  There are many approaches for the description of dissipative systems coupled
to some kind of environment. This environment can be described in different
ways; only effective models will be considered here. In the Bateman model, the
environment is represented by one additional degree of freedom and the
corresponding momentum. In two other canonical approaches, no environmental
degree of freedom appears explicitly but the canonical variables are connected
with the physical ones via non-canonical transformations. The link between the
Bateman approach and those without additional variables is achieved via
comparison with a canonical approach using expanding coordinates since, in this
case, both Hamiltonians are constants of motion. This leads to constraints that
allow for the elimination of the additional degree of freedom in the Bateman
approach. These constraints are not unique. Several choices are studied
explicitly and the consequences for the physical interpretation of the
additional variable in the Bateman model are discussed.
