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Mathieu equation and Elliptic curve [PDF]
Communications in Theoretical Physics, 2011 We present a relation between the Mathieu equation and a particular elliptic curve. We find that the Floquet exponent of the Mathieu equation, for both $q>1$, can be obtained from the integral of a differential one form along the two homology cycles of ...
He, Wei, Miao, Yan-Gang
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CHARTS STRUTT-INCE FOR GENERALIZED MATHIEU EQUATION [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2012 We have investigated the solution of the generalized Mathieu equation. With the aid of diagrams Stratton-Ince built the instability region, the condition can occur when the parametric resonance.
R.I. Parovik
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Influence of material distribution and damping on the dynamic stability of Bernoulli-Euler beams [PDF]
Bulletin of the Polish Academy of Sciences: Technical Sciences, 2023 The study analyzed the influence of materials and different types of damping on the dynamic stability of the Bernoulli-Euler beam. Using the mode summation method and applying an orthogonal condition of eigenfunctions and describing the analyzed system ...
Sebastian Garus +7 more
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Nonoscillation of damped linear differential equations with a proportional derivative controller and its application to Whittaker-Hill-type and Mathieu-type equations [PDF]
Opuscula Mathematica, 2022 The proportional derivative (PD) controller of a differential operator is commonly referred to as the conformable derivative. In this paper, we derive a nonoscillation theorem for damped linear differential equations with a differential operator using ...
Kazuki Ishibashi
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Some Novel Analytical Approximations to the (Un)damped Duffing–Mathieu Oscillators
Journal of Mathematics, 2022 Some novel exact solutions and approximations to the damped Duffing–Mathieu-type oscillator with cubic nonlinearity are obtained. This work is divided into two parts: in the first part, some exact solutions to both damped and undamped Mathieu oscillators
Haifa A. Alyousef +3 more
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Exact WKB analysis and TBA equations for the Mathieu equation
Physics Letters B, 2020 We derive the Thermodynamic Bethe Ansatz (TBA) equations for the exact WKB periods of the Mathieu equation in the weak coupling region. We will use the TBA equations to calculate the quantum corrections to the WKB periods, which are regarded as the ...
Keita Imaizumi
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An instrumental insight for a periodic solution of a fractal Mathieu–Duffing equation
Journal of Low Frequency Noise, Vibration and Active Control, 2023 The primary goal of the present study is to investigate how to obtain a periodic solution for a fractal Mathieu–Duffing oscillator. To achieve this, the fractal oscillator in the fractal space has been transformed into a damping Mathieu–Duffing equation ...
Yusry O El-Dib +2 more
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Classical limit of irregular blocks and Mathieu functions [PDF]
, 2015 The Nekrasov-Shatashvili limit of the N=2 SU(2) pure gauge (Omega-deformed) super Yang-Mills theory encodes the information about the spectrum of the Mathieu operator.
Piatek, Marcin, Pietrykowski, Artur R.
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Computation, 2021 The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform.
Nattakarn Numpanviwat, Pearanat Chuchard
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Absorption Cross Section of Scalar Field in Supergravity Background [PDF]
, 2000 It has recently been shown that the equation of motion of a massless scalar field in the background of some specific p branes can be reduced to a modified Mathieu equation.
Aharony +29 more
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