On the Asymptotic Stability of Oscillators with Unbounded Damping

Through a technique inspired by the invariance principle of LaSalle, a general growth condition on the damping coefficient h(t) of the equation 2nd derivative of x with respect to t + H(t)dx/dt + kx = 0, k 0, h(t) or = epsilon 0, is given, which is sufficient for the global asymptotic stability of t...

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Bibliographic Details
Main Authors: Artstein,Zvi, Infante,E F
Format: Report
Language:English
Subjects:
Asymptotic stability
DAMPING
DIFFERENTIAL EQUATIONS
NONLINEAR DIFFERENTIAL EQUATIONS
Numerical Mathematics
THEOREMS
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Summary:Through a technique inspired by the invariance principle of LaSalle, a general growth condition on the damping coefficient h(t) of the equation 2nd derivative of x with respect to t + H(t)dx/dt + kx = 0, k 0, h(t) or = epsilon 0, is given, which is sufficient for the global asymptotic stability of the origin, yet permits this coefficient to grow to infinity with time. The methods used do not depend on linearity, and are applied to obtain similar results to the nonlinear analog of this equation.