  Complete description of the classical and quantum dynamics of a particle in
an anisotropic, rotating, harmonic trap is given. The problem is studied in
three dimensions and no restrictions on the geometry are imposed. In the
generic case, for an arbitrary orientation of the rotation axis, there are two
regions of instability with different characteristics. The analysis of the
quantum-mechanical problem is made simple due to a direct connection between
the classical mode vectors and the quantum-mechanical wave functions. This
connection is obtained via the matrix Riccati equation that governs the time
evolution of squeezed states of the harmonic oscillator. It is also shown that
the inclusion of gravity leads to a resonant behavior -- the particles are
expelled from the trap.
