Open Access
Issue
MATEC Web Conf.
Volume 148, 2018
International Conference on Engineering Vibration (ICoEV 2017)
Article Number 10003
Number of page(s) 6
Section Modelling of Friction and Dynamics of Frictional Oscillators
DOI https://doi.org/10.1051/matecconf/201814810003
Published online 02 February 2018
  1. A. M. Lyapunov: Probleme General de la Stabilité du Mouvment. Annales Mathematical Study, 17, Princeton University Press, Princeton, New Jersey (1947)
  2. G. D. Birkhoff: Dynamical Systems, AMS Colloquium Publications, Providence, (1927)
  3. V. I. Oseledec: A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems. Trans. Mosc. Math. Soc. 19, 197-231 (1968)
  4. J.L. Kaplan, J. A. Yorke: Chaotic behavior of multidimensional difference equations, in Lecture Notes in Mathematics, Vol. 730, edited by H. O. Peitgen and H. O. Walther, pp. 228 -- 237, Springer, Berlin (1978) [CrossRef]
  5. V. C. Anishchenko: Complex oscillations in simple systems, 312, Nauka Publisher, Moscow (1990)
  6. M. Henon, C. Heiles: The applicability of the third integral of the motion: some numerical results, Astron. J. 69, 77 (1964) [NASA ADS] [CrossRef]
  7. G. Benettin, L. Galgani, J.M. Strelcyn: Kolmogorov entropy and numerical experiment, Phys. Rev. A 14, 2338- 2345 (1976) [NASA ADS] [CrossRef]
  8. I. Shimada, T. Nagashima: A numerical approach to ergodic problem of dissipative dynamical systems, Prog. Theor. Phys. 61(6), 1605-1616 (1979) [CrossRef]
  9. G. Benettin, L. Galgani, A. Giorgilli, J.M. Strelcyn: Lyapunov exponents for smooth dynamical systems and Hamiltonian systems; a method for computing all of them, part I: theory, Meccanica 15, 9-20 (1980) [NASA ADS] [CrossRef]
  10. G. Benettin, L. Galgani, A. Giorgilli, J.M. Strelcyn: Lyapunov exponents for smooth dynamical systems and Hamiltonian systems; a method for computing all of them, part II: numerical application. Meccanica 15, 21-30 (1980) [CrossRef]
  11. A. Wolf : Quantifying chaos with Lyapunov exponents, Chaos, Manchester University Press, Manchester, 273-290 (1986)
  12. T.S., Parker, L.O. Chua: Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, Berlin (1989)
  13. H. Nusse, J. Yorke : Dynamics : Numerical Explorations, Springer-Verlag (1994)
  14. A. Dąbrowski: Estimation of the largest Lyapunov exponent from the perturbation vector and its derivative dot product, Nonlinear Dynamics 67(1), 283-291 (2012) [CrossRef]
  15. M. Balcerzak, A. Dąbrowski, D. Pikunov: The fastest, simplified method of Lyapunov exponents spectrum estimation for continuous dynamical systems, Submitted to Nonlinear Dynamics
  16. A. Dąbrowski: The largest transversal Lyapunov exponent and master stability function from the perturbation vector and its derivative dot product (TLEVDP), Nonlinear Dynamics 69(3), 1225-1235 (2012) [CrossRef]
  17. M. Balcerzak, A. Dąbrowski, T. Kapitaniak, A. Jach: Optimization of the control system parameters with use of the new simple method of the largest Lyapunov exponent estimation, Mechanics and Mechanical Engineering 17(3), 225-239 (2013)
  18. K. Pijanowski, A. Dąbrowski, M. Balcerzak: New method of multidimensional control simplification and control system optimization, Mechanics and Mechanical Engineering 19(2), 127-139 (2015)
  19. A. Dąbrowski: Estimation of the the Largest Lyapunov exponent-like (LLEL) stability measure parameter from the perturbation vector and its derivative dot product (part 2) experiment simulation, Nonlinear Dynamics 78(3), 1601-1608 (2014) [CrossRef]
  20. M. Balcerzak, D. Pikunov: The fastest, simplified method of estimation of the Largest Lyapunov exponent for continuous dynamical systems with time delay, Mechanics and Mechanical Engineering (accepted)
  21. P. Müller: Calculation of Lyapunov exponents for dynamical systems with discontinuities, Chaos, Solitons Fractals 5(9), 1671-1681 (1995) [CrossRef]
  22. A. Stefanski, T. Kapitaniak: Estimation of the dominant Lyapunov exponent of non-smooth systems on the basis of maps synchronization, Chaos, Solitons & Fractals, 15(2), pp. 233-244 (2003) [CrossRef]
  23. L. Jin, Q.-S. Lu, E.H. Twizell: A method for calculating the spectrum of Lyapunov exponents by local maps in non-smooth impact-vibrating systems, Journal of Sound and Vibration, 298(4-5), pp. 1019-1033 (2006) [CrossRef]
  24. S. De Souza, I. Caldas: Controlling chaotic orbits in mechanical systems with impacts, Chaos, Solitons & Fractals, 19, 171-178 (2004) [CrossRef]
  25. R. C. Hilborn: Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, Oxford University Press (1994)
  26. M. Oestreich, N. Hinrichs, K. Pop : Bifurcation and stability analysis for a non-smooth frictional oscillator, Arch. Appl Mech. 66, 301-314 (1996) [CrossRef]
  27. M. Oestreich: Untersuchung von Schwingern mit nichtglatten Kennlinien, Fortsrchritt-Berichte VDI, Reiche 11: Schwingungstechnik, Nr. 258 (in German) (1998)
  28. U. Galvanetto: Numerical computation of Lyapunov exponents in discontinuous maps implicitly defined, Computer Physics Communications, 131(1-2), 1-9 (2000) [CrossRef]
  29. N. Hinrichs, M. Oestreich, K. Popp: Dynamics of oscillators with impact and friction, Chaos, Solitons & Fractals, 4(8), 535-58 (1997) [CrossRef]
  30. A. Stefanski, T. Kapitaniak: Using chaos synchronization to estimate the largest Lyapunov exponent of non-smooth systems, Discrete Dyn. Nat. Soc. 4, 207-215 (2000)? [CrossRef]

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