Time-delay two-dimension mathieu equation in synchrotron dynamics

• Autorzy: El-Dib Y. O.
• Języki publikacji: EN

Abstrakty

EN

Two dimensions Mathieu equation containing periodic terms as well as the delayed parameters has been investigated in the present work. The present system represents to a generalized form of the one-dimension delay Mathieu equation. The mathematical difficulty for delay the coupled Mathieu equation has been overcome by using the matrices method. Properties of inverse complex matrices enable us to transform the vector form of the solvability conditions to the scalar form. Small oscillation about a marginal state is introduced by using the method of multiple scales. Stability criteria for the complex matrices have been established and lead to obtain resonance curves. The analysis has been extended so that the delay 2-dimensions Mathieu equation containing weak complex damping part. Stability conditions and the transition curves that included the influence of both the delayed as well the complex damping terms has been obtained. The transition curves are analyzed using the method of harmonic balance. We note that the delayed higher dimension of the parametric excitation has a great interest and application to the design of nuclear accelerators.

Słowa kluczowe

EN

synchrotron dynamics; time-delay; two-dimension complex damped Mathieu equation; stability analysis; parametric resonance; inverse complex matrices method

PL

dynamika synchrotronu; opóźnienie; równanie Mathieu; analiza stateczności; parametric resonance; metoda macierzy odwrotnej

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2017
• Tom: Vol. 21, nr 3
• Strony: 499--511
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

El-Dib Y. O.

• Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Egypt

Bibliografia

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• [13] El-Dib, Y. O. and Matoog, R. T.: Stability of Streaming in an Electrified Maxwell Fluid Sheet Influenced by a Vertical Periodic Field in the Absence of Surface Charges, Journal of Colloid and Interface Science, 229, 29-52, 2000.
• [14] El-Dib, Y. O. and Matoog, R. T.: Electrorheological Kelvin-Helmoholtz instability of a fluid sheet, Journal of Colloid and Interface Science, 289, 223-241, 2005.
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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).