Results 191 to 200 of about 3,607 (229)
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Interplays between Harper and Mathieu equations
Physical Review E, 2001This paper deals with the application of relationships between Harper and Mathieu equations to the derivation of energy formulas. Establishing suitable matching conditions, one proceeds by inserting a concrete solution to the Mathieu equation into the Harper equation.
E, Papp, C, Micu
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On Mathieu equation with damping
Journal of Mathematical Physics, 1980A direct variational method is applied to the linear and nonlinear Mathieu equation with damping. It is found that the nature of the periodic solutions and the characteristic curves are modified due to the presence of the damping. A threshold value of β is required to overcome the damping for the existence of the periodic solutions.
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Nonoscillation of Mathieu equations with two frequencies
Applied Mathematics and Computation, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jitsuro Sugie, Kazuki Ishibashi
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1983
The Mathieu equation in its standard form $$\ddot x + (a - 2q\cos 2t)x = 0$$ (6.1) is the most widely known and, in the past, most extensively treated Hill equation. In many ways this is curious since the equation eludes solution in a usable closed form; yet many investigators have sought to describe experiments in terms of a Mathieu equation,
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The Mathieu equation in its standard form $$\ddot x + (a - 2q\cos 2t)x = 0$$ (6.1) is the most widely known and, in the past, most extensively treated Hill equation. In many ways this is curious since the equation eludes solution in a usable closed form; yet many investigators have sought to describe experiments in terms of a Mathieu equation,
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The Eigenvalues of Mathieu's Equation and their Branch Points
Studies in Applied Mathematics, 1981A comprehensive account is given of the behavior of the eigenvalues of Mathieu's equation as functions of the complex variable q. The convergence of their small‐q expansions is limited by an infinite sequence of rings of branch points of square‐root type at which adjacent eigenvalues of the same type become equal.
Hunter, C., Guerrieri, B.
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Matrix solution of periodic mathieu equations
Journal of Computational Physics, 1973Abstract The application of matrix methods to periodic Mathieu equations is discussed, and it is shown that accurate solutions may be found for any real value of the parameter, including the asymptotic case.
Ewig, Carl S., Harris, David O.
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Parametric Frequency Analysis of Mathieu–Duffing Equation
International Journal of Bifurcation and Chaos, 2021The classic linear Mathieu equation is one of the archetypical differential equations which has been studied frequently by employing different analytical and numerical methods. The Mathieu equation with cubic nonlinear term, also known as Mathieu–Duffing equation, is one of the many extensions of the classic Mathieu equation. Nonlinear characteristics
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General Perturbational Solution of the Mathieu Equation
Journal of the Society for Industrial and Applied Mathematics, 1962A general perturbational solution of the Mathieu equation is obtained in the form of an asymptotic series. The principal part of the solution is obtained by a modified variation of parameters technique which admits only slow (long-period) variations in the amplitude and phase.
Struble, R. A., Fletcher, J. E.
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Bifurcations in a Mathieu equation with cubic nonlinearities: Part II
Communications in Nonlinear Science and Numerical Simulation, 2000In a previous paper [6], the authors investigated the dynamics of the equation: d2xdt2+(δ+εcost)x+εAx3+Bx2dxdt+Cxdxdt2+Ddxdt3=0. We used the method of averaging in the neighborhood of the 2:1 resonance in the limit of small forcing and small nonlinearity.
Ng, Leslie, Rand, Richard
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Slow Passage through Resonance in Mathieu's Equation
Journal of Vibration and Control, 2002We investigate slow passage through the 2:1 resonance tongue in Mathieu's equation. Using numerical integration, we find that amplification or de-amplification can occur. The amount of amplification (or de-amplification) depends on the speed of travel through the tongue and the initial conditions.
Ng, Leslie +2 more
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