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Floquet Theory for Quaternion-Valued Differential Equations [PDF]

Qualitative Theory of Dynamical Systems, 2019
This paper describes the Floquet theory for quaternion-valued differential equations (QDEs). The Floquet normal form of fundamental matrix for linear QDEs with periodic coefficients is presented and the stability of quaternionic periodic systems is ...
Dong Cheng, K. Kou, Yonghui Xia
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Floquet theory in magnetic resonance: Formalism and applications.

Progress in Nuclear Magnetic Resonance Spectroscopy, 2021
K. Ivanov, Kaustubh R. Mote, M. Ernst, A. Equbal, P. Madhu   +4 more
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Canonical Floquet theory

Celestial Mechanics & Dynamical Astronomy, 1994
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Wiesel, William E., Pohlen, David J.
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Floquet theory: exponential perturbative treatment

Journal of Physics A: Mathematical and General, 2001
A celebrated Floquet theorem states that the solution \(Z(t)\) to the linear matrix differential equation \[ \frac{dZ}{dt}=A(t)Z(t), \qquad Z(0)=I, \] with a complex \(n\times n\)-matrix \(A\) whose entries are integrable periodic functions of \(t\) with period \(T,\) has the form \[ Z(t)=P(t)\exp(tF), \] where \(F\) and \(P\) are \(n\times n ...
Casas, F., Oteo, J. A., Ros, J.
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A time-domain stability analysis method for LLC resonant converter based on Floquet theory

, 2020
LLC resonant converters have been widely used in engineering fields, and the stability of LLC resonant converters is still a research hotspot due to its variable frequency. In this paper, a time-domain stability analysis method based on Floquet theory is
Hong Li, Y. Zou, Xiaheng Jiang, Chen Liu
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Doubly-periodic Floquet theory

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1984
The purpose of this paper is to develop a theory for differential equations with doubly-periodic coefficients analogous to the classic Floquet theory for differential equations with singly periodic coefficients. Unlike the classical theory the role of the exponent v of the differential equation is fundamental. If
Sleeman, B. D., Smith, P. D., Wright, G. P.   +2 more
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Analysis of a rotordynamic system with anisotropy and nonlinearity using the Floquet theory and the method of normal forms

Journal of Sound and Vibration, 2019
The system under analysis is composed of an asymmetric rotor, two asymmetric bearings and a nonlinear spring-damper system representing an annular gas seal.
D. Maldonado, A. Karev, P. Hagedorn, T. Ritto, R. Sampaio   +4 more
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Floquet Theory for a Volterra Equation

Journal of the London Mathematical Society, 1988
The authors discuss periodic solutions of the integrodifferential equation \[ dy(t)/dt=A(t)y(t)+\int^{t}_{0}C(t,s)y(s)ds+f(t), \] relating two different integrability properties of the resolvent to each other.
Becker, L. C., Burton, T. A., Krisztin, T.   +2 more
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