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Liouville theorem and reccurence

  1. Mar 26, 2009 #1
    1. The problem statement, all variables and given/known data

    A one dimensional damped oscillator with coordinate q satisfies the equation q_double dot+4*q_single dot+3q=0

    q_single dot=v
    v_single dot=-3*q-4*v

    show that the area a(t) of any region of points moving in (q,v) space has the time variation
    a(t)=a(0)*exp(-4*t).

    2. Relevant equations





    3. The attempt at a solution


    F=(F_1,F_2)=(v, -3*q-4v)

    div F=(d/dq,d/dv)*(F_1,F_2)

    div F= (0,-4)

    dv/dt=integral of R_0 div F(x,0)dx_1dx_2

    Not sure what to do after that.
     
  2. jcsd
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