  The simple, longitudinal, and transverse wobblers are systematically studied
within the framework of collective Hamiltonian, where the collective potential
and mass parameter included are obtained based on the tilted axis cranking
approach. Solving the collective Hamiltonian by diagonalization, the energies
and the wave functions of the wobbling states are obtained. The obtained
results are compared with those by harmonic approximation formula and particle
rotor model. The wobbling energies calculated by the collective Hamiltonian are
closer to the exact solutions by particle rotor model than harmonic
approximation formula. It is confirmed that the wobbling frequency increases
with the rotational frequency in simple and longitudinal wobbling motions while
decreases in transverse wobbling motion. These variation trends are related to
the stiffness of the collective potential in the collective Hamiltonian.
