THE HOMOLOGY CLASSES OF LARGE-SCALEPERIODIC ORBITS ON NONLINEAR SPACE

The large-scale periodic orbits of a nonlinear mechanics system can represent the homology classes, which are generally non-trivial, of the energy level surface and the topology properties of an energy level surface are determined by the that of the phase space and the large-scale properties of the Hamiltonian. These properties are used for estimate of the rank of the first homology group of energy level surfaces in the paper.

A LARGE-SCALE ESTIMATE OF THE NUMBEROF PERIODIC SMALL OSCILLATIONS OFNONLINEAR SYSTEMS

A conservative system performing a small oscillation near every equilibrium position is analysed in classical way. The paper tries to answer the following question: How many types of the periodic small oscillation in the whole configuration space of the system are there? Making some hypotheses, it expresses the lower bounds of the number of the types for two cases where critical points of the potential function are nondegenerate and degenerate respectively by the Betti numbers and dimension of the constraint manifold only.

Fast SSED-MoM /FEM Analysis for Electromagnetic Scattering of Large-Scale Periodic Dielectric Structures

A hybrid method combining simplified sub-entire domain basis function method of moment with finite element method( SSED-MoM /FEM) is accelerated for electromagnetic( EM) scattering analysis of large-scale periodic structures.The unknowns are reduced sharply with non-uniform mesh in FEM. The computational complexity of the hybrid method is dramatically declined by applying conjugate gradient-fast Fourier transform( CG-FFT) to the integral equations of both electric field and magnetic field. The efficiency is further improved by using OpenMP technique. Numerical results demonstrate that the SSED-MoM /FEM method can be accelerated for more than three thousand times with large-scale periodic structures.

CALCULATING ACCURATE PERIODIC MOTIONS OF HARMONICALLY FORCED PIECEWISE LINEAR OSCILLATORS

This paper presents an efficient numerical scheme for calculating the periodic motion of a harmonically forced piecewise linear oscillator very accurately. The scheme is based on the shooting technique with the traditional numerical Poincare mapping and its Jacobian replaced by the piecewise analytic ones. Thus, the scheme gets rid of the requirement of the current schemes for an assumed order of the oscillator trajectory passing through different linear regions. The numerical examples in the paper demonstrate that the new scheme, compared with the current schemes, enables one to cope with more complicated dynamics of harmonically forced piecewise linear oscillators.

Observation 20-s periodic signals on Mars from InSight,Sols 800-1,000

Seismometers of the InSight probe(Interior Exploration using Seismic Investigation,Geodesy and Heat Transport)currently operating on Mars have recorded not only seismic events but also high-frequency non-seismic periodic signals that appear to have been induced by variations in the Martian environment and the hardware.Here,we report an observation of a long-period signal with a dominant period of~20 s from Martian solar days(Sol)800 to Sol 1,000.This 20-s signal is detected mostly at quiet nighttime—from22:00 to 04:00 LMST(Local Mean Solar Time)—at the InSight landing site.The measurement of the particle motion suggests that this linearly polarized signal focuses on the horizontal plane with an angle of~30°from the north.By examining the temporal variation of the signal’s amplitude and polarization angle and its times of occurrence in relation to the planet’s atmospheric data,we suggest that this20-s signal may be relevant to wind and temperature variations on Mars.Furthermore,we study the possible influence of this 20-s signal on the noise autocorrelation and find that the stacked autocorrelograms can be quite different when the 20-s signal is present.

