  The su(2)-algebraic model interacting with an environment is investigated
from a viewpoint of treating the dissipative system. By using the
time-dependent variational approach with a coherent state and with the help of
the canonicity condition, the time-evolution of this quantum many-body system
is described in terms of the canonical equations of motion in the classical
mechanics. Then, it is shown that the su(1,1)-algebra plays an essential role
to deal with this model. An exact solution with appropriate initial conditions
is obtained by means of Jacobi's elliptic function. The implication to the
dissipative process is discussed.
