Analytical prediction of chaos in rotated Froude pendulum

Nonlinear Dynamics

Volumn 47, Issue 1-3, 2007, Pages 3-24

  Awrejcewicz, J ^a   Holicke, M ^a  

^a LODZ UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Froude pendulum; Homoclinic orbit; Melnikov's method

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; COMPUTER SIMULATION; ELECTRIC EXCITATION; FRICTION; HARMONIC ANALYSIS; NUMERICAL METHODS;

ANALYTICAL PREDICTION; COULOMB TYPE FRICTION; FROUDE PENDULUMS; HARMONIC EXCITATION;

PENDULUMS;

EID: 33846112576     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-006-9054-8     Document Type: Article

References (15)

1. Melnikov, V.K.: On the stability of the center for time periodic perturbations. Trans. Moscow Math. Soc. 12, 1-57 (1963)
2. Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New-York (1983)
3. Nayfeh, A.H.,Balachandran,B.: Applied Non linear Dynamics, Wiley, New York (1995)
4. Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New-York (1990)
5. Gruendler, J.: The existence of homoclinic orbits and the method of Melnikov for systems in R4. SIAM J. Math. Anal., 16(5), 907-931 (1985)
6. Simth, P.: The multiple scales method, homoclinic bifurcation and Melnikov's method for autonomous systems. Int. J. Bif. Chaos 8(11), 2099-2105 (1998)
7. Lenci, S., Rega, G.: Heteroclinic bifurcations and optimal control in the nonlinear rocking dynamics of generic and slender rigid blocks. Int. J. Bif. Chaos 15(6), 1901-1918 (2005)
8. Lenci, S., Rega, G.: Controlling nonlinear dynamics in a two-well impact systems. I. Attractors and bifurcation scenario under symmetric excitations. Int. J. Bif. Chaos 8(12), 2387-2407 (1998)
9. Lenci, S., Rega, G.: Controlling nonlinear dynamics in a two-well impact systems. II. Attractors and bifurcation scenario under unsymmetric optimal excitation. Int. J. Bif. Chaos 8(12), 2409-2424 (1998)
10. Lenci, S., Rega, G.: Higher-order Melnikov functions for single-DOF mechanical oscillators. Theoretical treatment and applications. Mathematical Problems in Engineering. 2, 145-168 (2004)
11. Awrejcewicz, J., Holicke, M.: Detection of Stick-Slip Chaotic Oscillations Using Melnikov's Method. In: Proceedings of the International Conference on 'Nonlinearity, Bifurcation, Chaos: The Doors to the Future', J. Awrejcewicz, C.-H. Lamarque (eds), Lódź, Poland, Sept. 16-18, pp. 65-68 (1996)
12. Awrejcewicz, J., Holicke, M.: Melnikov's method and stick-slip chaotic oscillations in very weakly forced mechanical systems. Int. J. Bif. Chaos 9(3), 505-518 (1999)
13. Holicke, M., Awrejcewicz, J.: Chaos generated by a destruction of four homoclinic orbits. In: Proceedings of the 7th Conference on Dynamical Systems - Theory and Applications. J. Awrejcewicz, A. Owczarek, J. Mrozowski (eds), Lódź, Poland, Dec. 8-11, pp. 161-169 (2003)
14. Holicke, M.: Analysis of chaotic motions of simple mechanical systems with friction using Melnikov method, PhD Thesis, Lódź (2004) (in Polish)
15. Osiński, Z.: Damping of the mechanical systems, PWN, Warsaw (1979) (in Polish)