  It is demonstrated that a two-component Bose-Einstein condensate (BEC) with
all-repulsive inter-atomic interactions loaded into a radially symmetric
harmonic trap supports robust non-coaxial vortices with approximately
orthogonal vortex lines in each of the components. These cross vortices are
excited from the linear modes by a sudden switch-on of the nonlinearity (via
Feshbach resonance) and are characterized by persistent dynamical regimes of
precession with nutation, resembling the motion of a rigid body. The obtained
dynamics can be understood qualitatively on the basis of a simple mechanical
model.
