The Effect of Slow Flow Dynamics on the Oscillations of a Singular Damped System with an Essentially Nonlinear Attachment

The Effect of Slow Invariant Manifold and Slow Flow Dynamics on the Energy Transfer and Dissipation of a Singular Damped System with an Essential Nonlinear Attachment

“…There are many theorems for this singular manifold which allow us to determine the long-term behavior of (9) [4][5][6].…”

“…Such systems can be treated with the use of methods such as singularity analysis or multiple scale analysis [4,5]. As it has been shown in previous works the slow flow of the system and the slow invariant manifolds (SIMs) obtained in the singular limit play a very important role in the dynamics under consideration [3,[6][7][8].…”

“…In this work we study a dissipative system of two linear oscillators coupled with an essential nonlinear oscillator. In previous works [6,7] we studied the SIM of the system and made a classification of its structure. Specifically, the structure of the SIM may be classified in three cases.…”

Analytical Homoclinic Solution of a Two-Dimensional Nonlinear System of Differential Equations

“…In what follows, we find the analytical solution of the homoclinic orbit of a one-degree-of-freedom system of differential equations that describes the Hamiltonian part of the slow flow of a three-degree-of-freedom dissipative system of linear coupled oscillators with an essentially nonlinear attachment [2].…”

“…The aim of the work in [2] was to study the asymptotic behavior of the system. Specifically, the initial dissipative system composed of two linear and one nonlinear oscillators was reduced to a nonautonomous damped strongly nonlinear second-order differential equation.…”