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.

简易烈度计记录的噪声水平评价:以泸定M_(S)6.8级地震为例

在我国地震预警和烈度速报系统中,烈度计被广泛使用。烈度计的频谱特征主要是通过检定实验室进行标定,但在破坏性地震中,烈度计响应特点缺少必要的研究分析。该文以2022年四川泸定M_(S)6.8级地震为例,对比分析了烈度计记录和强震仪记录在噪声水平、信噪比(signal-to-noise ratio,SNR)、高通滤波截止频率(f_(HP))取值以及有效周期范围(T_(max))方面的特点,综合评价了烈度计记录的频谱特征,分析了噪声影响。得到以下结论:在整个频域范围内,烈度计记录的SNR要比强震仪记录平均意义上低一个数量级,可以估计烈度计动态范围较强震仪大致低20 dB;烈度计记录的最佳f_(HP)取值相较于强震仪记录存在更大的不确定性,尤其是在竖直方向上;烈度计记录的最佳f_(HP)取值更大,反应谱T_(max)较传统强震仪记录在水平方向小1~2 s,在竖直方向小3 s左右。该研究结果有助于合理应用烈度计记录,服务地震学和地震工程学相关研究。

基于潮汐附加构造应力的2013年灯塔M_(S)5.1地震射出长波辐射变化分析

针对2013年1月23日辽宁灯塔M_(S)5.1地震,利用引潮力附加构造应力(Additional Tectonic Stress Caused By Tidal Force,ATSCTF)计算模型,计算得到震中位置(41.5°N,123.2°E)在地震前5周以及震后3周(2012年12月16日—2013年2月15日)的ATSCTF变化。地震发生时,ATSCTF垂直方向分量处于高相位点附近,显示引潮力对本次正断层走滑型地震具有诱发作用。以ATSCTF变化周期的各低相位点时间(2012年12月19日、2013年1月4日、2013年1月18日、2013年2月2日)数据分别为背景,各周期期后数据分别与背景逐日相减,计算研究区(36°N~46°N,118°E~128°E)范围内,National Oceanic and Atmospheric Administration(NOAA)卫星射出长波辐射数据(Outgoing Long Wave Radiation,OLR)在各ATSCTF周期时段分布及其变化。结果显示,无震的ATSCTF变化的A、B、D周期,震中附近OLR无变化;发震的ATSCTF变化的C周期,在空间上,该地区震前OLR仅震中及其南侧区域发生了显著连续升高变化过程,在时间上经历了初始微异常→异常加强→高峰→衰减→发震→平静的演化过程,与岩石应力加载—破裂经历:初始微动破裂→扩张破裂→应力闭锁→地震爆发→平静的力学演化过程中各阶段红外辐射特征一致;显示引潮力对处于临界状态的活动断层具有诱发作用,而OLR是地震构造应力应变过程辐射表征。

Accounting for Quadratic and Cubic Invariants in Continuum Mechanics–An Overview

The differential equations of continuum mechanics are the basis of an uncountable variety of phenomena and technological processes in fluid-dynamics and related fields.These equations contain derivatives of the first order with respect to time.The derivation of the equations of continuum mechanics uses the limit transitions of the tendency of the volume increment and the time increment to zero.Derivatives are used to derive the wave equation.The differential wave equation is second order in time.Therefore,increments of volume and increments of time in continuum mechanics should be considered as small but finite quantities for problems of wave formation.This is important for calculating the generation of sound waves and water hammer waves.Therefore,the Euler continuity equation with finite time increments is of interest.The finiteness of the time increment makes it possible to take into account the quadratic and cubic invariants of the strain rate tensor.This is a new branch in hydrodynamics.Quadratic and cubic invariants will be used in differential wave equations of the second and third order in time.

Confirmation of 24 h 50 min Lunar Periodicity, Apparently Inexplicable by Classical Factors, in Precession of Allais Pendulum

During 36 days the motion of two pendulums, which were restarted every hour, was continuously recorded. 869 “runs” were thus made, providing each time the precession during the run, as well as other parameters of the motion. Spectral analysis of precession and ellipticity revealed a lunar component of 24 h 50 min, which can only result from an astral action, through mechanisms yet to be discovered. Indeed, an analysis was carried out of the influence of all classical perturbing factors: direct or indirect action of classical gravity, temperature, Earth’s magnetic field, etc.… None of them can explain this component, given its amplitude and phase. Its amplitude excludes also an explanation by general relativity. This is consistent with a major result that Allais claimed to have obtained during each one of the six continuous one-month-long experiments he carried out from 1954 to 1960. The numerous and very precise data provided by an automatic alidade give additional information to those gathered by Allais. All that confirms all the scientific interest that there would be to resume long-duration pendulum observations on a much more important scale: continuous observations for at least 2 years, and if possible more.

