 #1
    1. The problem statement, all variables and given/known data
    Determine the stability property of the following equibrilium solution:

    (0,0) of

    [tex] \ddot{x}+ \alpha x +x=0 [/tex] with [tex] \alpha \in \mathbb{R} [/tex]

    2. Relevant equations
    - A solution is Lyapunov stable if for each [itex] \epsilon[/itex] there is a [itex] \delta [/itex] such that: [tex]||x(0)|| \leq \delta[/tex] yields [tex]||x(t)|| \leq \epsilon [/tex]

    - A solution is unstable if it isn't stable.

    - A solution is asymptotically stable if there is a delta such that: [tex] ||x(0)|| \leq \delta [/tex] yields [tex] \lim_{t \rightarrow \infty} ||x(t)|| = 0[/tex]

    Note: x can be a vector.

    3. The attempt at a solution

    I don't know how to use these defintions. Can I just use the 2-norm? Can someone explain me how this works?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?



Similar Discussions: Stability equibrilium solution
Loading...