x'' + P(x') x' + u(x) = F(t), P(x')>0, F(t+T)=F(t), ,<F(t)> = 0

Discussion in 'Math Research' started by Arboristeria, Feb 21, 2005.

  1. Arboristeria

    Arboristeria Guest

    Dear All,
    I am doing a bibliographical research on the asymptotic behavior of a
    periodically forced nonlinear oscillator with nonlinear (positive)
    "damping":

    $$ x'' + P(x') x' + u(x) = F(t) (EQ1)$$

    with generic IV:
    $$ x(0) = x_o x'(0) = v_o$$

    with "null mean" forcing with (minimal and positive) period $T$:

    $$ F(t+T)=F(t) $$

    $$ \frac{1}{T}\int_0^T{F(t)dt}=0 $$

    and positive and nonlinear (and nonconstant) damping:

    $$ P(x') >0 \forall x' \in \R $$

    Quite surprisingly for me, I did not find many recent papers on this so
    physically relevant subject. Mainly I did find some (interesting but)
    numerical study.

    I did find some interesting work on the case of constant (positive)
    damping, e.g. the paper



    I wonder if some of you might give me some also non recent
    bibliographical reference to review papers or book devoted to equation
    (EQ1)

    Ciao e grazie!
    g.
     
    Arboristeria, Feb 21, 2005
    #1
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  2. Hello g.,

    People have been playing around with those toy-systems a lot in chaos
    theory, for example the van der Pol oscillator. Furthermore lots of
    research has been done on kicked oscillators and coupled non-linear
    oscillators. I don't know if this involves phase-dependent damping though.

    HTH,

    Maarten
     
    Maarten van Reeuwijk, Mar 16, 2005
    #2
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