  Zitterbewegung is the exotic phenomenon associated either with the
relativistic electron-positron rapid oscillation or to the electron-hole
transitions in the narrow gap semiconductors. In the present work, we enlarge
concept of Zitterbewegung and show that the trembling motion may occur due to
the dramatic changes in the symmetry of the system. In particular, we exploit a
paradigmatic model of quantum chaos, quantum mathematical pendulum (universal
Hamiltonian). The symmetry group of this system is the Klein's four-group that
possess three invariant subgroups. The energy spectrum of the system
parametrically depends on the height of the potential barrier, and contains
degenerate and non-degenerate areas, corresponding to the different symmetry
subgroups. Change in the height of the potential barrier switches the symmetry
subgroup and leads to the trembling motion. We analyzed mean square
fluctuations of the velocity operator and observed that trembling enhances for
the highly excited states. We observed the link between the phenomena of
trembling motion and uncertainty relations of noncommutative operators of the
system.
