Action and Response functions.

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SUMMARY

This discussion centers on the analytical determination of action S and response R functions for a system defined by two canonical coordinates P and Q. Jorge inquires whether it is feasible to derive these functions while satisfying the specified relations involving functional derivatives. The consensus indicates that while the equations of motion can be established, finding explicit forms for S and R functions analytically may not be straightforward and could involve complex mathematical frameworks.

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  • Knowledge of Lagrangian and Hamiltonian mechanics
  • Experience with variational principles in physics
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jorgext
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Dear colleagues,
I have the following question in my head:
Give two canonical coordinates [tex]P[/tex], [tex]Q[/tex], and a corresponding set of equations of motions, not necessary solved.
Is it possible to find analytically the action [tex]S[/tex] and response [tex]R[/tex]functions of the system, which satisfy the relations:
[tex]\dfrac{\delta S}{\delta Q}=\dfrac{\delta R}{\delta \dot Q}[/tex]
[tex]\dfrac{\delta S}{\delta P}=\dfrac{\delta P}{\delta \dot P}[/tex]
Or this is just imagination?
Best Regards,
Jorge.
 
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