Motion stability study of double and ball pendulums
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Pendulum, stability, motion, spherical and Lyapunov’s theory.Abstract
This research examines the stability of periodic motion for a physics application, which results in a second order differential equation for systems, such as the double and spherical pendulums. The stability of the equilibrium modes is analysed using the Libanov and Getayer methods, along with the principle of energy conservation. Moreover, this study describes the periodic motion and explains
the phase-level solution paths and the stability conditions for the double and spherical pendulums by using the MATLAB program.
References
I. U. Winter, An Approach to Solving Ordinary Differential Equations (2002). http://www.ent.ohiou.edu/~urieli/odes/odes.htm.pdf.
E. Corinaldesi, Classical Mechanics for Physics Graduate Students, Co, Pte. Ltd, Boston, (1998).
L. E. Elsgolts, Differential Equations, India Press, Corpn. (1969).
A. Ohlhoff, P.H. Richter, Forces in the Double Pendulum, Zamm. angew. Math. Mech., (2006), 1–22.
M. I. Caiado, A. V. Sarychev, Remarks on Stability of Inverted Pendula, Journal of the Astronautical Sciences 63(4), (2005), 333–347.
G. F. Simmons, S. C. Krantz, Differential Equations, (2007), McGraw-Hill, America.
G. R. Fowles, Analytical Mechanics, (1977), 3rd Ed., America, Prentice-Hall.
A. E. Chinnery, C. D. Hall, Motion of a Rigid Body with an Attached Spring Mass Damper, Journal of Guidance, Control and Dynamics 18(6), (1995), 1404–1409.
D. R. Eral, E. B. Phillip, Elementary Differential Equations, (1980), 6th Ed., Co., Inc.
D. G. Zill, M. R. Cullen, Differential Equations with Boundary Value Problems, (1997), 4th Ed., U.S.A.
T. Ozaki, Nonlinear Time-series Stochastic Processes and Dynamical system (Handbook of Statistics) 5 ltd., (1982).
M. B. Priestley, Spectral Analysis and Time Series volume 1 Univariate Series (Academic Press. Inc.) London, (1981).
H. Tong, Nonlinear Time series; A Dynamical System Approach (Oxford University Press) London, (1990).
S. Wen, Introduction to Ordinary and Partial Differential Equations (Spring), (2015).
F. T. William, Elementary Differential Equations with Boundary Value Problem (New York), (2013).
A. N. Kawther, Numerical Analysis & Methods Using MATLAB, Iraq, (2019).
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