Abstract
This paper analyses the stability of a parametrically excited double pendulum rotating in the horizontal plane. The equations of motion for such a system contain time varying periodic coefficients. Floquet theory and the method of Hill's determinant are used to evaluate the stability of the linearized system. Stability charts are obtained for various sets of damping, parametric excitation, and rotation parameters. Several resonance conditions are found, and it is shown that the system stability can be significantly altered due to the rotation. Such systems can be used as preliminary models for studying the lag dynamics and control of helicopter blades and other gyroscopic systems.
Similar content being viewed by others
References
Sinha, S. C., and Wu, Der-Ho, “An efficient computational scheme for the analysis of periodic systems,” J. Sound and Vibrations, vol. I51, pp. 91-117, 1991.
Dugundji, J., and Chhaptar, C.K., “Dynamic stability of a pendulum under parametric excitation,” RJTS, Applied Mechanics, vol. 15, pp. 741-763, 1970.
Anderson, G. L., and Tadjbakhsh, I.G., “Stabilization of Ziegler's pendulum by means of the method of vibrational control,” Journal of Mathematical Analysis and Applications, vol. 143, pp. 198-223, 1989.
Pandiyan, R., and Sinha, S. C., “Analysis of time-periodic nonlinear dynamical systems undergoing bifurcations,” Nonlinear Dynamics, vol. 8, pp. 21-43, 1995.
Guttalu, R. S., and Flashner, H., “An analytical study of stability of periodic systems by Poincare mapping,” Proc. 15th Biennial Conference on Mechanical Vibrations and Noise (ASME Publication DE-vol. 84-1), pp. 387-397, 1995.
Guttalu, R. S., and Flashner, H., “Stability analisys of periodic systems by truncated point mappings,” Journal of Sound and Vibrations, vol. 189(1), pp. 33-54, 1996.
Visual Numerics Inc., IMSL Math/Library. Fortron subroutines for mathematical applications.
Leipholtz, H., Stability Theory, Academic Press: New York, NY, 1970.
Wolfram, Stephen, MATHEMATICA, Second Edition.
Hsu, C. S., “On the parametric excitation for a dynamic system having multiple degrees of freedom,” Journal of Applied Mechanics, pp. 367-370, 1962.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Marghitu, D.B., Sinha, S.C. & Boghiu, D. Stability and Control of a Parametrically Excited Rotating System. Part I: Stability Analysis. Dynamics and Control 8, 5–18 (1998). https://doi.org/10.1023/A:1008250112094
Issue Date:
DOI: https://doi.org/10.1023/A:1008250112094