On inhomogeneous nonholonomic Bilimovich system

Abstract

We consider a simple motivating example of non-Hamiltonian dynamical system with timedependent constraint obtained by imposing rheonomic nonintegrabe 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. We apply the Poincaré map method to study this cautionary example in order to disambiguate and discover multiscale temporal dynamics, specifically the coarse-grained dynamics which results from fast-scale nonlinear control via nonholonomic Bilimovich's constraint.