  We propose a Hamiltonian formalism for a generalized
Friedmann-Roberson-Walker cosmology model in the presence of both a variable
equation of state (EOS) parameter $w(a)$ and a variable cosmological constant
$\Lambda(a)$, where $a$ is the scale factor. This Hamiltonian system containing
1 degree of freedom and without constraint, gives Friedmann equations as the
equation of motion, which describes a mechanical system with a variable mass
object moving in a potential field. After an appropriate transformation of the
scale factor, this system can be further simplified to an object with constant
mass moving in an effective potential field. In this framework, the $\Lambda$
cold dark matter model as the current standard model of cosmology corresponds
to a harmonic oscillator. We further generalize this formalism to take into
account the bulk viscosity and other cases. The Hamiltonian can be quantized
straightforwardly, but this is different from the approach of the
Wheeler-DeWitt equation in quantum cosmology.
