  A triaxial particle-rotor Hamiltonian for three mutually perpendicular
angular momentum vectors corresponding to two high-$j$ quasiparticles and the
rotation of a triaxial collective core, is treated within a time-dependent
variational principle. The resulting classical energy function is used to
investigate the rotational dynamics of the system. It is found that the
classical energy function exhibits two minima starting from a critical angular
momentum value which depends on the single-particle configuration and the
asymmetry measure $\gamma$. The emergence of the two minima is attributed to
the breaking of the chiral symmetry. Quantizing the energy function for a given
angular momentum, one obtains a Schr\"{o}dinger equation with a coordinate
dependent mass term for a symmetrical potential which changes from a single to
a double well shape as the angular momentum pass the critical value. The
energies of the chiral partner bands for a given angular momentum are then
given by the lowest two eigenvalues. The procedure is exemplified for maximal
triaxiality and two $h_{11/2}$ quasiparticles, with the results used for the
description of the chiral doublet bands in $^{134}$Pr.
