Nonlinear Behavior of Flutter Unstable Dynamical Systems With Gyroscopic and Circulatory Forces

1977 ◽  
Vol 44 (4) ◽  
pp. 755-762 ◽  
Author(s):  
P. R. Sethna ◽  
S. M. Schapiro
Keyword(s):  
Dynamical Systems ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Nonlinear Behavior ◽  
Discrete Dynamical Systems ◽  
Hopf Bifurcations ◽  
Integral Manifolds ◽  
Method Of Integral Manifolds

Postflutter behavior of nonlinear discrete dynamical systems having a combination of gyroscopic and circulatory forces are studied. The study leads to Hopf bifurcations. The method of analysis is based on the method of Hopf and the method of integral manifolds. The results of the analysis are applied to an example and the accuracy of the analysis is checked against numerical solutions of the equations of motion.

scholarly journals The Stability Criteria with Compound Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yazhuo Zhang ◽  
Baodong Zheng
Keyword(s):  
Dynamical Systems ◽  
Spectral Property ◽  
Discrete Dynamical Systems ◽  
Asymptotical Stability ◽  
Hopf Bifurcations ◽  
Stability Criteria ◽  
Bifurcation Problem ◽  
Compound Matrices ◽  
The Stability ◽  
Schur Stability

The bifurcation problem is one of the most important subjects in dynamical systems. Motivated by M. Li et al. who used compound matrices to judge the stability of matrices and the existence of Hopf bifurcations in continuous dynamical systems, we obtained some effective methods to judge the Schur stability of matrices on the base of the spectral property of compound matrices, which can be used to judge the asymptotical stability and the existence of Hopf bifurcations of discrete dynamical systems.

A new perspective on constrained motion

1992 ◽  
Vol 439 (1906) ◽  
pp. 407-410 ◽  
Keyword(s):  
Dynamical Systems ◽  
Equations Of Motion ◽  
Discrete Dynamical Systems ◽  
Lagrangian Mechanics ◽  
Constrained Motion ◽  
New Perspective

The explicit general equations of motion for constrained discrete dynamical systems are obtained. These new equations lead to a simple and new fundamental view of lagrangian mechanics.

Canonical Kane’s Equations of Motion for Discrete Dynamical Systems

AIAA Journal ◽  
2019 ◽  
Vol 57 (10) ◽  
pp. 4226-4240
Author(s):  
Abdulrahman H. Bajodah ◽  
Dewey H. Hodges
Keyword(s):  
Dynamical Systems ◽  
Equations Of Motion ◽  
Discrete Dynamical Systems ◽  
Kane’S Equations ◽  
Kane's Equations

RATIONAL QUASIPERIODIC SOLUTIONS FOR DYNAMICAL SYSTEMS

1990 ◽  
Vol 04 (09) ◽  
pp. 635-638 ◽  
Author(s):  
J. SEIMENIS
Keyword(s):  
Dynamical Systems ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Rational Functions ◽  
Hamiltonian Equations ◽  
Quasiperiodic Solutions ◽  
Good Agreement

We investigate the possibility to give analytically approximate quasiperiodic solutions of the Hamiltonian equations of motion in simple rational functions. In this paper we give a formula for these solutions which is in very good agreement with the numerical solutions, although it is extremely simple.

scholarly journals Higher dimensional topology and generalized Hopf bifurcations for discrete dynamical systems

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Héctor Barge ◽  
José M. R. Sanjurjo
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Fixed Points ◽  
General Result ◽  
Discrete Dynamical Systems ◽  
Hopf Bifurcations ◽  
Substantial Role ◽  
Higher Dimensional ◽  
Low Dimensional

<p style='text-indent:20px;'>In this paper we study generalized Poincaré-Andronov-Hopf bifurcations of discrete dynamical systems. We prove a general result for attractors in <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula>-dimensional manifolds satisfying some suitable conditions. This result allows us to obtain sharper Hopf bifurcation theorems for fixed points in the general case and other attractors in low dimensional manifolds. Topological techniques based on the notion of concentricity of manifolds play a substantial role in the paper.</p>

scholarly journals Hidden Attractors in Discrete Dynamical Systems

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 616
Author(s):  
Marek Berezowski ◽  
Marcin Lawnik
Keyword(s):  
Dynamical Systems ◽  
Chaos Theory ◽  
Scientific Literature ◽  
Discrete Systems ◽  
Discrete Dynamical Systems ◽  
Continuous Systems ◽  
Hidden Attractors ◽  
Negative Effects ◽  
Chemical Reactors ◽  
Points Of View

Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on chemical reactors. This problem is important, especially when in a given dynamic process there are so-called hidden attractors. In the scientific literature, we can find many works that deal with this issue from both the theoretical and practical points of view. The vast majority of these works concern multidimensional continuous systems. Our work shows these attractors in discrete systems. They can occur in Newton’s recursion and in numerical integration.

A DYNAMICAL SYSTEM WITH CHAOTIC BEHAVIOR

1989 ◽  
Vol 03 (15) ◽  
pp. 1185-1188 ◽  
Author(s):  
J. SEIMENIS
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Infinite Number ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Hamiltonian Dynamical Systems

We develop a method to find solutions of the equations of motion in Hamiltonian Dynamical Systems. We apply this method to the system [Formula: see text] We study the case a → 0 and we find that in this case the system has an infinite number of period dubling bifurcations.

A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Parallel Computers ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Logistic Mapping ◽  
Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

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