Character of motion of oscillating pendulum systems at the boundary of the stable region

International Applied Mechanics

Volumn 35, Issue 8, 1999, Pages 853-859

  Lobas, L G ^a   Khrebet, V G ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22844456442     PISSN: 10637095     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02682241     Document Type: Article

References (13)

1. N. N. Bautin, Behavior of Dynamic Systems Near the Boundaries of the Stable Region [in Russian], Nauka, Moscow (1984).
2. L. G. Lobas and V. G. Khrebet. "Oscillating doubly connected pendulum systems," Prikl. Mekh., 29, No. 2, 82-88 (1993).
3. L. G. Lobas and V. G. Khrebet, "Dynamic behavior of an oscillating doubly connected pendulum system at the boundary of the stable region," Prikl. Mekh., 29, No. 4, 78-86 (1993).
4. L. G. Lobas and V. G. Khrebet, "Limiting periodic motions of oscillating doubly connected pendulum systems," Prikl. Mekh., 29, No. 8, 85-93 (1993).
5. L. G. Lobas and V. G. Khrebet, "Hopf bifurcation from a stable focus and evaluation of the attraction region in oscillating doubly connected pendulum systems." Prikl. Mekh., 29, No. 9, 62-68 (1993).
6. L. G. Lobas and V. G. Khrebet, "Existence and uniqueness of periodic motion in oscillating doubly connected pendulum systems,"Izv. Ross. Akad. Nauk Mekh. Tverd. Tela, No. 5, 23-31 (1993).
7. L. G. Lobas and V. G. Khrebet, "Integral manifold in the problem of Andronov-Hopf bifurcation in oscillating doubly connected pendulum systems," Prikl. Mekh., 30, No. 7, 85-93 (1994).
8. L. G. Lobas and V. G. Khrebet, "Hopf bifurcation and evaluation of the attraction region in oscillating doubly connected pendulum systems," Izv. Ross. Akad. Nauk Mekh. Tverd. Tela, No. 3, 61-66 (1994).
9. A. M. Lyapunov, Collected Works [in Russian), Vol. 2 of 3 vols., Izd-vo AN SSSR. Moscow. Leningrad (1956).
10. I. G. Malkin, Lyapunov and Poincare Methods in the Theory of Nonlinear Vibrations [in Russian], GITTL, Moscow, Leningrad (1949).
11. J. Marsden and M. McCracken. Hopf Bifurcation and its Applications [Russian translation], Mir, Moscow (1989).
12. P. J. Holmes, "Center manifolds, normal forms, and bifurcations of vector fields with application to coupling between periodic and steady motions," Physica, 2D, 449-481 (1981).
13. H. Troger and A. Steindl, Nonlinear Stability and Bifurcation Theory, Springer-Verlag, Vienna, New York (1991).