Floquet theory

1995 ◽  
pp. 355-363
Author(s):  
Odo Diekmann ◽  
Sjoerd M. Verduyn Lunel ◽  
Stephan A. van Gils ◽  
Hanns-Otto Walther
Keyword(s):  
Floquet Theory

Floquet Theory in Magnetic Resonance: Formalism and Applications

2021 ◽  
Author(s):  
Konstantin L. Ivanov ◽  
Kaustubh R. Mote ◽  
Matthias Ernst ◽  
Asif Equbal ◽  
Perunthiruthy K. Madhu
Keyword(s):  
Magnetic Resonance ◽  
Floquet Theory

scholarly journals Period-doubling bifurcation analysis and chaos control for load torque using FLC

2021 ◽  
Author(s):  
Eman Moustafa ◽  
Abdel-Azem Sobaih ◽  
Belal Abozalam ◽  
Amged Sayed A. Mahmoud
Keyword(s):  
Floquet Theory ◽  
Chaos Control ◽  
Fuzzy Logic Controller ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Parameter Variation ◽  
Period Doubling Bifurcation ◽  
Load Torque ◽  
Nonlinear Behaviors ◽  
Scientific Fields

AbstractChaotic phenomena are observed in several practical and scientific fields; however, the chaos is harmful to systems as they can lead them to be unstable. Consequently, the purpose of this study is to analyze the bifurcation of permanent magnet direct current (PMDC) motor and develop a controller that can suppress chaotic behavior resulted from parameter variation such as the loading effect. The nonlinear behaviors of PMDC motors were investigated by time-domain waveform, phase portrait, and Floquet theory. By varying the load torque, a period-doubling bifurcation appeared which in turn led to chaotic behavior in the system. So, a fuzzy logic controller and developing the Floquet theory techniques are applied to eliminate the bifurcation and the chaos effects. The controller is used to enhance the performance of the system by getting a faster response without overshoot or oscillation, moreover, tends to reduce the steady-state error while maintaining its stability. The simulation results emphasize that fuzzy control provides better performance than that obtained from the other controller.

scholarly journals The Rabi problem with elliptical polarization

2020 ◽  
Vol 75 (11) ◽  
pp. 937-962
Author(s):  
Heinz-Jürgen Schmidt
Keyword(s):  
Floquet Theory ◽  
Equation Of Motion ◽  
Quantum Spin ◽  
Heun Equation ◽  
Elliptical Polarization ◽  
Third Order ◽  
Polynomial Coefficients ◽  
Resonance Frequencies ◽  
Classical Quantum ◽  
Elliptically Polarized

AbstractWe consider the solution of the equation of motion of a classical/quantum spin subject to a monochromatical, elliptically polarized external field. The classical Rabi problem can be reduced to third-order differential equations with polynomial coefficients and hence solved in terms of power series in close analogy to the confluent Heun equation occurring for linear polarization. Application of Floquet theory yields physically interesting quantities like the quasienergy as a function of the problem’s parameters and expressions for the Bloch–Siegert shift of resonance frequencies. Various limit cases are thoroughly investigated.

scholarly journals Geometry of the Rabi Problem and Duality of Loops

2020 ◽  
Vol 75 (5) ◽  
pp. 381-391 ◽  
Author(s):  
Heinz-Jürgen Schmidt
Keyword(s):  
Magnetic Field ◽  
Differential Geometry ◽  
Floquet Theory ◽  
Bloch Sphere ◽  
Classical Spin ◽  
Periodic Magnetic Field

AbstractWe investigate the motion of a classical spin processing around a periodic magnetic field using Floquet theory, as well as elementary differential geometry and considering a couple of examples. Under certain conditions, the role of spin and magnetic field can be interchanged, leading to the notion of “duality of loops” on the Bloch sphere.

