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Mathcad polyroots function11/29/2022 ![]() The equations of motion are often derived by the Euler-Lagrange equations. ![]() One of the most important stages in the analysis of any mechanical model is to establish and find the solution of the dynamical equations which are referred to as equations of motion. They are mostly represented as nonlinear dynamical systems. The dynamics of coupled bodies and oscillators is significant in mechanics, engineering, electronics as well as biological systems. Furthermore, the resulting phase portrait analysis depicted spiral sources for each of the oscillating masses showing that the system under investigation is unstable.Ĭoupled Rigid Body, Differential Equations, Stability, Phase Portrait, MathCAD Simulation It is discovered that the coupled rigid pendulum gives rise to irregular oscillations with ever increasing amplitude. Finally, we performed MathCAD simulation of the resulting ordinary differential equations, describing the dynamics of the system and obtained the graphical profiles for each generalized coordinates representing the angles measured with respect to the vertical axis. We then proceeded to study the stability of the dynamical systems using the Jacobian linearization method and subsequently confirmed our result by phase portrait analysis. ![]() We obtained the equation of motion using the generalized coordinates and the Euler-Lagrange equations. Mathcad polyroots function free#The system is free to oscillate in the vertical plane. In this research article, we investigate the stability of a complex dynamical system involving coupled rigid bodies consisting of three equal masses joined by three rigid rods of equal lengths, hinged at each of their bases. Received: DecemAccepted: MaPublished: March 22, 2018 Mathcad polyroots function license#This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, NigeriaĬopyright © 2018 by authors and Scientific Research Publishing Inc. ![]()
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