Period-One Rotating Solutions of Horizontally Excited Pendulum Based on Iterative Harmonic Balance

In this study, the iterative harmonic balance method was used to develop analytical solutions of period-one rotations of a pendulum driven horizontally by harmonic excitations. The performance of the method was evaluated by two criteria, one based on the system energy error and the other based on the global residual error. As a comparison, analytical solutions based on the multi-scale method were also considered. Numerical solutions obtained from the Dormand-Prince method (ODE45 in MATLAB&#169) were used as the baseline for evaluation. It was found that under lower-level excitations, the multi-scale method performed better than the iterative method. At higher-level excitations, however, the performance of the iterative method was noticeably more accurate.

基于NaIO_(3)转化NaIO_(4)回用合成S-甘油醛缩丙酮及其寡聚研究

S-甘油醛缩丙酮是合成手性药物的重要中间体。以L-抗坏血酸为原料,经缩酮化,硼氢化钠还原,高碘酸钠氧化制得S-甘油醛缩丙酮,收率为46.8%;探讨了含碘酸钠母液转化成高碘酸钠以循环套用,回收率为83.90%;初步考察了S-甘油醛缩丙酮的聚合度与时间的关系,并推测其寡聚化合物的结构和反应机理;用^(1)H NMR、IR和LC-MS等对化合物结构进行表征。

1例藏族完全型Shone综合征患者的围术期护理

文章总结了1例藏族完全型Shone综合征患者的围术期护理经验。护理要点包括术前密切监测患者四肢血压,做好安全护理,预防晕厥、猝死等意外事件发生,术后加强肺康复护理,做好阶段性运动干预、疼痛护理、个体化饮食护理,同时全程做好多方位跨文化护理。经过精心治疗和护理,患者术后恢复良好,痊愈出院。

Progress of CACNA1S Gene and Hypokalemic Periodic Paralysis

CACNA1 S gene is the gene encoding L-type calcium channel αa-subunit. CACNA1 S gene mutations can cause hypokalemic periodic pa- ralysis （HOKPP）. The related research speculated that CACNA1 S gene was the candidate genes which affect meat quality traits. In the present ar- ticle, the biological characteristics of CACNA1 S gene, structure, genetic diseases and the research development were respectively reviewed so as to provide a reference for further research.

Noether's theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws

This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by E1-Nabulsi. First, the E1-Nabulsi dynamical model which is based on a fractional integral extended by periodic laws is introduced, and E1-Nabulsi-Hamilton＇s canoni- cal equations for non-conservative Hamilton system with holonomic or nonholonomic constraints are established. Second, the definitions and criteria of E1-Nabulsi-Noether symmetrical transformations and quasi-symmetrical transformations are presented in terms of the invariance of E1-Nabulsi-Hamilton action under the infinitesimal transformations of the group. Fi- nally, Noether＇s theorems for the non-conservative Hamilton system under the E1-Nabulsi dynamical system are established, which reveal the relationship between the Noether symmetry and the conserved quantity of the system.

What can the changes in shield resistance tell us during the period of shearer's cutting and neighboring shields' advance?

In order to determine the influence of shearer's cutting and neighboring shields' advance on the support resistance variation, leg pressure data of all 235 shields in the panel LW61 of Cumberland coal mine were analyzed. The results show that the relationship between the leg pressure increment and the distance from shield to front drum of shearer is a quadratic function and that the higher leg pressure increment before shield advance tends to be related to adverse roof conditions. In addition, the three proposed leg pressure increment-related parameters and the three traditional parameters(time-weighted average pressure, setting pressure, and final pressure) of approximately 32000 shield supporting cycles were calculated by a self-developed software package to analyze the correlation between them. The results show that there is a powerful connection between them, and that the three proposed leg pressure increment-related parameters could be used as the indexes to evaluate the interaction between shields and the roof, and to identify the periodic weighting.

Periodic Solutions for a Class of Neutral Functional Differential Equations with Distributed and Discrete Delays

Based on Krasnoselskii's fixed point theorem,matrix measure and functional analysis methods,some new sufficient conditions for the existence of periodic solutions of neutral functional differential equations with distributed and discrete delays are obtained. Moreover,we construct an example to illustrate the feasibility of our results.

