  The recently reported wobbling bands in $^{135}$Pr are investigated by the
collective Hamiltonian, in which the collective parameters, including the
collective potential and the mass parameter, are respectively determined from
the tilted axis cranking (TAC) model and the harmonic frozen alignment (HFA)
formula. It is shown that the experimental energy spectra of both yrast and
wobbling bands are well reproduced by the collective Hamiltonian. It is
confirmed that the wobbling mode in $^{135}$Pr changes from transverse to
longitudinal with the rotational frequency. The mechanism of this transition is
revealed by analyzing the effective moments of inertia of the three principal
axes, and the corresponding variation trend of the wobbling frequency is
determined by the softness and shapes of the collective potential.
