  We present alternative explicit forms of the standard Hamiltonian for systems
with one degree of freedom. This new class of infinite Hamiltonians is called
Newton-equivalent Hamiltonian zoo, producing the same equation of motion. These
Hamiltonians are directly solved from the Hamilton's equations and come with
extra-parameters, which are interpreted as scaling factors for the time
evolution on phase space. Moreover, each Hamiltonian in the zoo can be used as
a generating function for a Hamiltonian hierarchy.
