Divergent bifurcations of a double pendulum under the action of an asymmetric follower force

International Applied Mechanics

Volumn 40, Issue 7, 2004, Pages 821-828

  Koval'chuk, V V ^a   Lobas, V L ^b  

^a STATE UNIVERSITY OF INFRASTRUCTURE AND TECHNOLOGIES   (Ukraine)

^b STATE UNIVERSITY OF NEW YORK   (United States)

Author keywords

Asymmetric follower force; Chaos; Divergent bifurcation; Double pendulum; Regular dynamics

Indexed keywords

CHAOS THEORY; EIGENVALUES AND EIGENFUNCTIONS; EQUATIONS OF MOTION; FORCE MEASUREMENT; PERTURBATION TECHNIQUES; PROBLEM SOLVING; STIFFNESS; SYSTEM STABILITY; VISCOSITY;

MATHEMATICAL TOOLS; ORIENTATION PARAMETERS; PLANE-PARALLEL MOTION; TAYLOR SERIES;

PENDULUMS;

EID: 7544237251     PISSN: 10637095     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:INAM.0000046227.50540.17     Document Type: Article

References (15)

1. N. N. Bautin, Behavior of Dynamic Systems at the Stability Boundaries [in Russian], Nauka, Moscow (1984).
2. V. G. Verbitskii and L. G. Lobas, "Real bifurcations of dynamic systems with elementary symmetry and varying control parameters," Probl. Upravl. Inform., No. 6, 47-62 (1995).
3. L. G. Lobas, "Nonlinear stability and pitchfork bifurcations in dynamic systems with elementary symmetry," Prikl. Mat. Mekh., 60, No. 2, 327-332 (1996).
4. L. L. Lobas, "Stability domain of an inverted double pendulum with asymmetric follower force," Dop. NAN Ukrainy, No. 11, 45-49 (2002).
5. J. M. T. Thompson, Instabilities and Catastrophes in Science and Engineering, Wiley, New York (1982).
6. V. A. Dzhupanov and Sv. V. Lilkova-Markova, "Dynamic stability of a fluid-conveying cantilevered pipe on an additional combined support," Int. App. Mech., 39, No. 2, 185-191 (2003).
7. L. G. Lobas, "Nonlinear stability and triple-equilibrium bifurcations in finite-dimensional dynamic systems with symmetry," Eng. Simul., 18, No. 5, 713-725 (1996).
8. L. G. Lobas, "The dynamics of finite-dimensional system under nonconservative position forces," Int. Appl. Mech., 37, No. 1, 38-65 (2001).
9. L. G. Lobas and L. L. Lobas, "Bifurcations and catastrophes of the equilibrium states of an overturned double pendulum subjected to an asymmetric follower force," Stab. Contr: Theor. Appl., 4, No. 2, 110-118 (2002).
10. L. G. Lobas, L. D. Patricio, and I. G. Boruk, "Equilibrium of an inverted mathematical double-link pendulum with a follower force," Int. Appl. Mech., 38, No. 3, 372-376 (2002).
11. L. L. Lobas, "Influence of an asymmetric follower force on the stationary states of a double-link pendulum," Int. Appl. Mech., 37, No. 12, 1618-1623 (2001).
12. B. Qinsheng and Y. Pei, "Double Hopf bifurcations and chaos of a nonlinear vibration system," Nonlinear Dynamics, 19, 313-332 (1999).
13. R. Scheidt, H. Troger, and K. Zeman, "Coupled flutter and divergence bifurcation of a double pendulum," Int. J. Nonlin. Mech., 19, No. 2, 163-176 (1984).
14. V. A. Storozhenko, "A technique for identification of the principal central axis of inertia in an inhomogeneous rigid body," Int. Appl. Mech., 39, No. 12, 1464-1472 (2003).
15. H. Troger and A. Steindl, Nonlinear Stability and Bifurcation Theory, Springer-Verlag, Vienna-New York (1991).