  In this paper an approach is proposed to represent a class of dissipative
mechanical systems by corresponding infinite-dimensional Hamiltonian systems.
This approach is based upon the following structure: for any non-conservative
classical mechanical system and arbitrary initial conditions, there exists a
conservative system; both systems share one and only one common phase curve;
and, the value of the Hamiltonian of the conservative system is, up to an
additive constant, equal to the total energy of the non-conservative system on
the aforementioned phase curve, the constant depending on the initial
conditions. We describe in detail this relationship calling the conservative
system ``substitute`` conservative system. By considering the dissipative
mechanical system as a special fluid in a domain $D$ of the phase space, viz. a
collection of particles in this domain, we are prompted to develop this system
as an infinite-dimensional Hamiltonian system of an ideal fluid. By comparing
the description of the ideal fluid in Lagrangian coordinates, we can consider
the Hamiltonian and the Lagrangian as the respective integrals of the
Hamiltonian and the Lagrangian of the substitute conservative system over the
initial value space and define a new Poisson bracket to express the equations
of motion in Hamiltonian form. The advantage of the approach is that the value
of the canonical momentum density $\pi$ is identical with that of the
mechanical momentum $m\dot{q}$ and the value of canonical coordinate $q$ is
identical with that of the coordinate of the dissipative mechanical system.
Therefore we need not to decouple the Newtonian equations of motion into
several one-dimensional ordinary differential equations.
