  In the paper [Eur. J. of Appl. Math. \textbf{20}, (2009) 269--287] by da
Costa et al. the twist-Fr\'eedericksz transition in a nematic liquid crystal
one-dimensional cell of lenght $L$ was studied imposing an antisymmetric net
twist Dirichlet condition at the cell boundaries. In the present paper we
extend that study to the more general case of net twist Dirichlet conditions
without any kind of symmetry restrictions. We use phase-plane analysis tools
and appropriately defined time-maps to obtain the bifurcation diagrams of the
model when $L$ is the bifurcation parameter, and related these diagrams with
the one in the symmetric situation. The stability of the bifurcating solutions
is investigated by applying the method of Kenjiro Maginu [J. Math. Anal. Appl.
\textbf{63}, (1978) 224--243].
