# Hamiltonian & Generalised cooordinates

1. Apr 28, 2010

### Plutoniummatt

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

Let $$T = \frac{1}{2}T_{ij}\dot{q_{i}}\dot{q_{j}}$$ and $$V = \frac{1}{2}V_{ij}q_{i}q_{j}$$. Verify that the equation of motion $$T_{ij}\ddot{q_{j}} + V_{ij}q_{j} = 0$$ imply that the energy T + V is conserved. Can the constancy of T+V be used to deduce the equations of motion?

2. Relevant equations

non

3. The attempt at a solution

Using the product rule, i can show the time derivative of T+V is zero given the equations of motion. But I have to assume T and V are symmetric, is this always true?

I don't know how to deduce equations of motion from constancy of T+V though.