  Two types of non-holonomic constraints (imposing a prescription on velocity)
are analyzed, connected to an end of a (visco)elastic rod, straight in its
undeformed configuration. The equations governing the nonlinear dynamics are
obtained and then linearized near the trivial equilibrium configuration. The
two constraints are shown to lead to the same equations governing the
linearized dynamics of the Beck (or Pfluger) column in one case and of the Reut
column in the other. Therefore, although the structural systems are fully
conservative (when viscosity is set to zero), they exhibit flutter and
divergence instability. In addition, the Ziegler's destabilization paradox is
found when dissipation sources are introduced. It follows that these features
are proven to be not only a consequence of 'unrealistic non-conservative loads'
(as often stated in the literature), rather, the models proposed by Beck, Reut,
and Ziegler can exactly describe the linearized dynamics of structures subject
to non-holonomic constraints, which are made now fully accessible to
experiments.
