Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Multiply your original equation with y' and scrutinize the slip of paper you have written it on.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook