# Derivation in classical mechanics

I'm studying classical mechanics and I'm stumbling in the quantity of differential identities.

Being S the action, H the hamiltonian, L the lagrangian, T the kinetic energy and V the potential energy, following the relationships:

But, the big question is: that's all? Or has exist more?

Seems be missing
$$\frac{\partial S}{\partial q'} \;\;\; \frac{\partial S}{\partial p} \;\;\; \frac{\partial S}{\partial p'} \;\;\; \frac{\partial S}{\partial q'} \;\;\; \frac{\partial L}{\partial p} \;\;\; \frac{\partial L}{\partial p'} \;\;\; \frac{\partial H}{\partial p'} \;\;\; \frac{\partial H}{\partial q'} \;\;\; \frac{\partial V}{\partial q'} \;\;\; \frac{\partial V}{\partial p} \;\;\; \frac{\partial V}{\partial p'} \;\;\; \frac{\partial T}{\partial q} \;\;\; \frac{\partial T}{\partial p} \;\;\; \frac{\partial T}{\partial p'}$$
These relation exist? Make sense? If yes, how will be the identities?

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Dale
Mentor
2021 Award
Once you write down the Hamiltonian or the Lagrangian then you certainly can write down all of the rest of those quantities, but there is no point it doing so. You can already solve the equations of motion without them.

Once you write down the Hamiltonian or the Lagrangian then you certainly can write down all of the rest of those quantities

How? Give me examples...

Staff Emeritus