Normal form transformations for structural dynamics: An introduction for linear and nonlinear systems. [PDF]
Journal of Structural Dynamics, 2022 The aim of this paper is to provide an introduction to using normal form transformations for linear and nonlinear structural dynamics examples. Starting with linear single-degree-of-freedom systems, a series of examples are presented that eventually lead to the analysis of a system of two coupled nonlinear oscillators.
openaire +2 more sources
A generalized frequency detuning method for multidegree-of-freedom oscillators with nonlinear stiffness [PDF]
, 2013 In this paper, we derive a frequency detuning method for multi-degree-of-freedom oscillators with nonlinear stiffness. This approach includes a matrix of detuning parameters, which are used to model the amplitude dependent variation in resonant ...
Neild, S.A +3 more
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Normal Forms of Nonlinear Control Systems
Chaos in Automatic Control, 2018 Numerous papers were published during the last decade on the normal forms of nonlinear control systems with applications in bifurcation and its control. The approach is motivated by Poincare’s theory of normal forms for classical dynamical systems using ...
W. Kang, A. Krener, A. Krener
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Self-similar cuspidal formation by runaway thermocapillary forces in thin liquid films
New Journal of Physics, 2019 Many physical systems give rise to dynamical behavior leading to cuspidal shapes which represent a singularity of the governing equation. The cusp tip often exhibits self-similarity as well, indicative of scaling symmetry invariant in time up to a change
Chengzhe Zhou, Sandra M Troian
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Single-Mode and Dual-Mode Nongomogeneous Dissipative Structures in the Nonlocal Model of Erosion
Моделирование и анализ информационных систем, 2015 We consider a periodic boundary-value problem for a nonlinear equation with the deviating spatial argument in the case when the deviation is small. This equation is called a spatially nonlocal erosion equation.
A. M. Kovaleva, D. A. Kulikov
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On Matching, and Even Rectifying, Dynamical Systems through Koopman Operator Eigenfunctions [PDF]
SIAM Journal on Applied Dynamical Systems, 2017 Matching dynamical systems, through different forms of conjugacies and equivalences, has long been a fundamental concept, and a powerful tool, in the study and classification of nonlinear dynamic behavior (e.g. through normal forms).
E. Bollt +3 more
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Physical Review Special Topics. Accelerators and Beams, 2013 We present a mathematical analysis of planar motion of energetic electrons moving through a planar dipole undulator, excited by a fixed planar polarized plane wave Maxwell field in the x-ray free electron laser (FEL) regime.
James A. Ellison +3 more
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Equivariant singularity theory with distinguished parameters: Two case studies of resonant Hamiltonian systems [PDF]
, 1998 We consider Hamiltonian systems near equilibrium that can be (formally) reduced to one degree of freedom. Spatio-temporal symmetries play a key role. The planar reduction is studied by equivariant singularity theory with distinguished parameters.
Vegter, G +15 more
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Discrete-time synchronization of chaotic systems for secure communication [PDF]
, 2012 This paper deals with the problem of designing an exact nonlinear reconstructor for discrete-time chaotic encrypted messages. More precisely, we investigate the problem of designing a discrete-time dead-beat observer for nonlinear systems with unknown ...
Belmouhoub, Inaâm +7 more
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Phase portraits of Abel quadratic differential systems of second kind with symmetries [PDF]
, 2019 Altres ajuts: Universitat Jaume I grant P1-1B2015-16We provide normal forms and the global phase portraits on the Poincaré disk of the Abel quadratic differential equations of the second kind having a symmetry with respect to an axis or to the origin ...
Valls, Clàudia +5 more
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