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Complexification-averaging method via the averaged Lagrangian
Nonlinear Dynamics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generalized method of averaging and the Von Zeipel method
Thermophysics Specialist Conference, 1965Abstract The generalized method of averaging is applied to a perturbed vector system of differential equations of the appropriate form, where there are several “rapidly rotating” phases. It is assumed that no resonances occur, and the averaged equations are derived through the second order in the perturbation parameter. The arbitrariness which arises
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On the Equivalence of the Melnikov Functions Method and the Averaging Method
Qualitative Theory of Dynamical Systems, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Melnikov's method and averaging
Celestial Mechanics, 1982Consider the differential equation \(\dot x=f^ 0(x)+\epsilon f^ 1(\omega t,x;\epsilon)\), \(x\in D\subset R^ n\) where \(f^ 0\) and \(f^ 1\) are sufficiently smooth, \(f^ 1\) is \(2\pi\)-periodic in \(\omega\) t and \(\epsilon\) is a small positive parameter. Let the unperturbed system \(\dot x=f^ 0(x)\) have a hyperbolic point.
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A note on the averaging method
Celestial Mechanics, 1978A simple problem of a two-body system perturbed by the disturbing function epsilon/r-squared is considered to show that the time-averaged equations of the true and mean anomaly are not necessarily equal. Secular effects due to perturbations in the mean and true anomalies are different not only in value but also in sign.
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1967
On a recent hiking holiday I walked 12 miles on the first day, 15 on the next, then 10, 0, 20 and 9 miles. Altogether I walked 66 miles in 6 days or an average of 11 miles each day. This number 11, called the average, is not the distance I walked on any day but rather a number to give some fair representation of my average performance.
D. M. Neal, D. J. New
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On a recent hiking holiday I walked 12 miles on the first day, 15 on the next, then 10, 0, 20 and 9 miles. Altogether I walked 66 miles in 6 days or an average of 11 miles each day. This number 11, called the average, is not the distance I walked on any day but rather a number to give some fair representation of my average performance.
D. M. Neal, D. J. New
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The Continuous Averaging Method
2009There are several problems in perturbation theory, where standard methods do not lead to satisfactory results. We mention as examples the problem of an inclusion of a diffeomorphism into a flow in the analytic set up, and the problem of quantitative description of exponentially small effects in dynamical systems. In these cases one possible approach is
Dmitry Treschev, Oleg Zubelevich
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Modeling and analysis of lignite particle drying based on the volume averaging method
Drying Technology, 2022Keji Wan +2 more
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