Using a Grandfather Pendulum Clock to Measure the World’s Shortest Time Interval, the Planck Time (With Zero Knowledge of <i>G</i>)

Haug has recently introduced a new theory of unified quantum gravity coined “Collision Space-Time”. From this new and deeper understanding of mass, we can also understand how a grandfather pendulum clock can be used to measure the world’s shortest time interval, namely the Planck time, indirectly, without any knowledge of G. Therefore, such a clock can also be used to measure the diameter of an indivisible particle indirectly. Further, such a clock can easily measure the Schwarzschild radius of the gravity object and what we will call “Schwarzschild time”. These facts basically prove that the Newton gravitational constant is not needed to find the Planck length or the Planck time;it is also not needed to find the Schwarzschild radius. Unfortunately, there is significant inertia towards new ideas that could significantly alter our perspective on the fundamentals in the current physics establishment. However, this situation is not new in the history of science. Still, the idea that the Planck time can be measured totally independently of any knowledge of Newton’s gravitational constant could be very important for moving forward in physics. Interestingly, an old instrument that today is often thought of as primitive instrument can measure the world’s shortest possible time interval. No atomic clock or optical clock is even close to be able to do this.

Periodic Solution of n-Species Gilpin-Ayala Competition System with Impulsive Perturbations

The principle aim of this paper is to explore the existence of periodic solution of n-Species Gilpin-Ayala competition system with impulsive perturbations. Sufficient and realistic conditions are obtained by using Mawhin's continuation theorem of the coincidence degree. Further, some numerical simulations show that our model can occur in many forms of complexities including periodic oscillation and chaotic strange attractor.

Risk assessment of water security in Haihe River Basin during drought periods based on D-S evidence theory

The weights of the drought risk index （DRI）, which linearly combines the reliability, resiliency, and vulnerability, are difficult to obtain due to complexities in water security during drought periods. Therefore, drought entropy was used to determine the weights of the three critical indices. Conventional simulation results regarding the risk load of water security during drought periods were often regarded as precise. However, neither the simulation process nor the DRI gives any consideration to uncertainties in drought events. Therefore, the Dempster-Shafer （D-S） evidence theory and the evidential reasoning algorithm were introduced, and the DRI values were calculated with consideration of uncertainties of the three indices. The drought entropy and evidential reasoning algorithm were used in a case study of the Haihe River Basin to assess water security risks during drought periods. The results of the new DRI values in two scenarios were compared and analyzed. It is shown that the values of the DRI in the D-S evidence algorithm increase slightly from the original results of Zhang et al. （2005）, and the results of risk assessment of water security during drought periods are reasonable according to the situation in the study area. This study can serve as a reference for further practical application and planning in the Haihe River Basin, and other relevant or similar studies.

离散时间迭代的LCC-S型无线电能传输系统建模及稳定性分析

为了建立LCC-S型无线电能传输(WPT)系统的模型并分析其稳定性,采用离散时间迭代的思想,建立了开环控制模式下LCC-S型WPT系统的模型,该模型可以描述系统的连续动态特性。在此基础上,进一步推导了电压型比例积分控制LCC-S型WPT系统的离散时间迭代模型,同时利用Pade近似将延时时间纳入数字控制系统。基于雅可比矩阵特征根的稳定性分析评估了控制器参数、延时时间和主电路参数对系统稳定性的影响,准确预测了系统的稳定范围。同时利用特征根预测了系统不稳定时的振荡周期。然后,对稳定边界受控制器参数和主电路参数变化的影响进行了研究。此外,将LCC-S型WPT系统的EDF模型、GSSA模型和离散时间迭代模型进行临界稳定预测值的对比。最后,仿真和实验验证所建立模型和稳定性分析的正确性。

SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS FOR THE NON-NEWTONIAN FILTRATION EQUATIONS WITH NONLINEAR SOURCES AND A TIME-VARYING DELAY

This paper is concerned with the non-Newtonian filtration equations with non- linear sources and a time-varying delay. By an extension of Mawhin＇s continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results.

Factors influencing electromagnetic scattering from the dielectric periodic surface

The scattering characteristics of the periodic surface of infinite and finite media are investigated in detail.The Fourier expression of the scattering field of the periodic surface is obtained in terms of Huygens’ s principle and Floquet’s theorem.Using the extended boundary condition method(EBCM) and T-matrix method, the scattering amplitude factor is solved,and the correctness of the algorithm is verified by use of the law of conservation of energy.The scattering cross section of the periodic surface in the infinitely long region is derived by improving the scattering cross section of the finite period surface.Furthermore, the effects of the incident wave parameters and the geometric structure parameters on the scattering of the periodic surface are analyzed and discussed.By reasonable approximation, the scattering calculation methods of infinite and finite long surfaces are unified.Besides, numerical results show that the dielectric constant of the periodic dielectric surface has a significant effect on the scattering rate and transmittance.The period and amplitude of the surface determine the number of scattering intensity peaks, and, together with the incident angle, influence the scattering intensity distribution.

Existence and Multiplicity of Periodic solutions for the Non-autonomous Second-order Hamiltonian Systems

In this paper,we study the existence and multiplicity of periodic solutions of the non-autonomous second-order Hamiltonian systems■where T> 0.Under suitable assumptions on F,some new existence and multiplicity theorems are obtained by using the least action principle and minimax methods in critical point theory.