EDP Sciences logo
Web of Conferences logo
Search
Menu
All issues Volume 148 (2018) MATEC Web Conf., 148 (2018) 10003 References
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) [Google Scholar]
  2. G. D. Birkhoff: Dynamical Systems, AMS Colloquium Publications, Providence, (1927) [Google Scholar]
  3. V. I. Oseledec: A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems. Trans. Mosc. Math. Soc. 19, 197-231 (1968) [Google Scholar]
  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] [Google Scholar]
  5. V. C. Anishchenko: Complex oscillations in simple systems, 312, Nauka Publisher, Moscow (1990) [Google Scholar]
  6. M. Henon, C. Heiles: The applicability of the third integral of the motion: some numerical results, Astron. J. 69, 77 (1964) [Google Scholar]
  7. G. Benettin, L. Galgani, J.M. Strelcyn: Kolmogorov entropy and numerical experiment, Phys. Rev. A 14, 2338- 2345 (1976) [NASA ADS] [CrossRef] [Google Scholar]
  8. I. Shimada, T. Nagashima: A numerical approach to ergodic problem of dissipative dynamical systems, Prog. Theor. Phys. 61(6), 1605-1616 (1979) [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  11. A. Wolf : Quantifying chaos with Lyapunov exponents, Chaos, Manchester University Press, Manchester, 273-290 (1986) [Google Scholar]
  12. T.S., Parker, L.O. Chua: Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, Berlin (1989) [Google Scholar]
  13. H. Nusse, J. Yorke : Dynamics : Numerical Explorations, Springer-Verlag (1994) [Google Scholar]
  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] [Google Scholar]
  15. M. Balcerzak, A. Dąbrowski, D. Pikunov: The fastest, simplified method of Lyapunov exponents spectrum estimation for continuous dynamical systems, Submitted to Nonlinear Dynamics [Google Scholar]
  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] [Google Scholar]
  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) [Google Scholar]
  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) [Google Scholar]
  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] [Google Scholar]
  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) [Google Scholar]
  21. P. Müller: Calculation of Lyapunov exponents for dynamical systems with discontinuities, Chaos, Solitons Fractals 5(9), 1671-1681 (1995) [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  24. S. De Souza, I. Caldas: Controlling chaotic orbits in mechanical systems with impacts, Chaos, Solitons & Fractals, 19, 171-178 (2004) [CrossRef] [Google Scholar]
  25. R. C. Hilborn: Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, Oxford University Press (1994) [Google Scholar]
  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] [Google Scholar]
  27. M. Oestreich: Untersuchung von Schwingern mit nichtglatten Kennlinien, Fortsrchritt-Berichte VDI, Reiche 11: Schwingungstechnik, Nr. 258 (in German) (1998) [Google Scholar]
  28. U. Galvanetto: Numerical computation of Lyapunov exponents in discontinuous maps implicitly defined, Computer Physics Communications, 131(1-2), 1-9 (2000) [CrossRef] [Google Scholar]
  29. N. Hinrichs, M. Oestreich, K. Popp: Dynamics of oscillators with impact and friction, Chaos, Solitons & Fractals, 4(8), 535-58 (1997) [CrossRef] [Google Scholar]
  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] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.