# Derivation in classical mechanics

1. Jun 15, 2014

### Jhenrique

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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2. Jun 15, 2014

### Staff: Mentor

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.

3. Jun 16, 2014

### Jhenrique

How? Give me examples...

4. Jun 17, 2014