  We make use of the Quantum Hamilton-Jacobi (QHJ) theory to investigate
conditional quasi-solvability of the quantum symmetric top subject to combined
electric fields (symmetric top pendulum). We derive the conditions of
quasi-solvability of the time-independent Schroedinger equation as well as the
corresponding finite sets of exact analytic solutions. We do so for this
prototypical trigonometric system as well as for its anti-isospectral
hyperbolic counterpart. An examination of the algebraic and numerical spectra
of these two systems reveals mutually closely related patterns. The QHJ
approach allows to retrieve the closed-form solutions for the spherical and
planar pendula and the Razavy system that had been obtained in our earlier work
via Supersymmetric Quantum Mechanics as well as to find a cornucopia of
additional exact analytic solutions.
