Results 161 to 170 of about 71,208 (194)

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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Stability Analysis Of The Non-Linear Mathieu Equation

Journal of Sound and Vibration, 1993
Summary: The nonlinear Mathieu equation is analyzed within the framework of the method of normal forms. Analytical conditions for explosive instability are obtained, and expressions for the period as well as the amplitude of the stable response are derived.
Mond, M., Cederbaum, G., Khan, P. B., Zarmi, Y.   +3 more
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Stability by solutionperturbation: Mathieu’s equation

2007
Abstract where m is any positive integer. A well-known result in matrix algebra states that if E has eigenvalues μi , then Em has eigenvalues μm i . The system will only have a solution of period T if there exists a unit eigenvalue. It will have a solution of period mT if μm = 1, which means that μ must be an mth root of unity.
D W Jordan, P Smith
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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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Solution of Mathieu's Type of Secular Equations

Journal of Mathematical Physics, 1970
A discussion is given for the general solution of a secular equation with all other matrix elements equal to zero except Hii, Hi i+h, and Hi+h i. Both the eigenvalue and the amplitudes of the corresponding eigenfunction are expressed in terms of continued fractions of the matrix elements.
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Asymptotic solutions of mathieu equation with damping

Applied Mathematics and Mechanics, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Uniform asymptotic expansions of solutions of the Mathieu equation and the modified Mathieu equation

Journal of Soviet Mathematics, 1979
By the method of the model equation, uniform asymptotic expansions of the Floquet solutions of the Mathieu equation and two linearly independent solutions of the modified Mathieu equation are obtained for any real values of the separation parameter contained in these equations.
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Computation and Applications of Mathieu Functions: A Historical Perspective

SIAM Review, 2021
Chris Brimacombe, Madhusoodan Gunasingam
exaly  

Mathieu Equation

2020
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A QUASIPERIODIC MATHIEU EQUATION

1997
RICHARD RAND, RANDOLPH ZOUNES, RACHEL HASTINGS   +2 more
openaire   +1 more source