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
Messages
8
Reaction score
0
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.
 
Physics news on Phys.org
Any comments?
 
Thread 'Question about pressure of a liquid'
I am looking at pressure in liquids and I am testing my idea. The vertical tube is 100m, the contraption is filled with water. The vertical tube is very thin(maybe 1mm^2 cross section). The area of the base is ~100m^2. Will he top half be launched in the air if suddenly it cracked?- assuming its light enough. I want to test my idea that if I had a thin long ruber tube that I lifted up, then the pressure at "red lines" will be high and that the $force = pressure * area$ would be massive...
I feel it should be solvable we just need to find a perfect pattern, and there will be a general pattern since the forces acting are based on a single function, so..... you can't actually say it is unsolvable right? Cause imaging 3 bodies actually existed somwhere in this universe then nature isn't gonna wait till we predict it! And yea I have checked in many places that tiny changes cause large changes so it becomes chaos........ but still I just can't accept that it is impossible to solve...
Back
Top