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Experimental investigation of perpetual points in mechanical systems

Publication ,  Journal Article
Brzeski, P; Virgin, LN
Published in: Nonlinear Dynamics
December 1, 2017

In dissipative dynamical systems, equilibrium (stationary) points have a dominant organizing effect on transient motion in phase space, especially in nonlinear systems. These time-independent solutions are readily defined in the context of ordinary differential equations, that is, they occur when all the time derivatives are simultaneously zero. However, there has been some recent interest in perpetual points: points at which the higher time derivatives are zero, but not necessarily the first. Previous work has focused on analytic work (including simulation) and some experimental studies of electric circuits. This paper focuses attention on the occurrence of these points in a simple mechanical system, including experimental verification. Thus, points of zero acceleration can be found in which the corresponding velocity is a maximum or minimum, but not zero. Specifically, the rigid-arm pendulum is used to generate data for which acceleration (and its derivative) can be evaluated. In this paper an experimental (mechanical) setup is described, specifically designed to investigate perpetual points, including a description of the data analysis approaches developed to identify their location.

Duke Scholars

Published In

Nonlinear Dynamics

DOI

EISSN

1573-269X

ISSN

0924-090X

Publication Date

December 1, 2017

Volume

90

Issue

4

Start / End Page

2917 / 2928

Related Subject Headings

  • Acoustics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences
 

Citation

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Brzeski, P., & Virgin, L. N. (2017). Experimental investigation of perpetual points in mechanical systems. Nonlinear Dynamics, 90(4), 2917–2928. https://doi.org/10.1007/s11071-017-3852-z
Brzeski, P., and L. N. Virgin. “Experimental investigation of perpetual points in mechanical systems.” Nonlinear Dynamics 90, no. 4 (December 1, 2017): 2917–28. https://doi.org/10.1007/s11071-017-3852-z.
Brzeski P, Virgin LN. Experimental investigation of perpetual points in mechanical systems. Nonlinear Dynamics. 2017 Dec 1;90(4):2917–28.
Brzeski, P., and L. N. Virgin. “Experimental investigation of perpetual points in mechanical systems.” Nonlinear Dynamics, vol. 90, no. 4, Dec. 2017, pp. 2917–28. Scopus, doi:10.1007/s11071-017-3852-z.
Brzeski P, Virgin LN. Experimental investigation of perpetual points in mechanical systems. Nonlinear Dynamics. 2017 Dec 1;90(4):2917–2928.
Journal cover image

Published In

Nonlinear Dynamics

DOI

EISSN

1573-269X

ISSN

0924-090X

Publication Date

December 1, 2017

Volume

90

Issue

4

Start / End Page

2917 / 2928

Related Subject Headings

  • Acoustics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences