  Rotation of triaxially deformed nucleus has been an interesting subject in
the study of nuclear structure. In the present series of work, we investigate
wobbling motion and chiral rotation by employing the microscopic framework of
angular-momentum projection from cranked triaxially deformed mean-field states.
In this first part the wobbling motion is studied in detail. The consequences
of the three dimensional cranking are investigated. It is demonstrated that the
multiple wobbling rotational bands naturally appear as a result of fully
microscopic calculation. They have the characteristic properties, that are
expected from the macroscopic triaxial-rotor model or the phenomenological
particle-triaxial-rotor model, although quantitative agreement with the
existing data is not achieved. It is also found that the excitation spectrum
reflects dynamics of the angular-momentum vector in the intrinsic frame of the
mean-field (transverse vs. longitudinal wobbling). The results obtained by
using the Woods-Saxon potential and the schematic separable interaction are
mainly discussed, while some results with the Gogny D1S interaction are also
presented.
