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TECHNICAL BRIEF

# Dynamics of a Nonlinear Electromechanical Device With a Pendulum Arm

[+] Author and Article Information
J. B. Mogo

Laboratory of Modeling and Simulation in Engineering and Biological Physics, Faculty of Science, University of Yaounde I, Box 812, Yaounde, Cameroonjbmogo@yahoo.com

P. Woafo1

Laboratory of Modeling and Simulation in Engineering and Biological Physics, Faculty of Science, University of Yaounde I, Box 812, Yaounde, Cameroonpwoafo1@yahoo.fr

1

Corresponding author.

J. Comput. Nonlinear Dynam 2(4), 374-378 (Jun 07, 2007) (5 pages) doi:10.1115/1.2756080 History: Received April 28, 2006; Revised June 07, 2007

## Abstract

This paper considers the dynamics of an electromechanical device with a pendulum arm. Conditions under which the pendulum does not experience a complete rotation are obtained. Various types of nonlinear behaviors including chaos are observed.

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## Figures

Figure 1

The electromechanical device

Figure 2

The pendulum mechanism. ur and uθ are the polar unit vectors.

Figure 3

Numerical boundary criterion for rotation in the (ω,Ec) plane. (a) α=0.95; (b) α=0.0, the other parameters are γe=1.40, λm=0.07, λe=0.30, ω2=0.11, and γm=0.10.

Figure 4

Bifurcation diagram when E varies for α=0.95, λe=0.30, γe=1.40, ω=1.0, λm=0.07, ω2=0.11, and γm=0.10.

Figure 5

State space of the pendulum for (a) E=0.7, period 1; (b) E=42, period 2; (c) E=46, chaotic solution, (d) E=50, period 3. The other parameters are γe=1.40, λe=0.30, α=0.95, ω=1.0, λm=0.07, ω2=0.11, and γm=0.10.

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