Analytical Prediction of Chaos in a Two Degrees-of-freedom Mechanical System with Friction

• Autorzy: Awrejcewicz, J. , Sendkowski, D.
• Konferencja: Symposium Vibrations in Physical Systems (XXI ; 26-29.05.2004 ; Poznań-Kierz, Polska)
• Języki publikacji: EN

Słowa kluczowe

PL

stopnie swobody; układ mechaniczny; metoda Mielnikowa

EN

degrees of freedom; mechanical system; Melnikov techniques

• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2004
• Tom: Vol. 21
• Strony: 83--86
• Opis fizyczny: Bibliogr. 7 poz., rys., wz.

Twórcy

autor

Awrejcewicz, J.

• Technical University of Lodz, Department of Automatics and, Biomechanics (K–16), 1/15 Stefanowski St., 90-924 Łódź, Poland,

autor

Sendkowski, D.

• Technical University of Lodz, Department of Automatics and, Biomechanics (K–16), 1/15 Stefanowski St., 90-924 Łódź, Poland,

Bibliografia

• 1. Awrejcewicz J., Delfs J. Dynamics of a self-excited stick-slip oscillator with two degrees-of-freedom. Part I. Investigation of equilibria, Eur. J. Mech. A/Sol., (4)(1990) pp. 269-282.
• 2. Awrejcewicz J., Delfs J. Dynamics of a self-excited stick-slip oscillator with two degrees-of-freedom. Part II. Slip-stick, slip-slip, stick-slip transitions, periodic and chaotic orbits, Eur. J. Mech. A/Sol., 9(5)(1990) pp. 397-418.
• 3. Awrejcewicz J, Holicke M.M. Melnikov’s method and stick-slip chaotic oscillations in very weakly forced mechanical systems, J. Bifurcation and Chaos 9(3), 1999, pp.505-518.
• 4. Awrejcewicz J., Lamarque C.H. Bifurcations and Chaos in Nonsmooth Mechanical Systems, World Scientific, New Jersey, London, Singapore, Hong-Kong, 2003 .
• 5. Gelfreich J. Melnikov method and exponentially small splitting of separatrices, Phys. D, 101(1997), pp. 227-248.
• 6. Grtuendler J. The existance of homoclinic orbits and the method of Melnikov for systems in R , SIAM J. Math. Anal., 16(1985), pp.907-931.
• 7. Melnikov V.K. On the stability of the center for time-periodic perturbations, Trans. Moscow Math. Soc., 12(1963), pp. 1-56.

Uwagi

This work is partially supported by the grant 5 T07A 019 23 and by Department of Mathematics of the Central European University in Budapest.