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On the Stability Analysis of a Coupled Rigid Body

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Document pages: 13 pages

Abstract: In this research article, we investigate the stability of a complex dynamicalsystem involving coupled rigid bodies consisting of three equal masses joinedby three rigid rods of equal lengths, hinged at each of their bases. The systemis free to oscillate in the vertical plane. We obtained the equation of motionusing the generalized coordinates and the Euler-Lagrange equations. We thenproceeded to study the stability of the dynamical systems using the Jacobianlinearization method and subsequently confirmed our result by phase portraitanalysis. Finally, we performed MathCAD simulation of the resulting ordinarydifferential equations, describing the dynamics of the system and obtainedthe graphical profiles for each generalized coordinates representing theangles measured with respect to the vertical axis. It is discovered that thecoupled rigid pendulum gives rise to irregular oscillations with ever increasingamplitude. Furthermore, the resulting phase portrait analysis depicted spiralsources for each of the oscillating masses showing that the system under investigationis unstable.

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