Periodic Motion Planning and Control for Double Rotary Pendulum via Virtual Holonomic Constraints

Periodic motion planning for an under-actuated system is rather difficult due to differential dynamic constraints imposed by passive dynamics, and it becomes more difficult for a system with higher underactuation degree, that is with a higher difference between the number of degrees of freedom and the number of independent control inputs. However, from another point of view, these constraints also mean some relation between state variables and could be used in the motion planning.We consider a double rotary pendulum, which has an underactuation degree 2. A novel periodic motion planning is presented based on an optimization search. A necessary condition for existence of the whole periodic trajectory is given because of the higher underactuation degree of the system. Moreover this condition is given to make virtual holonomic constraint(VHC) based control design feasible. Therefore, an initial guess for the optimization of planning a feasible periodic motion is based on this necessary condition. Then, VHCs are used for the system transformation and transverse linearization is used to design a static state feedback controller with periodic matrix function gain. The controller gain is found through another optimization procedure. The effectiveness of initial guess and performance of the closed-loop system are illustrated through numerical simulations.

The interannual periodicity of precipitation and its links to the large-scale circulations over the Third Pole

To understand the spatio-temporal variability of precipitation(P)in the Third Pole region(centered on the Tibetan Plateau-TP),it is necessary to quantify the interannual periodicity of P and its relationship with large-scale circulations.In this study,Morlet wavelet transform was used to detect significant(p<0.05)periodic characteristics in P data from meteorological stations in four climate domains in the Third Pole,and to reveal the major large-scale circulations that triggered the variability of periodic P,in addition to bringing large amounts of water vapour.The wavelet transform results were as follows.(1)Significant quasiperiodicity varied from 2 to 11 years.The high-frequency variability mode(2 to 6 years quasi-periods)was universal,and the low-frequency variability mode(7 to 11 years quasi-periods)was rare,occurring mainly in the westerlies and Indian monsoon domains.(2)The majority of periods were base periods(53%),followed by two-base periods.Almost all stations in the Third Pole(95%)showed one or two periods.(3)Periodicity was widely detected in the majority of years(84%).(4)The power spectra of P in the four domains were dominated by statistically significant high-frequency oscillations(ie.,with short periodicity).(5)Large-scale circulations directly and indirectly influenced the periodic P variability in the different domains.The mode of P variability in the different domains was influenced by interactions between large-scale circulation features and not only by the dominant circulation and its control of water vapour transport.The results of this study will contribute to better understanding of the causal mechanisms associated with P variability,which is important for hydrological science and waterresourcemanagement.

RESEARCH OF THE PERIODIC MOTION AND STABILITY OF TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEMS

The periodic motion and stability for a class of two-degree-of-freedom nonlinear oscillating systems are studied by using the method of Liapunov function. The sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions are obtained.

PERIODIC MOTIONS OF SPINNING RIGID SPACECRAFT UNDER INFLUENCE OF GRAVITATIONAL AND MAGNETIC FIELDS

The motion of a magnetized axisymmetric spacecraft about its center of mass in a circular orbit is considered, taking the gravitational and magnetic effects of the central body into account. Equations of motion of the reduced system are transformed to equations of plane motion of a charged particle under the action of electric and magnetic fields. Stationary motions of the system are determined and periodic motions near to them are constructed using the Lyapounoff theorem of the holomorphic integral.

Bifurcation of Periodic Motion of Rigid Rotor System Supported by Angular Contact Ball Bearings

Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.

Scaling of motion and governing equations for baroclinic large-scale motions in equatorial ocean

An obvious characteristic of the baroclinic large-scale motions in the equatorial ocean is that the meridional scale H of motion is far smaller than the zonal scale L. The scaling of motion carefully with this striking characteristic in this paper results in two conclusions, i. e., the Coriolis terms associated with the horizontal component of the rotation vector cannot be neglected in the governing equations; and the use of the absence of heating is not suitable to the equatorial region. In this paper the equatorial β-plane nondimensional governing equations with the small parametersδ_0 andδ_1 have been Obtained.

