Bifurcation and chaos analysis of a nonlinear electromechanical coupling relative rotation system

Hopf bifurcation and chaos of a nonlinear electromechanical coupling relative rotation system are studied in this paper. Considering the energy in air-gap field of AC motor, the dynamical equation of nonlinear electromechanical coupling relative rotation system is deduced by using the dissipation Lagrange equation. Choosing the electromagnetic stiffness as a bifurcation parameter, the necessary and sufficient conditions of Hopf bifurcation are given, and the bifurcation characteristics are studied. The mechanism and conditions of system parameters for chaotic motions are investigated rigorously based on the Silnikov method, and the homoclinic orbit is found by using the undetermined coefficient method. Therefore, Smale horseshoe chaos occurs when electromagnetic stiffness changes. Numerical simulations are also given, which confirm the analytical results.

Hopf bifurcation control for a coupled nonlinear relative rotation system with time-delay feedbacks

This paper investigates the Hopf bifurcations resulting from time delay in a coupled relative-rotation system with time- delay feedbacks. Firstly, considering external excitation, the dynamical equation of relative rotation nonlinear dynamical system with primary resonance and 1：1 internal resonance under time-delay feedbacks is deduced. Secondly, the averaging equation is obtained by the multiple scales method. The periodic solution in a closed form is presented by a perturbation approach. At last, numerical simulations confirm that time-delay theoretical analyses have influence on the Hopf bifurcation point and the stability of periodic solution.

Grazing bifurcation analysis of a relative rotation system with backlash non-smooth characteristic

Grazing bifurcation of a relative rotation system with backlash non-smooth characteristic is studied along with the change of the external excitation in this paper. Considering the oil film, backlash, time-varying stiffness and time-varying error, the dynamical equation of a relative rotation system with a backlash non-smooth characteristic is deduced by applying the elastic hydrodynamic lubrication（EHL） and the Grubin theories. In the process of relative rotation, the occurrence of backlash will lead to the change of dynamic behaviors of the system, and the system will transform from the meshing state to the impact state. Thus, the zero-time discontinuous mapping（ZDM） and the Poincare mapping are deduced to analyze the local dynamic characteristics of the system before as well as after the moment that the backlash appears（i.e.,the grazing state）. Meanwhile, the grazing bifurcation mechanism is analyzed theoretically by applying the impact and Floquet theories. Numerical simulations are also given, which confirm the analytical results.

Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation

This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The. criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincare map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using nomfeedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to periodmotions by adding an excitation term.

Precise relative rotation sensing using slow light

A novel relative rotation sensor based on slow light is proposed and analysed. A theoretical analysis shows that the high sensitivity of the proposed rotation sensor is achieved through an electromagneticaIly-induced-transparency medium. Unlike the tradition detection method, the idea of rotation sensing is to detect group delay between counterpropagating wave packets. It can be used to realize an ultra-precise rotation sensor.

Recasting theory of elasticity with micro-finite elements

In the classical theory of elasticity,a body is initially modeled as a homogeneous and dense assemblage of constituent ＂material particles＂.The kernel concept of elastic deformation is the displacement of the particle that associates the current configuration with the reference one.In this paper,we exploit an alternative constituent ＂micro-finite element＂,and use the stretch of the element as the essential quality to recast the theory of elasticity.It should be realized that such a treatment means that the elastic body can be modeled as a finite covering of elements and consequently characterized by a manifold.The recasting of the elasticity theory becomes more feasible for dealing with defects and topological evolution.

Multiple rotation averaging using only the relative rotation angle

In this work,we propose multiple rotation averaging using only the relative rotation angle,which is a straightforward camera pose optimization method.We use the axis-angle representation to parameterize the rotation and use only relative rotation angles to constrain absolute rotations instead of complete relative rotations.When used with an inertial measurement unit(IMU),our method can obviate the need to estimate and maintain extrinsic parameters between the camera and IMU.This advantage makes our method immune to extrinsic parameters and flexible.We performed extensive evaluations on both synthetic data and publicly available real datasets,which showed that our method was comparable with the state-of-the-art method and achieved a significant gain in accuracy for the visual measurement when applied to the case in which the camera and IMU are tightly fixed.

Stability of Rotation Relations of Three Unitaries with the Flip Action in C^(*)-Algebras

The authors show that ifΘ=(θ_(jk))is a 3×3 totally irrational real skewsymmetric matrix,whereθ_(jk)∈[0,1)for j,k=1,2,3,then for anyε>0,there existsδ>0 satisfying the following:For any unital C^(*)-algebra A with the cancellation property,strict comparison and nonempty tracial state space,any four unitaries u1,u2,u3,w∈A such that(1)■,wujw-1=uj-1,w2=1A for j,k=1,2,3;(2)τ(aw)=0 and■for all n∈N,all a∈C^(*)(u1,u2,u3),j,k=1,2,3 and all tracial statesτon A,where C^(*)(u1,u2,u3)is the C^(*)-subalgebra generated by u1,u2 and u3,there exists a 4-tuple of unitaries■in A such that■and■for j,k=1,2,3.The above conclusion is also called that the rotation relations of three unitaries with the flip action is stable under the above conditions.

Real-time recognition of human lower-limb locomotion based on exponential coordinates of relative rotations

This paper proposes a data-driven method using a parametric representation of relative rotations to classify human lower-limb locomotion, which is designed for wearable robots. Three Inertial measurement units(IMUs) are mounted on the subject's waist,left knee, and right knee, respectively. Features for classification comprise relative rotations, angular velocities, and waist acceleration. Those relative rotations are represented by the exponential coordinates. The rotation matrices are normalized by Karcher mean and then the Support Vector Machine(SVM) method is used to train the data. Experiments are conducted with a time-window size of less than 40 ms. Three SVM classifiers telling 3, 5 and 6 rough lower-limb locomotion types respectively are trained, and the average accuracies are all over 98%. With the combination of those rough SVM classifiers, an easy SVMbased ensembled-system is proposed to classify 16 fine locomotion types, achieving the average accuracy of 98.22%, and its latency is 18 ms when deployed to an onboard computer.

Practical Reference-Frame-Independent Measurement-Device-Independent Quantum Key Distribution Systems Against the Worst Relative Rotation of Reference Frames

Reference-frame-independent measurement-device-independent QKD(RFI-MDI-QKD), immune to both the slow unknown drift of reference frames and detector side channel attacks, can generate information-theoretic secure keys. Despite its natural resistance to the slow drift of reference frames, the performance of practical RFI-MDI-QKD systems descends with the increasing drift of reference frames. In this paper, we demonstrate the worst relative rotation of reference frames for practical RFI-MDI-QKD systems, and investigate their performance against the worst-case scenario,both of which are unclear to date. Simulation results show that, practical RFI-MDI-QKD systems can achieve quite good performance even against the worst-case scenario, which clearly demonstrates that it is possible to implement practical MDI-QKD systems with freely drifting reference frames.