TITLE:
On the Stability Analysis of a Coupled Rigid Body
AUTHORS:
Olaniyi S. Maliki, Victor O. Anozie
KEYWORDS:
Coupled Rigid Body, Differential Equations, Stability, Phase Portrait, MathCAD Simulation
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.3,
March
22,
2018
ABSTRACT: 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. The system
is free to oscillate in the vertical plane. We obtained the equation of motion
using the generalized coordinates and the Euler-Lagrange equations. 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. 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. It is discovered that the
coupled rigid pendulum gives rise to irregular oscillations with ever increasing
amplitude. Furthermore, the resulting phase portrait analysis depicted spiral
sources for each of the oscillating masses showing that the system under investigation
is unstable.