Study on High Accuracy Hybrid Controller for Periodic Motion Control

In order to realize high accuracy control for periodic motion,a hybrid controller with grey prediction was presented in this paper.Incorporating the grey prediction,repetitive control,and the traditional Proportional-Integral-Differential(PID)control,a design method of the grey prediction repetitive PID(GRPID)control algorithm was investigated,according to the characteristics of the periodic motion control.The hybrid control algorithm can estimate unsure parameters and disturbance of system using grey prediction,and compensate control in terms of the prediction results,and this may improve control quality and robustness of repetitive control for controlling periodic motion.An example was carried out to verify the feasibility of the controller.The simulation results show that this algorithm has better performances than that of the conventional repetitive control system.It indicates the presented control method is more suitable for control system of periodic motion.

The Phenomena of Bifurcation and Catastrophe of Large-Scale Horizontal Motion in the Atmosphere under the Effect of Rossby Parameter

The stability question of large-scale horizontal motion in the atmosphere under the effect of Rossby parameter is discussed in this paper by using the qualitative analysis theory of ordinary differential equations. The following aspects are reviewed: The stability of large-scale horizontal motion in the atmosphere accords with the common inertial stability criterion when the effect of Rossby parameter is not considered (Yang, 1983), and that, on the other hand, the motion will bifurcate two times with the variation of absolute vorticity of basic Zephyr flow at the initial position under the effect of Rossby parameter. Furthermore, in the inertial stable region, if the effect of geostrophic deviation at the initial position is considered, the motion will not only bifurcate but also generate a catastrophe.

Identifying Periodical Activities Independent of Video Content

In this research, a completely new and accurate method has been presented for detecting periodic activities with the help of machine vision. The proposed method is independent of motion tracking complex algorithms unlike the previous strategies and it is fully independent of contents and types of activities by performing low level calculation. Not using of heavy computations while improving the ability of periodicity detection is regarded as the unique feature of this method. The use of general and flexible framework in this method causes to facilitate the machine vision periodic activities identification process.

Pulse-like ground motion observed during the 6 February 2023 M_(W)7.8 Pazarcık Earthquake(Kahramanmaraş,SE Türkiye)

In this study,we analyzed 100 three-component strong ground motion records observed within 200 km of the causative fault of the 6 February 2023 M_(W)7.8 Pazarcık(Kahramanmaraş)Earthquake in SE Türkiye.The wavelet method was utilized to identify and analyze the characteristics of pulse-like ground motions in the near-fault region,while considering the uncertainty of the pulse orientation during the analysis.Our investigation focused on the effects of the focal mechanism and rupture process on the spatial distribution,pulse orientation,and maximum pulse direction of the observed pulse-like ground motion.We also analyzed the amplitude and period of the observed ground pulses and the effect of long-period amplification on the ground motion response spectra.Our results indicated the following:(1)A total of 21 typical ground velocity pulses were observed during this earthquake,exhibiting complex characteristics due to the influence of the strike-slip mechanism and rupture directivity.Most ground pulses(17 out of 21)were recorded within 20 km of the fault,in a wide range of orientations,including normal and parallel to the fault direction.The waveforms exhibited unidirectional features,indicating the effects of left-lateral fault slip.Distinct pulses observed more than 20 km from the fault were mainly oriented normal to the fault.The waveforms were bidirectional with double-or multi-round trips as a result of rupture directivity.(2)The amplitudes of the observed pulses ranged from 30.5 to 220.0 cm/s,with the largest peak velocity of 220.0 cm/s observed at Station 3138.The pulse periods ranged from 2.3 to 14.5 s,with the longest pulse period of 14.5 s observed at Station 3116.The amplitude and period of the pulses observed during this earthquake were comparable to those of similar-magnitude global earthquakes.The amplitude of the pulses decreased significantly with increasing fault distance,whereas the pulse period was not significantly affected by the fault distance.(3)Compared with non-pulse records,the velocity pulse records had a pronounced amplification effect on the acceleration response spectra near the pulse period,with factors ranging from 2.1 to 5.8.The larger velocity pulses also significantly amplified the velocity response spectra,particularly over the long periods.This significant amplification effect of the pulses on the response spectra leads to empirical models underestimating the long-period earthquake ground motion.

