Results 241 to 250 of about 1,438,024 (273)

Interplays between Harper and Mathieu equations

Physical Review E, 2001
This 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, 1980
A 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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The Eigenvalues of Mathieu's Equation and their Branch Points

Studies in Applied Mathematics, 1981
A 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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General Perturbational Solution of the Mathieu Equation

Journal of the Society for Industrial and Applied Mathematics, 1962
A 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, 2000
In 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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Matrix solution of periodic mathieu equations

Journal of Computational Physics, 1973
Abstract 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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Slow Passage through Resonance in Mathieu's Equation

Journal of Vibration and Control, 2002
We 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, Rand, Richard, O'Neil, Michael   +2 more
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An Experimental Investigation of a Nonlinear Mathieu Equation

IMA Journal of Applied Mathematics, 1987
The behaviour of the simplest periodic solutions of two nonlinear Mathieu equations is considered. One of the most interesting features of the experimental solutions is that their amplitudes are usually of order unity, so that the nonlinear term cannot be treated as a small perturbation.
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Response of a Nonlinear Form of the Mathieu Equation

The Journal of the Acoustical Society of America, 1971
This communication presents the results of an investigation of the response of a nonlinear form of the Mathieu equation in the first unstable region. The equation of interest is a Mathieu equation plus a cubic nonlinearity. The response consists of a modulated one-half subharmonic of the parametric-excitation frequency.
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On the Width of the Instability Intervals of the Mathieu Equation

SIAM Journal on Mathematical Analysis, 1984
It is shown that the width of the m-th instability interval of the Mathieu equation is given asymptotically by \[ (8h^{2m}/4^ m[(m- 1)!]^ 2)[1+O(h^ 4/m^ 2)]. \] The method of proof is based on a continued fraction technique using three term recursion formulas.
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