468,259 research outputs found
Stability, Resonance and Lyapunov Inequalities for Periodic Conservative Systems
This paper is devoted to the study of Lyapunov type inequalities for periodic
conservative systems. The main results are derived from a previous analysis
which relates the best Lyapunov constants to some especial (constrained or
unconstrained) minimization problems. We provide some new results on the
existence and uniqueness of solutions of nonlinear resonant and periodic
systems. Finally, we present some new conditions which guarantee the stable
boundedness of linear periodic conservative systems.Comment: 19 page
Center or Limit Cycle: Renormalization Group as a Probe
Based on our studies done on two-dimensional autonomous systems, forced
non-autonomous systems and time-delayed systems, we propose a unified
methodology - that uses renormalization group theory - for finding out
existence of periodic solutions in a plethora of nonlinear dynamical systems
appearing across disciplines. The technique will be shown to have a non-trivial
ability of classifying the solutions into limit cycles and periodic orbits
surrounding a center. Moreover, the methodology has a definite advantage over
linear stability analysis in analyzing centers
A new SSI algorithm for LPTV systems: Application to a hinged-bladed helicopter
Many systems such as turbo-generators, wind turbines and helicopters show intrinsic time-periodic behaviors. Usually, these structures are considered to be faithfully modeled as linear time-invariant (LTI). In some cases where the rotor is anisotropic, this modeling does not hold and the equations of motion lead necessarily to a linear periodically time- varying (referred to as LPTV in the control and digital signal field or LTP in the mechanical and nonlinear dynamics world) model. Classical modal analysis methodologies based on the classical time-invariant eigenstructure (frequencies and damping ratios) of the system no more apply. This is the case in particular for subspace methods. For such time-periodic systems, the modal analysis can be described by characteristic exponents called Floquet multipliers. The aim of this paper is to suggest a new subspace-based algorithm that is able to extract these multipliers and the corresponding frequencies and damping ratios. The algorithm is then tested on a numerical model of a hinged-bladed helicopter on the ground
DELAY DIFFERENTIAL EQUATIONS AND THEIR APPLICATION TO MICRO ELECTRO MECHANICAL SYSTEMS
Delay differential equations have a wide range of applications in engineering. This work is devoted to the analysis of delay Duffing equation, which plays a crucial role in modeling performance on demand Micro Electro Mechanical Systems (MEMS). We start with the stability analysis of a linear delay model. We also show that in certain cases the delay model can be efficiently approximated with a much simpler model without delay. We proceed with the analysis of a non-linear Duffing equation. This model is a significantly more complex mathematical model. For instance, the existence of a periodic solution for this equation is a highly nontrivial question, which was established by Struwe. The main result of this work is to establish the existence of a periodic solution to delay Duffing equation. The paper claimed to establish the existence of such solutions, however their argument is wrong. In this work we establish the existence of a periodic solution under the assumption that the delay is sufficiently small
Continuation and stability deduction of resonant periodic orbits in three dimensional systems
In dynamical systems of few degrees of freedom, periodic solutions consist
the backbone of the phase space and the determination and computation of their
stability is crucial for understanding the global dynamics. In this paper we
study the classical three body problem in three dimensions and use its dynamics
to assess the long-term evolution of extrasolar systems. We compute periodic
orbits, which correspond to exact resonant motion, and determine their linear
stability. By computing maps of dynamical stability we show that stable
periodic orbits are surrounded in phase space with regular motion even in
systems with more than two degrees of freedom, while chaos is apparent close to
unstable ones. Therefore, families of stable periodic orbits, indeed, consist
backbones of the stability domains in phase space.Comment: Proceedings of the 6th International Conference on Numerical Analysis
(NumAn 2014). Published by the Applied Mathematics and Computers Lab,
Technical University of Crete (AMCL/TUC), Greec
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Variable domain transformation for linear PAC analysis of mixed-signal systems
This paper describes a method to perform linear AC analysis on mixed-signal systems which appear strongly nonlinear in the voltage domain but are linear in other variable domains. Common circuits like phase/delay-locked loops and duty-cycle correctors fall into this category, since they are designed to be linear with respect to phases, delays, and duty-cycles of the input and output clocks, respectively. The method uses variable domain translators to change the variables to which the AC perturbation is applied and from which the AC response is measured. By utilizing the efficient periodic AC (PAC) analysis available in commercial RF simulators, the circuit’s linear transfer function in the desired variable domain can be characterized without relying on extensive transient simulations. Furthermore, the variable domain translators enable the circuits to be macromodeled as weakly-nonlinear systems in the chosen domain and then converted to voltage-domain models, instead of being modeled as strongly-nonlinear systems directly
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