Abstract
In this paper, some stability results were reviewed. A suitable and complete Lyapunov function for the hard spring model was constructed using the Cartwright method. This approach was compared with the existing results which confirmed a superior global stability result. Our contribution relies on its application to high damping door constructions. (2010 Mathematics Subject Classification: 34B15, 34C15, 34C25, 34K13.)
Highlights
In real life, most problems that occur are non-linear in nature and may not have analytic solutions except by approximations or simulations and so trying to find an explicit solution may in general be complicated and sometimes impossible
In line with the above review and ongoing research in this direction, the objective of this paper is to investigate the stability analysis of periodic solutions of the Duffing type
We adapt the method of construction of Lyapunov function used in [23] and extend it to the second order non-linear differential equation of the Duffing type of the form (3.1)
Summary
Most problems that occur are non-linear in nature and may not have analytic solutions except by approximations or simulations and so trying to find an explicit solution may in general be complicated and sometimes impossible. Duffing’s equation is a second order non-linear differential equation used to model such problems of non-linear nature [1]. In [6], differential equation which describes a non-linear oscillation was first introduced by Duffing’s with cubic stiffness constant. The general form of Duffing’s equation is:. Where p (t ) is continuous and 2π-periodic in t ∈. The study of periodic solution of Duffing’s equation is like that of the study of classical Hamiltonian equation of motion which is characterized by multiplicity
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