  A triaxial core rotating around the middle axis, i.e. 2-axis, is cranked
around the 1-axis, due to the coupling of an odd proton from a high j orbital.
Using the Bargmann representation of a new and complex boson expansion of the
angular momentum components, the eigenvalue equation of the model Hamiltonian
acquires a Schr\"{o}dinger form with a fully separated kinetic energy. From a
critical angular momentum, the potential energy term exhibits three minima, two
of them being degenerate. Spectra of the deepest wells reflects a chiral-like
structure. Energies corresponding to the deepest and local minima respectively,
are analytically expressed within a harmonic approximation. Based on a
classical analysis, a phase diagram is constructed. It is also shown that the
transverse wobbling mode is unstable. The wobbling frequencies corresponding to
the deepest minimum are used to quantitatively describe the wobbling properties
in $^{135}$Pr. Both energies and e.m. transition probabilities are described.
