Expression of strain and rotation tensor in geodetic coordinates

In this paper, unit moving trihedron is first constructed for a point on the surface of a revolution ellipsoid. Via translation, the origin of the trihedron coincides with that of Cartesian coordinates established at the center of the ellipsoid, and then through two coordinate rotations, the trihedron completely coincides with the Cartesian coordinates. Transformation formulae between the moving trihedron and unit Cartesian coordinate frameworks as well as transformation of point displacement between two unit coordinate frameworks are presented. Based on the above transformation formulae between two different coordinate frameworks, due to the fact that the displacement and moving trihedron of the point are both functions of the geodetic coordinates, components in the corresponding axis for differential of displacement vector and geodetic curves arc differential at the point in geodetic system can be obtained through complicated derivation. Displacement gradient matrix at the point in geodetic system is also given. Finally, expressions of strain and rotation tensor in geodetic coordinates are presented. Geometric meanings of the rotation tensor are explained in detail. The intrinsic relationship between strain tensors of sphere and ellipsoid are also discussed.

Complex coordinate rotation method based on gradient optimization

In atomic,molecular,and nuclear physics,the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states.Here,we propose a novel implementation of this method based on the gradient optimization(CCR-GO).The main strength of the CCR-GO method is that it does not require manual adjustment of optimization parameters in the wave function;instead,a mathematically well-defined optimization path can be followed.Our method is proven to be very efficient in searching resonant positions and widths over a variety of few-body atomic systems,and can significantly improve the accuracy of the results.As a special case,the CCR-GO method is equally capable of dealing with bound-state problems with high accuracy,which is traditionally achieved through the usual extreme conditions of energy itself.

Reference Coordinate System of Nonlinear Beam Element Based on the Geometrically Exact Formulation under Large Spatial Rotations and Deformations

Analysis of slender beam structures in a three-dimensional space is widely applicable in mechanical and civil engineering. This paper presents a new procedure to determine the reference coordinate system of a beam element under large rotation and elastic deformation based on a newly introduced physical concept: the zero twist sectional condition, which means that a non-twisted section between two nodes always exists and this section can reasonably be regarded as a reference coordinate system to calculate the internal element forces. This method can avoid the disagreement of the reference coordinates which might occur under large spatial rotations and deformations. Numerical examples given in the paper prove that this procedure guarantees the numerical exactness of the inherent formulation and improves the numerical efficiency, especially under large spatial rotations.

Effects of Coordinate Rotation on Turbulent Flux Measurements during Wintertime Haze Pollution in Beijing, China

Eddy-covariance observations from the Beijing 325-m meteorological tower are used to evaluate the effects of coordinate rotation on the turbulent exchange of momentum and scalars during wintertime haze pollution(January-February 2013). Two techniques are used in the present evaluation; namely, the natural wind coordinate(NWC) and the planar fit coordinate(PFC), with the latter being applied by means of two methods for linear regression(i.e., overall and sector-wise). The different techniques show a general agreement in both turbulent fluxes and transport efficiencies, especially evident at the lower, 140-m level above the ground(compared to the higher, 280-m level), perhaps implying that the selection of a technique for coordinate rotation(NWC or PFC) is less of a concern for a sufficiently low level, despite the complexities of urban terrain. Additionally, sector-wise regression is a recommended approach for practical application of the PFC in a complex urban environment subjected to particulate pollution, because this method is found to produce a better correlation between the mean vertical velocity at the 140- and 280-m heights.

Novel Method for Spatial Angle Measurement Based on Rotating Planar Laser Beams

Spatial angle measurement, especially the measurement of horizontal and vertical angle, is a basic method used for industrial large-scale coordinate measurement. As main equipments in use, both theodolites and laser trackers can provide very high accuracy for spatial angle measurement. However, their industrial applications are limited by low level of automation and poor parallelism. For the purpose of improving measurement efficiency, a lot of studies have been conducted and several alternative methods have been proposed. Unfortunately, all these means are either low precision or too expensive. In this paper, a novel method of spatial angle measurement based on two rotating planar laser beams is proposed and demonstrated. Photoelectric receivers placed on measured points are used to receive the rotating planner laser signals transmitted by laser transmitters. The scanning time intervals of laser planes were measured, and then measured point＇s horizontal/vertical angles can be calculated. Laser plane＇s angle parameters are utilized to establish the abstract geometric model of transmitter. Calculating formulas of receiver＇s horizontal/vertical angles have been derived. Measurement equations＇ solvability conditions and judgment method of imaginary solutions are also presented after analyzing. Proposed method for spatial angle measurement is experimentally verified through a platform consisting of one laser transmitter and one optical receiver. The transmitters used in new method are only responsible for providing rotating light plane signals carrying angle information. Receivers automatically measure scanning time of laser planes and upload data to the workstation to calculate horizontal angle and vertical angle. Simultaneous measurement of multiple receivers can be realized since there is no human intervention in measurement process .Spatial angle measurement result indicates that the repeatable accuracy of new method is better than 10＂. Proposed method can improve measurement＇s automation degree and speed while ensuring measurement accuracy.

Disturbance observer based finite-time coordinated attitude tracking control for spacecraft on SO(3)

To solve the problem of attitude synchronization control for spacecraft formation flying(SFF)suffering from external disturbances under a directed communication topology,a sliding mode disturbance observer(SMDO)based on the finite-time control strategy is developed to observe the time-varying external disturbance via estimating the upper bound of its first derivative.Meanwhile,the rotation matrix is employed to describe the attitude of SFF for the purpose of the avoidance of singularity and unwinding phenomenon.As for the attitude synchronization and the tracking control architecture,a sliding mode surface(SMS)is given such that the control objective can be achieved.The effectiveness and the validity of the proposed method are elaborated via theoretical analysis and numerical simulations.

The Establishment of the Projections of Four to Seven-Dimensional Rectangular Coordinate Systems into the Three-Dimensional Space

Starting from the finite rotation group,the author makes a penetrating study of 4 to 7-dimensional hypercube so that we have acquired the projection models of 4 to 7-dimeneional spatial rectangular coordinate systems into the three-dimensional space to have the 4 to 7-dimensional geometric figures demonstrated correctly.

GNSS广播ERP参数评估

中国北斗卫星导航系统(BeiDou Navigation Satellite System,BDS)、美国GPS、日本准天顶卫星系统(Quasi-Zenith Satellite System,QZSS)、印度区域导航卫星系统(Indian Regional Navigation Satellite System,IRNSS)等系统在导航电文中播发了地球自转参数(earth rotation parameter,ERP),即极移和世界时(Universal Time,UT)-协调世界时(Universal Time Coordinated,UTC)(ΔUT1).广播ERP主要用于需要在地球参考系和惯性参考系之间转换的GNSS星载应用,如卫星精密定轨、地月导航等.通过国际GNSS服务(International GNSS Service,IGS)收集了BDS、GPS、QZSS、IRNSS的广播ERP数据,评估了各GNSS的广播ERP不连续性,得到GPS和IRNSS的极移不连续性为0.9~1.4 mas,ΔUT1不连续性约为0.2 ms;QZSS的极移不连续性约为0.1 mas,ΔUT1不连续性约为0.02 ms;BDS的极移不连续性约为4.5 mas,ΔUT1不连续性约为1.3 ms.通过与国际地球自转和参考系服务(International Earth Rotation Service,IERS)14C04序列比较显示,QZSS极移误差约为0.6 mas,ΔUT1误差约为0.27 ms;GPS和IRNSS的极移误差约为2.4 mas,对于ΔUT1,GPS误差约为0.36 ms,IRNSS的ΔUT1误差相差较大,约为10.47 ms;由于更新间隔较长,BDS极移误差约为6 mas,ΔUT1误差约为1.2 ms;与GPS相比,BDS极移与ΔUT1误差分别差了近1.5倍和2.5倍.

用于FPGA平台上图像快速旋转的改进CORDIC算法

坐标旋转数字算法(CORDIC)被广泛应用于消旋、相机边框等系统中。在对传统CORDIC算法分析的基础上提出了重编码预测和多倍迭代优化的方法,并用MATLAB进行了仿真,又在VIVADO上进行了FPGA验证与对比。实验结果表明,上述优化相对传统CORDIC算法以及VIVADO自带的CORDIC IP核显著减少了迭代次数,消耗了更少的资源,计算的精度也有了一定的提升。

双转台五轴数控机床旋转轴位置无关几何误差辨识

针对双转台五轴数控机床旋转轴几何误差辨识精度问题,提出一种在机床坐标系下的旋转轴位置无关几何误差(PIGEs)辨识模型。建立了刀具球与工件球在机床坐标系下的实际初始坐标,通过逆矩阵得到工件球在所测轴的实际初始位置,基于4种测量模式建立了包含球杆仪安装误差与旋转轴PIGEs的杆长变化量数学模型。仿真分析了PIGEs对测量模式的影响,结果表明刀具球在两旋转轴轴线交点位置时,平行度误差不影响球杆仪杆长变化量。最后,通过实验辨识出旋转轴8项PIGEs,并对旋转轴PIGEs的4项位置误差进行补偿。实验结果表明,补偿后的位置误差最大绝对值由203.5μm减小至5.1μm,所提出的辨识模型可以有效提高五轴机床精度。

