Question

For a system lagrangian is a function of q only then how to find hamiltonian

Answer 1

First of all, the hamiltonian contains the coordinates qi and their momenta pi. You have to calculate the velocities q˙i. For that, you'll need the Hamilton-Jacobi equations

q˙i=∂H∂pi

The Legendre transform, as noted in the comments, is involutive, so the lagrangian is just the Legendre transform of the hamiltonian

L=∑ipiq˙i−H

where you have to express everywhere the momenta in terms of the velocities.

Worked-out example: harmonic oscillator. The well-known hamiltonian is

H=p22m+12mω2q2

From the Hamilton-Jacobi we get (unsurprisingly) that

q˙=∂H∂p=pm

And plug it in the Legendre transform

L=q˙p−H=q˙(q˙m)−(q˙m)22m−12mω2q2=12mq˙2−12mω2q2

Which is indeed the lagrangian for the harmonic oscillator.