Urgent Help! state-variables and differential equations

Discussion in 'Math' started by Eng_Bandar, Sep 30, 2012.

  1. Eng_Bandar

    Thread Starter Active Member

    Feb 27, 2010
    How can I solve the following differential equations to get the state-space equation?

    my'' = -km' - gm

    x1 = y \rightarrow x1' = x2
    x2 = y' \rightarrow x2' = y''
    x3 = m
    u = m'

    Eq1 x1' = x2
    Eq2 x3 x2'' = - kx3' - gx3

    The problem that I face with Eq2 specifically x3.x2''
    I know X' = Ax + Bu and I know how I get it if it is only like this x2'' = ....
    but there there is another variable times x2

    Any suggestions!
  2. CircuitZord


    Oct 8, 2012
    Kind of hard to see what you're doing there, but I was under the impression that each successive x: x1, x2, x3, etc. is assigned the next derivative.