Action and Response functions.

AI Thread Summary
The discussion centers on the feasibility of analytically deriving the action S and response R functions for a system defined by two canonical coordinates P and Q, along with their equations of motion. The key relations proposed are the variational derivatives of S and R with respect to Q and P, respectively. Participants are invited to explore whether these relations can be satisfied or if they are merely theoretical constructs. The inquiry raises fundamental questions about the connection between action and response functions in classical mechanics. The thread seeks insights and comments on this complex topic.
jorgext
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Dear colleagues,
I have the following question in my head:
Give two canonical coordinates P, Q, and a corresponding set of equations of motions, not necessary solved.
Is it possible to find analytically the action S and response Rfunctions of the system, which satisfy the relations:
\dfrac{\delta S}{\delta Q}=\dfrac{\delta R}{\delta \dot Q}
\dfrac{\delta S}{\delta P}=\dfrac{\delta P}{\delta \dot P}
Or this is just imagination?
Best Regards,
Jorge.
 
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