A note on the periodic orbits of a self excited rigid body

The aim of the present paper is to study the periodic orbits of a perturbed self excited rigid body with a fixed point. For studying these periodic orbits we shall use averaging theory of first order.

Dynamic Visual Servoing With Chaos Control for Redundant Robots

This paper presents a new dynamic visual control system for redundant robots with chaos compensation. In order to implement the visual servoing system, a new architecture is proposed that improves the system maintainability and traceability. Furthermore, high performance is obtained as a result of parallel execution of the different tasks that compose the architecture. The control component of the architecture implements a new visual servoing technique for resolving the redundancy at the acceleration level in order to guarantee the correct motion of both end-effector and joints. The controller generates the required torques for the tracking of image trajectories. However, in order to guarantee the applicability of this technique, a repetitive path tracked by the robot-end must produce a periodic joint motion. A chaos controller is integrated in the visual servoing system and the correct performance is observed in low and high velocities. Furthermore, a method to adjust the chaos controller is proposed and validated using a real three-link robot.

Efficient split eld FDTD analysis of third-order nonlinear materials in two-dimensionally periodic media

In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one- and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finite- difference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.