# Legrende transform of a Lagrangian

1. Jan 5, 2013

### Uku

1. The problem statement, all variables and given/known data

I am given a Lagrangian, which, per assignment text, describes a single degree of freedom:

$L= \frac{I}{2}(\dot{q}+\omega)^2-kq^2$

I need to find the Hamiltonian.

Now, what I am wondering, when performing the Legrende transform:

$H=\sum_{j}p_{j}\dot{q}_{j}-L(q_{j},\dot{q}_{j},t)$

Do I concider $\omega$ as velocity, eg. there are two members of the sum: $\sum_{j}p_{j}\dot{q}_{j}$? The assignment states one degree of freedom.. so I'm a bit insecure on that.

U.

2. Jan 5, 2013

### TSny

If there is only one degree of freedom ($q$), then $\omega$ would just be a constant or some parameter. So, only one term $p\dot q$ in the transformation.