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D’Alembert’s reduction principle

  1. Nov 15, 2009 #1
    Hey guys, I'm stuck on this problem! I have no idea how to even go about solving it. I tried searching the net for D'Alembert's principle but nothing was helpful. Any suggestions on how to go about solving it will be much appreciated!!

    Find with the aid of D’Alembert’s reduction principle the FS of the ODE system.

    x1(t)= x1(t)/t - x2(t)

    x2(t)= x1(t)/t2+ 2x2(t)/2

    for which a particular solution x(t)=(t2, -t) is known.
  2. jcsd
  3. Nov 15, 2009 #2
    Is this an ODE System or algebric equations System?

    What is FS (sorry I don't know :P)?
  4. Nov 15, 2009 #3

    this is an ODE. FS stands for fundamental system.
  5. Nov 17, 2009 #4
    There are no derivatives, therefore this is not a ODE. Secondly [tex](t^2,-t)[/tex] is not a solution.
    Missing derivatives, and the second line should be,
    [tex]x_2' = x_2/t^2 + 2 x_2/t [/tex]
    Last edited: Nov 17, 2009
  6. Nov 20, 2009 #5
    that's the point,
    (t^2,-t) is the solution of the algebric equations (as he written them)
    so i'm a bit confused
  7. Nov 20, 2009 #6


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    Science Advisor

    Mathrocks, do you mean
    dx1(t)/dt= x1(t)/t - x2(t)

    dx2(t)/dt= x1(t)/t2+ 2x2(t)/2
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