About the meaning "on-shell" vs "off-shell" in Hamiltonian mechanics

[cianfa72]

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About the meaning "on-shell" vs "off-shell" in the context of Hamiltonian/Lagrangian mechanics

In the derivation of Hamiltonian mechanics, the concept of "on-shell" vs "off-shell" is involved in the calculation.

I searched it for like off-shelf, however it seems it makes sense in the context of four-momentum in special relativity.

What is the meaning of that concept in the context of Hamiltonian/Lagrangian mechanics ? Thanks.

 

[anuttarasammyak]

You might have already read https://en.wikipedia.org/wiki/On_shell_and_off_shell