Floquet theory for a Volterra integro-dynamic system

2014 ◽  
Vol 93 (9) ◽  
pp. 2002-2013 ◽  
Author(s):  
R.P. Agarwal ◽  
V. Lupulescu ◽  
D. O’Regan ◽  
A. Younus
Keyword(s):  
Dynamic System ◽  
Floquet Theory

An Application of the Poincare´ Map to the Stability of Nonlinear Normal Modes

1980 ◽  
Vol 47 (3) ◽  
pp. 645-651 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Floquet Theory ◽  
Poincaré Map ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Theory Approach ◽  
Poincare Map ◽  
Linearized Stability ◽  
Nonlinear Normal ◽  
The Stability ◽  
Two Degree Of Freedom

The stability of periodic motions (nonlinear normal modes) in a nonlinear two-degree-of-freedom Hamiltonian system is studied by deriving an approximation for the Poincare´ map via the Birkhoff-Gustavson canonical transofrmation. This method is presented as an alternative to the usual linearized stability analysis based on Floquet theory. An example is given for which the Floquet theory approach fails to predict stability but for which the Poincare´ map approach succeeds.

Determination of Instability Boundaries for a Highly Flexible Prismatic-Jointed Robot Performing Repetitive Maneuvers

1991 ◽  
Author(s):  
Keith W. Buffinton
Keyword(s):  
Floquet Theory ◽  
Equations Of Motion ◽  
Perturbation Techniques ◽  
Axial Motion ◽  
The Third ◽  
Straightforward Application ◽  
Method Yield ◽  
Robotic Devices ◽  
Axially Moving

Abstract Presented in this work are the equations of motion governing the behavior of a simple, highly flexible, prismatic-jointed robotic manipulator performing repetitive maneuvers. The robot is modeled as a uniform cantilever beam that is subject to harmonic axial motions over a single bilateral support. To conveniently and accurately predict motions that lead to unstable behavior, three methods are investigated for determining the boundaries of unstable regions in the parameter space defined by the amplitude and frequency of axial motion. The first method is based on a straightforward application of Floquet theory; the second makes use of the results of a perturbation analysis; and the third employs Bolotin’s infinite determinate method. Results indicate that both perturbation techniques and Bolotin’s method yield acceptably accurate results for only very small amplitudes of axial motion and that a direct application of Floquet theory, while computational expensive, is the most reliable way to ensure that all instability boundaries are correctly represented. These results are particularly relevant to the study of prismatic-jointed robotic devices that experience amplitudes of periodic motion that are a significant percentage of the length of the axially moving member.

Influence of Interaction Between Torsion and Bending on Long-Term Nonlinear Rotor Dynamics

1999 ◽  
Author(s):  
Jiazhong Zhang ◽  
Bram de Kraker ◽  
Dick H. van Campen
Keyword(s):  
Critical Speed ◽  
Floquet Theory ◽  
Rotor Dynamics ◽  
Steady State Response ◽  
Bending Vibrations ◽  
Bending Vibration ◽  
State Response ◽  
Stability And Bifurcation ◽  
The Stability

Abstract An elementary system with gears and excited by unbalance mass has been constructed for analyzing the interaction between torsion and bending vibration in rotor dynamics. For this system, only the interaction caused primarily by unbalance mass has been investigated. The stability and bifurcation characteristics of the system have been studied by numerical computation based on Hopf bifurcation and Floquet theory. The results show that the interaction between torsion and bending vibrations can affect the stability and bifurcation of the unbalance response, in particular the onset speed of instability. In addition to the above, the interaction also affects the steady-state response. To investigate the influence of unbalance mass, the periodic solution and its stability have been studied near the first bending critical speed of the decoupled system. All the results show that the coupling of torsion and bending vibrations can have a significant influence on the nonlinear dynamics of the whole system.

scholarly journals An Impulsively Controlled Three-Species Prey-Predator Model with Stage Structure and Birth Pulse for Predator

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yanyan Hu ◽  
Mei Yan ◽  
Zhongyi Xiang
Keyword(s):  
Small Amplitude ◽  
Floquet Theory ◽  
Stage Structure ◽  
Critical Value ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Birth Pulse ◽  
Impulsive Equation ◽  
Predator Model ◽  
Predator System

We investigate the dynamic behaviors of a two-prey one-predator system with stage structure and birth pulse for predator. By using the Floquet theory of linear periodic impulsive equation and small amplitude perturbation method, we show that there exists a globally asymptotically stable two-prey eradication periodic solution when the impulsive period is less than some critical value. Further, we study the permanence of the investigated model. Our results provide valuable strategy for biological economics management. Numerical analysis is also inserted to illustrate the results.

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