Results 1 to 4 of 4

Math Help - Representing DE as systems

  1. #1
    Newbie
    Joined
    Aug 2011
    Posts
    12

    Representing DE as systems

    Here is my revision question. I dont know where to start. Can someone please show me how to do this?
    Attached Thumbnails Attached Thumbnails Representing DE as systems-capture.png  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: Representing DE as systems

    Welcome to MHF, jonnyl!

    A system of the form \ddot x = g(\dot x, x, t) can be rewritten with x_1=x and x_2=\dot x.

    From this you get the system \left[ \begin{array}{lll}\dot x_1 &=& x_2 \\ \dot x_2 &=& g(x_2, x_1, t) \end{array} \right.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2011
    Posts
    12

    Re: Representing DE as systems

    So how would i represent this as a 3 dimensional system?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: Representing DE as systems

    Quote Originally Posted by jonnyl View Post
    So how would i represent this as a 3 dimensional system?
    To convert the ODE to an autonomous system, you need to eliminate the dependency on the time variable t.
    Introduce x_3=\cos \omega t.
    Now find \dot x_3 by using only x_1,x_2,x_3. Can you?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: February 13th 2011, 11:40 AM
  2. Representing two's compliment
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 14th 2010, 08:41 AM
  3. Help for representing sets
    Posted in the Discrete Math Forum
    Replies: 14
    Last Post: January 9th 2010, 09:51 AM
  4. matrix representing L
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: May 1st 2009, 09:38 PM
  5. Representing prime number as 3k-1
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: June 12th 2006, 06:20 PM

Search Tags


/mathhelpforum @mathhelpforum