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Transition curves in a parametrically excited pendulum with a force of elliptic type

Publication ,  Journal Article
Sah, SM; Mann, B
Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
December 8, 2012

This article investigates the equilibria and stability of a pendulum when the support has a prescribed motion defined by an elliptic function. Stability charts are generated in the parameter plane for different values of the elliptic function modulus. Numerical integration and Floquet theory are used to generate stability charts that are later obtained through harmonic balance analysis. It is shown that the size and location of the instability tongues is directly linked to the elliptic function modulus. Comparisons are also made between the stability charts of Mathieu's equation and those of the pendulum when the prescribed motion is defined by an elliptic function. © 2012 The Royal Society.

Duke Scholars

Published In

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

DOI

EISSN

1471-2946

ISSN

1364-5021

Publication Date

December 8, 2012

Volume

468

Issue

2148

Start / End Page

3995 / 4007

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Sah, S. M., & Mann, B. (2012). Transition curves in a parametrically excited pendulum with a force of elliptic type. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468(2148), 3995–4007. https://doi.org/10.1098/rspa.2012.0328
Sah, S. M., and B. Mann. “Transition curves in a parametrically excited pendulum with a force of elliptic type.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2148 (December 8, 2012): 3995–4007. https://doi.org/10.1098/rspa.2012.0328.
Sah SM, Mann B. Transition curves in a parametrically excited pendulum with a force of elliptic type. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2012 Dec 8;468(2148):3995–4007.
Sah, S. M., and B. Mann. “Transition curves in a parametrically excited pendulum with a force of elliptic type.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 468, no. 2148, Dec. 2012, pp. 3995–4007. Scopus, doi:10.1098/rspa.2012.0328.
Sah SM, Mann B. Transition curves in a parametrically excited pendulum with a force of elliptic type. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2012 Dec 8;468(2148):3995–4007.
Journal cover image

Published In

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

DOI

EISSN

1471-2946

ISSN

1364-5021

Publication Date

December 8, 2012

Volume

468

Issue

2148

Start / End Page

3995 / 4007

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences