Aeroelastic characteristics of slender wing/bodies with freeplay non-linearities

This article presents a time domain approach to the flutter analysis of a missile-type wing/body configuration with concentrated structural non-linearities. The missile wing is considered fully movable and its rotation angle contains the structural freeplay-type non-linearity. Although a general formulation for flexible configurations is developed, only two rigid degrees of freedom are taken into account for the results: pitching of the whole wing/body configuration and wing rotation angle around its hinge. An unsteady aerodynamic model based on the slender-body approach is used to calculate aerodynamic generalized forces. Limit-cycle oscillations and chaotic motion below the flutter speed are observed in this study.

Optically Induced Reorientation in Nematic Cylindrical Structures

Cyclindrical structures of nematics give rise to several opto-optical effects related to molecular reorientation. One of these effects is the formation of diffraction ring patterns similar to the ones observed in planar cells, but differing in shape. Another effect has been observed, namely a quasi-chaotic motion of rings with a very large angular spread; this motion can be obtained using a cw laser and high power densities. The phenomenon could be attributed to thermal motion, however, there are some features that cannot be explained by a purely thermal effect, e.g., a wavelength dependence of the threshold and the frequencies of the ring motion.

Nonlinear dynamics of a satellite with deployable solar panel arrays

The multibody dynamics of a satellite in circular orbit, modeled as a central body with two hinge-connected deployable solar panel arrays, is investigated. Typically, the solar panel arrays are deployed in orbit using preloaded torsional springs at the hinges in a near symmetrical accordion manner, to minimize the shock loads at the hinges. There are five degrees of freedom of the interconnected rigid bodies, composed of coupled attitude motions (pitch, yaw and roll) of the central body plus relative rotations of the solar panel arrays. The dynamical equations of motion of the satellite system are derived using Kane's equations. These are then used to investigate the dynamic behavior of the system during solar panel deployment via the 7-8th-order Runge-Kutta integration algorithms and results are compared with approximate analytical solutions. Chaotic attitude motions of the completely deployed satellite in circular orbit under the influence of the gravity-gradient torques are subsequently investigated analytically using Melnikov's method and confirmed via numerical integration. The Hamiltonian equations in terms of Deprit's variables are used to facilitate the analysis. (C) 2003 Published by Elsevier Ltd.

Secular and tidal evolution of circumbinary systems

We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation for the spins, and the viscous linear model for tides. We derive the averaged equations of motion in a simplified vectorial formalism, which is suitable to model the long-term evolution of a wide variety of circumbinary systems in very eccentric and inclined orbits. In particular, this vectorial approach can be used to derive constraints for tidal migration, capture in Cassini states, and stellar spin–orbit misalignment. We show that circumbinary planets with initial arbitrary orbital inclination can become coplanar through a secular resonance between the precession of the orbit and the precession of the spin of one of the stars. We also show that circumbinary systems for which the pericenter of the inner orbit is initially in libration present chaotic motion for the spins and for the eccentricity of the outer orbit. Because our model is valid for the non-restricted problem, it can also be applied to any three-body hierarchical system such as star–planet–satellite systems and triple stellar systems.

Nonlinear dynamics and chaotic motions in feedback-controlled two- and three-degree-of-freedom robots

The dynamics of a feedback-controlled rigid robot is most commonly described by a set of nonlinear ordinary differential equations. In this paper we analyze these equations, representing the feedback-controlled motion of two- and three-degrees-of-freedom rigid robots with revolute (R) and prismatic (P) joints in the absence of compliance, friction, and potential energy, for the possibility of chaotic motions. We first study the unforced or inertial motions of the robots, and show that when the Gaussian or Riemannian curvature of the configuration space of a robot is negative, the robot equations can exhibit chaos. If the curvature is zero or positive, then the robot equations cannot exhibit chaos. We show that among the two-degrees-of-freedom robots, the PP and the PR robot have zero Gaussian curvature while the RP and RR robots have negative Gaussian curvatures. For the three-degrees-of-freedom robots, we analyze the two well-known RRP and RRR configurations of the Stanford arm and the PUMA manipulator respectively, and derive the conditions for negative curvature and possible chaotic motions. The criteria of negative curvature cannot be used for the forced or feedback-controlled motions. For the forced motion, we resort to the well-known numerical techniques and compute chaos maps, Poincare maps, and bifurcation diagrams. Numerical results are presented for the two-degrees-of-freedom RP and RR robots, and we show that these robot equations can exhibit chaos for low controller gains and for large underestimated models. From the bifurcation diagrams, the route to chaos appears to be through period doubling.

Dynamical Instabilities and Deterministic Chaos in Ballistic Electron Motion in Semiconductor Superlattices

We consider the motion of ballistic electrons within a superlattice miniband under the influence of an alternating electric field. We show that the interaction of electrons with the self-consistent electromagnetic field generated by the electron current may lead to the transition from regular to chaotic dynamics. We estimate the conditions for the experimental observation of this deterministic chaos and discuss the similarities of the superlattice system with the other condensed matter and quantum optical systems.

A multi-objective approach for the motion planning of redundant manipulators

Kinematic redundancy occurs when a manipulator possesses more degrees of freedom than those required to execute a given task. Several kinematic techniques for redundant manipulators control the gripper through the pseudo-inverse of the Jacobian, but lead to a kind of chaotic inner motion with unpredictable arm configurations. Such algorithms are not easy to adapt to optimization schemes and, moreover, often there are multiple optimization objectives that can conflict between them. Unlike single optimization, where one attempts to find the best solution, in multi-objective optimization there is no single solution that is optimum with respect to all indices. Therefore, trajectory planning of redundant robots remains an important area of research and more efficient optimization algorithms are needed. This paper presents a new technique to solve the inverse kinematics of redundant manipulators, using a multi-objective genetic algorithm. This scheme combines the closed-loop pseudo-inverse method with a multi-objective genetic algorithm to control the joint positions. Simulations for manipulators with three or four rotational joints, considering the optimization of two objectives in a workspace without and with obstacles are developed. The results reveal that it is possible to choose several solutions from the Pareto optimal front according to the importance of each individual objective.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Chaotic dynamics of electric-field domains in periodically driven superlattices

Self-sustained time-dependent current oscillations under dc voltage bias have been observed in recent experiments on n-doped semiconductor superlattices with sequential resonant tunneling. The current oscillations are caused by the motion and recycling of the domain wall separating low- and high-electric-field regions of the superlattice, as the analysis of a discrete drift model shows and experimental evidence supports. Numerical simulation shows that different nonlinear dynamical regimes of the domain wall appear when an external microwave signal is superimposed on the dc bias and its driving frequency and driving amplitude vary. On the frequency-amplitude parameter plane, there are regions of entrainment and quasiperiodicity forming Arnold tongues. Chaos is demonstrated to appear at the boundaries of the tongues and in the regions where they overlap. Coexistence of up to four electric-field domains randomly nucleated in space is detected under ac+dc driving.

Dynamic portrait of the planetary 2/1 mean-motion resonance - I. Systems with a more massive outer planet

We analyse the global structure of the phase space of the planar planetary 2/1 mean-motion resonance in cases where the outer planet is more massive than its inner companion. Inside the resonant domain, we show the existence of two families of periodic orbits, one associated to the librational motion of resonant angle (sigma-family) and the other related to the circulatory motion of the difference in longitudes of pericentre (Delta pi-family). The well-known apsidal corotation resonances (ACR) appear as intersections between both families. A complex web of secondary resonances is also detected for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system. The construction of dynamical maps for various values of the total angular momentum shows the evolution of the families of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems. For low-moderate eccentricities, several different stable modes exist outside the ACR. For larger eccentricities, however, all stable solutions are associated to oscillations around the stationary solutions. Finally, we present a possible link between these stable families and the process of resonance capture, identifying the most probable routes from the secular region to the resonant domain, and discussing how the final resonant configuration may be affected by the extension of the chaotic layer around the resonance region.

Dynamic portrait of the planetary 2/1 mean-motion resonance - II. Systems with a more massive inner planet

This paper presents the second part in our study of the global structure of the planar phase space of the planetary three-body problem, when both planets lie in the vicinity of a 2/1 mean-motion resonance. While Paper I was devoted to cases where the outer planet is the more massive body, the present work is devoted to the cases where the more massive body is the inner planet. As before, outside the well-known Apsidal Corotation Resonances (ACR), the phase space shows a complex picture marked by the presence of several distinct regimes of resonant and non-resonant motion, crossed by families of periodic orbits and separated by chaotic zones. When the chosen values of the integrals of motion lead to symmetric ACR, the global dynamics are generally similar to the structure presented in Paper I. However, for asymmetric ACR the resonant phase space is strikingly different and shows a galore of distinct dynamical states. This structure is shown with the help of dynamical maps constructed on two different representative planes, one centred on the unstable symmetric ACR and the other on the stable asymmetric equilibrium solution. Although the study described in the work may be applied to any mass ratio, we present a detailed analysis for mass values similar to the Jupiter-Saturn case. Results give a global view of the different dynamical states available to resonant planets with these characteristics. Some of these dynamical paths could have marked the evolution of the giant planets of our Solar system, assuming they suffered a temporary capture in the 2/1 resonance during the latest stages of the formation of our Solar system.

Chaotic transport in reversed shear tokamaks

For tokamak models using simplified geometries and reversed shear plasma profiles, we have numerically investigated how the onset of Lagrangian chaos at the plasma edge may affect the plasma confinement in two distinct but closely related problems. Firstly, we have considered the motion of particles in drift waves in the presence of an equilibrium radial electric field with shear. We have shown that the radial particle transport caused by this motion is selective in phase space, being determined by the resonant drift waves and depending on the parameters of both the resonant waves and the electric field profile. Moreover, we have shown that an additional transport barrier may be created at the plasma edge by increasing the electric field. In the second place, we have studied escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall, when there are resonant modes due to the action of an ergodic magnetic limiter. A non-monotonic safety factor profile has been used in the analysis of field line topology in a region of negative magnetic shear. We have observed that, if internal modes are perturbed, the distributions of field line connection lengths and magnetic footprints exhibit spatially localized escape channels. For typical physical parameters of a fusion plasma, the two Lagrangian chaotic processes considered in this work can be effective in usual conditions so as to influence plasma confinement. The reversed shear effects discussed in this work may also contribute to evaluate the transport barrier relevance in advanced confinement scenarios in future tokamak experiments.

Mean Motion in Stochastic Plasmas With a Space-Dependent Diffusion Coefficient

Radial transport in the tokamap, which has been proposed as a simple model for the motion in a stochastic plasma, is investigated. A theory for previous numerical findings is presented. The new results are stimulated by the fact that the radial diffusion coefficients is space-dependent. The space-dependence of the transport coefficient has several interesting effects which have not been elucidated so far. Among the new findings are the analytical predictions for the scaling of the mean radial displacement with time and the relation between the Fokker-Planck diffusion coefficient and the diffusion coefficient from the mean square displacement. The applicability to other systems is also discussed. (c) 2009 WILEY-VCH GmbH & Co. KGaA, Weinheim

Chaotic thermalization in classical gauge theories

We explore the idea that chaos concepts might be useful for understanding the thermalization in gauge theories. The SU(2) Higgs model is discussed as a prototype of system with gauge fields coupled to matter fields. Through the numerical solution of the equations of motion, we are able to characterize chaotic behavior via the corresponding Lyapunov exponent. Then it is demonstrated that the system's approach to equilibrium can be understood through direct application of the principles of Statistical Mechanics. © 2013 AIP Publishing LLC.