Hamiltonian equations are a representation of Hamiltonian mechanics. Please see the link.

The total energy of the system simply described in classical mechanics called as Hamiltonian.

Dirk Ter Haar has written:

'Elements of Hamiltonian mechanics'

Percy Deift has written:

'The bidiagonal singular value decomposition and Hamiltonian mechanics' -- subject(s): Accessible book

Hamiltonian is the proper adjective for Hamilton. For instance: The Hamiltonian view on the structure of government was much different from that of Jefferson.