一种避障场景下的快速航迹恢复算法

针对现有大部分避障场景中无人机避障算法未考虑无人机航迹恢复、少数航迹恢复算法恢复效果不佳的缺点,提出了一种避障场景下的无人机快速航迹恢复算法。综合考虑环境约束与无人机机动性能约束,通过旋转坐标系、判断无人机转弯方向、利用二分法对无人机整个避障及航迹恢复过程中的多个关键航迹点坐标进行计算,最终规划出一条安全高效的无人机避障及航迹恢复航迹。对比实验结果表明,快速航迹恢复算法规划出的避障及航迹恢复航迹更短,可以在距离障碍物更近的航迹点开始避障,避障及航迹恢复用时更短,航迹偏离度更小,整体航迹更优,对于绝大多数侦察场景中无人机需尽量保持沿离线航迹巡航的情况更加有利。

构网型风氢耦合系统电解槽轮值优化控制

针对制氢电解槽阵列能量分配效率偏低的问题,文中结合电解槽自身物理特性和整体系统要求,分析电解槽阵列输入功率与效率的耦合关系。构建多电解槽阵列的效率函数和约束条件,通过拉格朗日函数将其转化为无约束问题,以实现电解槽阵列功率自适应分配的控制,保证系统处于最优工作状态。在最优工作状态进行电解槽阵列轮值优化控制策略,提高电解槽的使用寿命。考虑风电功率波动情况,提出构网型直驱风电机组,提高并网点的电压和频率稳定性。最后通过MATLAB/Simulink搭建的风氢耦合模型进行验证,与传统能量分配方式相比,该方法可以明显提升电解槽阵列协调工作效率,同时也增加了电解槽的使用寿命,为风电的大规模制氢提供了有效途径。

基于共旋坐标法的钢悬链线立管管土作用数值分析

为分析钢悬链立管(SCR)在顶部浮体小范围垂降、侧向漂移运动下的立管触地段垂向、侧向管土作用,将立管初始贯入海床及侧向移动过程作为准静态问题,在共旋坐标框架内建立三维有限梁单元模型,并耦合p-y加载曲线模拟立管初始贯入海床过程,并对比了线性、双线性及非线性管土模型在计算管土响应上的差异,分析了立管顶部水平牵引载荷、海流作用及土体抗剪强度对立管触地段垂向管土作用的影响,进一步研究了浮体小范围漂移工况下的侧向牵引力、土体特性参数对立管触地段侧向、垂向组合的管土作用影响。结果表明:在共旋坐标框架下,非线性管土模型对立管贯入海床的响应模拟更准确;顶部水平牵引力及海流流速增大,均会导致立管贯入海床深度及垂向土阻力减小;土体抗剪强度增大导致立管贯入深度减小但垂向及侧向土阻力增大;顶部浮体侧向牵引力增大致使立管触地段的侧向位移及土阻力增大,但垂向土阻力减小;侧向摩擦系数的增大可显著提高立管触地段的侧向稳定性。本文所述共旋坐标法利用刚体与变形解耦的特性高效求解了立管全局运动及触地段的管土作用,为立管与海床作用研究提供了参考。

基于空间三维欧拉角估计的靶场外弹道数据处理方法研究

针对雷达测试远程飞行试验获取的外弹道数据在转换至炮位发射坐标系过程中,事后数据处理结果落点距离偏差较大的问题,提出了一种基于空间三维欧拉角的弹道数据处理方法,该方法估计雷达发射坐标系旋转至炮位发射坐标系的空间三维欧拉角,对雷达发射坐标系进行三轴方向的旋转,使其与炮位发射坐标系三轴指向在空间上方向一致,然后再进行坐标系平移,得到包含地球曲率因素的炮位发射坐标系数据处理结果。将该弹道数据处理方法得到的弹道落点,以及传统平移处理方法得到的弹道落点与真实落点的距离偏差分布情况进行对比分析,结果表明:基于空间三维欧拉角的数据处理落点偏差更小,落点数据精度更高,平均偏差缩小百分比达48.9%。本研究对于弹体的寻找、销毁与回收具有十分重要意义。

