  A new interpretation for the wobbling bands in $^{163}$Lu is given within a
particle-triaxial rotor semi-classical formalism. While in the previous papers
the bands TSD1, TSD2, TSD3 and TSD4 are viewed as the ground, one, two and
three phonon wobbling bands, here the corresponding experimental results are
described as the ground band with spin equal to I=R+j, for R=0,2,4,...(TSD1),
the ground band with I=R+j and R=1,3,5,...(TSD2), the one phonon excitations of
TSD2 (TSD3), with the odd proton moving in the orbit $j=i_{13/2}$, and the
ground band of I=R+j, with R=1,3,5,... and $j=h_{9/2}$ (TSD4). The moments of
inertia (MoI) of the core for the first three bands are the same, and
considered to be free parameters. Due to the core polarization effect caused by
the particle-core coupling, the MoI's for TSD4 are different. The energies and
the e.m. transitions are quantitatively well described. Also, the phase diagram
of the odd system is drawn. In the parameter space one indicates where the
point associated with the fitted parameters is located and also which is the
region of transversal wobbling mode as well as where the wobbling motion is
forbidden.
