  We consider the gravitational collapse of self-gravitating spherical dust
cloud in the Hamiltonian formalism. We address both homogeneous and
inhomogeneous cases. Our novel derivation of the Hamiltonian of the system is
based on the improved variational principle that was proposed in \cite{KMM}.
The present derivation differs from usual treatments due to the presence of an
extra boundary term added to the Hilbert action. As expected, the standard
equations of motion are retrieved. However, differently from other treatments,
the total Hamiltonian obtained with our procedure in the Schwarzschild
time-gauge is identical to the total mass of the system as measured from
infinity, as it would be expected. Implications for the quantization of the
system are suggested.
