  The constants of motion of the following systems are deduced: a relativistic
particle with linear dissipation, a no-relativistic particle with a time
explicitly depending force, a no-relativistic particle with a constant force
and time depending mass, and a relativistic particle under a conservative force
with position depending mass. The problem of getting the Hamiltonian for these
systems is determined by getting the velocity as an explicit function of
position and generalized linear momentum, and this problem can be solved a
first approximation for the first above system.

Classical Physics