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2nd order DEQ: conserved quantity pt 2

  1. Mar 13, 2007 #1
    1. The problem statement, all variables and given/known data

    Consider y'' = - sin(y)

    find a conserved quantity for this equation

    2. Relevant equations

    This looks an awful lot like a simplified version of a nonlinear pendulum equation

    3. The attempt at a solution

    For a conserved quantity I guessed: E = -cos(y) + y' because we need a y'' upon differentiating E and also we will need to cancel out the -sin(y)

    => dE/dt = sin(y)*y' + y''

    => y'' = (dE/dt) - sin(y)*y' = -sin(y)

    => dE/dt = sin(y)*y' - sin(y) = sin(y)*(y'-1) and does not equal zero so E is not conserved.

    Please help me find a conserved quantity!
  2. jcsd
  3. Mar 13, 2007 #2


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    Mess around with combinations of (y')^2 and cos(y). Why did I choose those two?
  4. Mar 13, 2007 #3
    Thanks. E = (1/2)y'^2 -cos(y) works. The y'^2 allows for an additional y' term that can cancel later!
  5. Mar 13, 2007 #4


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    Dearly Missed

    Multiply your original equation with y' and scrutinize the slip of paper you have written it on.
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