  A particle-triaxial rigid core Hamiltonian is semi-classically treated. The
coupling term corresponds to a particle rigidly coupled to the triaxial core,
along a direction that does not belong to any principal plane of the inertia
ellipsoid.The equations of motion for the angular momentum components provide a
sixth-order algebraic equation for one component and subsequently equations for
the other two. Linearizing the equations of motion, a dispersion equation for
the wobbling frequency is obtained. The equations of motion are also considered
in the reduced space of generalized phase space coordinates. Choosing
successively the three axes as quantization axis will lead to analytical
solutions for the wobbling frequency, respectively. The same analysis is
performed for the chirally transformed Hamiltonian. With an illustrative
example one identified wobbling states whose frequencies are mirror image to
one another. Changing the total angular momentum I, a pair of twin bands
emerged. Note that the present formalism conciliates between the two signatures
of triaxial nuclei, i.e., they could coexist for a single nucleus.
