Solve Hamiltonian Problem: Have Ideas on q2=Acos(q2)+Bsin(q2)+C?

[kamil600]

Have you got any clues how to prove q₂=Acos(q₂)+Bsin(q₂)+C using hamiltonian H =(1/2)*(p₁² q₁⁴ + p₂² q₂² - 2aq₁) , where a,A,B,C=const.
I've tried to solve hamiltonian eqations what let me to equations which I can't solved.
How you got any ideas solving this problem?

 

[Thaakisfox]

You could try some canonical transformation of the variables.
This is just a tip, I didnt do any calculations.. :D

 

[kamil600]

It might be good idea, but do you have any other clues how to solve it without canonical transformation?

 

[ppyadof]

Have you tried working out any partial derivatives of your hamiltonian?

 

[kamil600]

Yes, I tried prove it using hamiltonian equations (which are partial derivatives of hamiltonian), but always it let me to equations which I can't solve. If the quickes way to prove it is canonical transformation maby someone can tell me how to prove this problem using it.