Abstract
The effect of the type of springs on the equilibrium states of an inverted pendulum is examined. The angular and linear eccentricities of the follower force are taken into account
Similar content being viewed by others
References
L. G. Lobas, “The equations of an inverted pendulum with an arbitrary number of links and an asymmetric follower force,” Int. Appl. Mech., 43, No. 5, 560–567 (2007).
L. G. Lobas, V. V. Kovalchuk, and O. V. Bambura, “Evolution of the equilibrium states of an inverted pendulum,” Int. Appl. Mech., 43, No. 3, 344–350 (2007).
L. G. Lobas, V. V. Koval’chuk, and O. V. Bambura, “Equilibrium states of a pendulum with an asymmetric follower force,” Int. Appl. Mech., 43, No. 4, 460–466 (2007).
A. I. Lurie, Analytical Mechanics, Springer, Berlin-New York (2002).
J. M. T. Thompson, Instabilities and Catastrophes in Science and Engineering, Wiley, New York (1982).
H. Ziegler, “On the concept of elastic stability,” in: Advances in Applied Mechanics, Vol. 4, Acad. Press, New York (1956), pp. 351–403.
J.-D. Jin and Y. Matsuzaki, “Bifurcations in a two-degree-of-freedom elastic system with follower forces,” J. Sound Vibr., 126, No. 2, 265–277 (1988).
J.-D. Jin and Y. Matsuzaki, “Stability and bifurcations of a double pendulum subjected to a follower force,” in: Proc. A1AA/ASME/ASCE/AHS/ASC 30th Structures, Structural Dynamics and Materials Conf. (Mobile, Ala, April 3–5, 1989) Pt. 1, Washington (1989), pp. 432–439.
L. G. Lobas, “Generalized mathematical model of an inverted multilink pendulum with follower force,” Int. Appl. Mech., 41, No. 5, 566–572 (2005).
L. G. Lobas, “Dynamic behavior of multilink pendulums under follower forces,” Int. Appl. Mech., 41, No. 6, 587–613 (2005).
L. G. Lobas and V. V. Koval’chuk, “Influence of the nonlinearity of the elastic elements on the stability of a double pendulum with follower force in the critical case,” Int. Appl. Mech., 41, No. 4, 455–461 (2005).
V. L. Lobas, “Influence of the nonlinear characteristics of elastic elements on the bifurcations of equilibrium states of a double pendulum with follower force,” Int. Appl. Mech., 41, No. 2, 197–202 (2005).
Y. Matsuzaki and S. Futura, “Codimension three bifurcation of a double pendulum subjected to a follower force with imperfection,” in: Proc. AIAA Dyn. Spec. Conf. (Long Beach, Calif., April 5–6, 1990), Washington (1990), pp. 387–394.
S. Otterbein, “Stabilisierung des n-Pendels und der Indische Seiltrick,” Arch. Rat. Mech. Anal., 78, No. 4, 381–393 (1982).
A. Pflüger, Stabilitätsprobleme der Elastostatic, Springer, Berlin-Göttingen-Heidelberg (1950).
Y. A. Shinohara, “A geometric method for numerical solution of non-linear equations and its application to non-linear oscillations,” Publ. RJMS, Kyoto Univ., 8, No. 1, 13–42 (1972).
H. Troger and A. Steindl, Nonlinear Stability and Bifurcation Theory, Springer-Verlag, Vienna-New York (1991).
H. Ziegler, “Die Stabilitätskriterien der Elastomechanik,” Ing.-Arch., 20, No. 1, 49–56 (1952).
H. Ziegler, “Linear elastic stability,” ZAMP, 4, No. 2, 89–121; No. 3, 167–185 (1953).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 126–137, June 2007.
Rights and permissions
About this article
Cite this article
Lobas, L.G., Koval’chuk, V.V. & Bambura, O.V. Theory of inverted pendulum with follower force revisited. Int Appl Mech 43, 690–700 (2007). https://doi.org/10.1007/s10778-007-0068-9
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10778-007-0068-9