Jerzy Warminski, Ph.D., D.Sc., Eng.
Professor of Theoretical and Applied Mechanics

The main attention of my research is paid to non-linear dynamics of mechanical systems including the latest trends in mechanics like: non-linear vibrations, chaos theory, bifurcation and stability analysis.

In the research I apply analytical perturbation methods e.g. the multiple time scale method, Krylov-Bogolyubov-Mitropolski method, harmonic balance or Poincaré method. The transition from regular to chaotic vibrations I predict numerically by bifurcation diagrams, Poincaré maps, Lyapunov exponents or in some specific cases by analytically by Melnikov method. Having a mathematical model I use continuation methods to find bifurcation points and to verify stability of the solution. In the numerical investigations I use original differential equations or modulation equations (slow-flow) obtained by analytical methods.