2nd order DEQ: conserved quantity pt 2

  • Thread starter fusi0n
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  • #1
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Homework Statement



Consider y'' = - sin(y)

find a conserved quantity for this equation

Homework Equations



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

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!
 

Answers and Replies

  • #2
Dick
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Mess around with combinations of (y')^2 and cos(y). Why did I choose those two?
 
  • #3
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Mess around with combinations of (y')^2 and cos(y). Why did I choose those two?
Thanks. E = (1/2)y'^2 -cos(y) works. The y'^2 allows for an additional y' term that can cancel later!
 
  • #4
arildno
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Multiply your original equation with y' and scrutinize the slip of paper you have written it on.
 

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