On inhomogeneous nonholonomic Bilimovich system

A.V. Borisov, A.V. Tsiganov, E.A. Mikishanina

Research output: Contribution to journalLetterpeer-review

1 Scopus citations


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 Poincaré 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.
Original languageEnglish
Article number105573
JournalCommunications in Nonlinear Science and Numerical Simulation
Early online date17 Oct 2020
StatePublished - Mar 2021
Externally publishedYes

Scopus subject areas

  • Modelling and Simulation
  • Mathematical Physics


  • Time-dependent non-Hamiltonian system
  • Poincaré maps


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