精密单点定位结果转换至CGCS2000坐标方法

为了解决精密单点定位结果存在坐标框架历元不明确、时间坐标基准不统一、使用速度场转换精度,导致难以应用到实际工程中的问题,分别采用全域七参数转换法、局域七参数转换法,以及使用点位速度进行转换的基线法、反距离加权法、欧拉矢量法对上海区域利用精密单点定位结果转换至CGCS2000坐标进行研究,并分析了其适用性。结果表明七参数方法精度略高于使用速度进行转换的方法,转换精度达到毫米级,可以满足实际工程中的需要,且局域七参数转换法精度略高于全域七参数转换法。使用速度进行转换的方法中基线法的转换精度最高,可以达到毫米级。在实际工程应用中推荐使用七参数转换方法将精密单点定位结果转换到CGCS2000坐标系下,以充分发挥精密单点定位技术的优势。

分布式能源接入交流微网的单相逆变器功率智能分配策略设计

逆变器并联并网系统往往通过两个逆变器通信分别控制进行并联并网,存在通信延迟、不稳定、传输效率低等问题,为此提出了一种分布式能源接入交流微网的单相逆变器功率智能分配策略设计。首先,建立了单相逆变器及并联系统的数学模型,并推导了其相关参数之间的函数关系,分析了并联系统中的环流现象,提出采用电势差均流方法来减小环流影响,在并联设计中,采用电压电流环循环控制实现逆变器组按任意比例分配电流;其次,采用SOGI-PLL进行锁相,使用电流环开闭环交替控制方式实现全桥逆变器组在无通信条件下功率智能分配;再次,设计仿真电路初步验证了所提出的SOGI控制实现锁相的正确性和快速性;最后,搭建了实验样机以验证方案可行性,实验结果表明,在输入50 V直流电压时,该系统可实现输出50 Hz、24 V交流电压,且输出交流电压总谐波畸变率(THD)不大于2%,逆变器1的效率η高达92%,I_(o)在0~2 A变化时,负载调整率S_(I1)≤0.2%,在并网状态下可实现逆变器之间功率按任意比例智能分配。

孔系零件FANUC 0i系统固定循环编程技巧及应用

孔系结构在板类、盘类及箱体类零件中应用广泛,为了简化孔系零件的编程,寻找出灵活、通用的孔系零件固定循环编程方法。介绍了孔加工固定循环的概念及指令格式后,以盖板圆周孔系、盘类零件圆周孔系及板类零件矩形阵列孔系为例,结合固定循环指令在直角坐标系、坐标系旋转、宏程序、增量、子程序等编程方法中的应用,总结出圆周孔系和矩形阵列孔系的通用编程模板,供企业生产加工参考使用。

低时延CORDIC算法设计与ASIC实现

传统流水线CORDIC(Coordinate Rotation Digital Computer,CORDIC)算法精度不高,输出延时较大,并且需要依靠剩余角度计算进行旋转方向的判断,占用较大的资源。针对以上问题,本文采用角度二极化重编码方法消除剩余角度计算,通过折叠角度区间将角度映射于区间[0,π/4]。结合查找表以及合并迭代技术,减少角度计算的迭代次数和硬件单元,降低输出时延,只需要3个周期就能完成CORDIC计算。使用结果重映射方法完成正弦和余弦的全象限实现。寄存器资源消耗为传统算法的35.37%,输出时延减少85%。基于180nm CMOS工艺,完成CORDIC算法的ASIC实现。正弦和余弦的平均绝对误差分别为2.5472×10^(-6)、1.9396×10^(-6),相比较于传统CORDIC算法,精度提升一个数量级。

Vorticity vector-potential method based on time-dependent curvilinear coordinates for two-dimensional rotating flows in closed configurations

In this study, a vorticity vector-potential method for two-dimensional viscous incompressible rotating driven flows is developed in the time-dependent curvilinear coordinates. The method is applicable in both inertial and non-inertial frames of reference with the advantage of a fixed and regular calculation domain. The numerical method is applied to triangle and curved triangle configurations in constant and varying rotational angular velocity cases respectively. The evolutions of flow field are studied. The geostrophic effect, unsteady effect and curvature effect on the evolutions are discussed.

Theoretical study of micro-optical structure fabrication based on sample rotation and two-laser-beam interference

A method for fabricating a micro-optical structure based on sample rotation and two-laser-beam interference is proposed. The rotation process is analyzed using the coordinate transformation in matrix presentation and the theoretical expressions of the optical field distributions corresponding to different sample rotations. By rotating the samples and changing the laser wavelength, various special micro-optical structures can be obtained, such as equally spaced concentric rings and irregular trapezoidal lattices; these structures are demonstrated by simulating the corresponding optical field distributions. The proposed approach may be developed into a low-cost laser interference lithography technology for the fabrication of various micro-optical structures.