(adsbygoogle = window.adsbygoogle || []).push({}); 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!

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# 2nd order DEQ: conserved quantity pt 2

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