The Problem of Quasiperiodic Photonic Structures Solved by Considering the Cut of 2D Periodic Structure

The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure. And the problem is solved in a manner similar to 2D periodic photonic structures. A mechanical analogy (quasiperiodic orbits) helps to bring conceptual clarity.

A Simple Model for the Calculation of Diffusion Coefficient in a Periodic Potential

Motivated by developing a simple model to calculate the diffusion coefficient in moderate friction region, a simplified model is proposed to deal with the diffusion of Brownian particles in a periodic potential. Where the internal noise is a Gaussian white noise, and the basic cell of the periodic potential is composed of a parabolic potential linked with a harmonic potential. When the particles cross the joint point of the potential, a time coarse-graining scheme is used to obtain a simple analytical expression of the probability distribution. The particles drift and diffuse from the first barrier to the second barrier, the passing probability over the second barrier corresponding to the escape rate becomes decrease serves as the long-jump probability. The theoretical result is confirmed by numerical simulation results. The approach can be extended to color noise case.

Revealing the Fluttering Motions of Mid-Water Trawl Codend Through Sea Trials:Case Study of Antarctic Krill Trawl Codend

The dynamic coupling between the fluttering motions and hydrodynamic characteristics of codend is essential in understanding the trawl selectivity through fish response and the drag force acting on the whole trawl.This study investigated the effect of towing speed,warp length,warp tension,and catch size on the fluttering motions of Antarctic krill trawl codend during net shooting,towing,and hauling by using sea trial data.The time-periodicity of codend oscillation was analyzed by the Morlet wavelet transform method.Results indicated that the period of codend oscillation was between 50 s and 90 s and showed an increasing trend with the warp tension but a decreased value at the towing stage.The coefficient amplitude of codend oscillation was between 0 and 4 at the net shooting and hauling stages,and between 0.2 and 0.6 at the towing stage.The amplitude of codend oscillation increased with the warp tension,towing speed,and catch size,but decreased with the increase of the warp length.In addition,the period of codend oscillation increased with the towing speed at the net shooting and hauling stages,but decreased at the towing stage.These results from codend fluttering motions can improve the understanding of fish behavior and gear shape that modify the hydrodynamic force on the codend instantaneously.

Long-period ground motion characteristic of the 1999 Jiji (Chi-Chi),Taiwan,main-shock and aftershocks

This paper investigates long-period ground motion characteristic of the 1999 Jiji （Chi-Chi）, Taiwan, mainshock and aftershocks on the basis of lots of high quality digital strong motion records. The study attaches the importance to the variation of strength of the long-period ground motion with the magnitude, distance, and site condition. In the meantime, the near-fault long-period ground motion characteristic is analyzed. The result shows that the shape of the long-period response spectrum is mainly controlled by site condition and magnitude （the spectrum of class D＋E is wider than that of class B＋C, and the spectrum of larger magnitude is wider than that of smaller magni- tude）, and the effect of fault distance on the shape is not evident. And near-fault long-period ground motion characteristic depends on fault activity apparently, that is to say, the long-term ground motion in the hanger is stronger than that in the footwall, and the long-term ground motion in the north is stronger than that in the south.

波浪作用下小尺度多船并排锚泊横摇运动试验研究

采用物理模型试验方法研究双船、三船和四船并排锚泊时各船的运动量,并与单船艏艉锚泊情况进行了对比,重点分析了横浪作用下各船的横摇运动规律,探究了波浪周期和并排锚泊船数对多船并排锚泊时横摇运动的影响。结果表明,多船并排锚泊时,横摇运动响应随着波浪周期的增大而逐渐减小。双船并排锚泊时,横摇运动响应同单船相比减少了40%~50%;三船和四船并排锚泊时,横摇运动响应同单船相比减少50%~60%,四船并排锚泊时横摇运动响应减小的幅度与三船并排时相比差别不大。