  We consider a simple motivating example of a non-Hamiltonian dynamical system
with time-dependent constraints obtained by imposing rheonomic non-integrable
Bilimovich's constraint on a freely rotating rigid body. Dynamics of this
low-dimensional nonlinear nonautonomous dynamic system involves different kinds
of stable and unstable attractors, quasi and strange attractors, compact and
noncompact invariant attractive curves, etc. To study this cautionary example
we apply the Poincar\'{e} map method to disambiguate and discover multiscale
temporal dynamics, specifically the coarse-grained dynamics resulting from
fast-scale nonlinear control via nonholonomic Bilimovich's constraint.
