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

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Homework Help Overview

The discussion revolves around proving the equation q2=Acos(q2)+Bsin(q2)+C using a Hamiltonian framework, specifically H =(1/2)*(p12 q14 + p22 q22 - 2aq1), where a, A, B, and C are constants. Participants are exploring the relationship between Hamiltonian mechanics and the given equation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various methods to approach the problem, including canonical transformations and the use of partial derivatives of the Hamiltonian. There is a focus on whether these methods can lead to a solution or if alternative approaches are necessary.

Discussion Status

The discussion is ongoing, with some participants suggesting potential methods such as canonical transformations, while others express uncertainty about their effectiveness. There is no explicit consensus on the best approach, and participants are actively seeking additional insights or alternative strategies.

Contextual Notes

Participants mention difficulties in solving the Hamiltonian equations and express a desire for guidance on proving the equation without relying solely on canonical transformations. The constraints of the problem and the constants involved are noted but not resolved.

kamil600
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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?
 
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You could try some canonical transformation of the variables.
This is just a tip, I didnt do any calculations.. :D
 
It might be good idea, but do you have any other clues how to solve it without canonical transformation?
 
Have you tried working out any partial derivatives of your hamiltonian?
 
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.
 

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