  We obtain lagrangian for $k$-essence scalar field $\phi(r,t)$ with scalar
curvature $k$ of Friedmann-Lemaitre-Robertson-Walker (FLRW) metric . Obtained
lagrangian has two generalised co-ordinates $\phi$ and logarithm of scale
factor ($q=\ln a$). Classical Hamiltonian $({\mathcal H})$ is obtained in terms
of two corresponding conjugate momentum $p_{q}$ and $p_{\phi}$. Solving
Hamilton's equation of motion , we obtain classical solution for scale factor
$a(t)$, energy density $\rho$, equation of state parameter $\omega$ and
deceleration parameter $q_{0}$ . At late time as $t\rightarrow\infty$, we have
an exponential growth of scale factor with time, energy density $\rho$ becomes
constant, which we can identify as dark energy density, equation of state
parameter becomes $\omega\approx -1$ and deceleration parameter becomes $
q_{0}\approx -1$. All this results indicates an accelerated expansion of
universe driven by negative pressure known as dark energy.
