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.

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.

Numerical study on three-dimensional flow field of continuously rotating detonation in a toroidal chamber

Gaseous detonation propagating in a toroidal chamber was numerically studied for hydrogen/oxygen/nitrogen mixtures. The numerical method used is based on the three-dimensional Euler equations with detailed finiterate chemistry. The results show that the calculated streak picture is in qualitative agreement with the picture recorded by a high speed streak camera from published literature. The three-dimensional flow field induced by a continuously rotating detonation was visualized and distinctive features of the rotating detonations were clearly depicted. Owing to the unconfined character of detonation wavelet, a deficit of detonation parameters was observed. Due to the effects of wall geometries, the strength of the outside detonation front is stronger than that of the inside portion. The detonation thus propagates with a constant circular velocity. Numerical simulation also shows three-dimensional rotating detonation structures, which display specific feature of the detonation- shock combined wave. Discrete burning gas pockets are formed due to instability of the discontinuity. It is believed that the present study could give an insight into the interest- ing properties of the continuously rotating detonation, and is thus beneficial to the design of continuous detonation propulsion systems.

Analytical solution for the time-fractional heat conduction equation in spherical coordinate system by the method of variable separation

In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system.The method of variable separation is used to solve the timefractional heat conduction equation.The Caputo fractional derivative of the order 0 〈 α≤ 1 is used.The solution is presented in terms of the Mittag-Leffler functions.Numerical results are illustrated graphically for various values of fractional derivative.

A Co(Ⅱ) Coordinated Polymer with 2-Fold Interpenetration 3D Architecture Based on 5-(Imidazol-1-ylmethyl)isophthalate: Hydrothermal Synthesis, Crystal Structure and Properties

One cobalt coordinated polymer with 2-fold parallel interpenetration 3D architecture based on flexible 5-（imidazol-1-ylmethyl）isophthalate （L2-） as a main ligand and 4,4＇-bipyridine （bpy） as a nitrogen-containing ancillary ligand, {[CoL（bpy）0.5（H2O）3]2}n （1）, has been obtained under hydrothermal conditions and characterized by elemental analysis, powder X-ray diffraction （PXRD）, IR spectra, Uv/vis spectra, thermal gravimetric analyses （TGA） and single-crystal X-ray diffraction. It crystallizes in monoclinic, space group C2/c with a = 26.323（4）, b = 14.696（2）, c = 26.630（4） A, β= 157.747（4）°, V = 3901.2（1） A3, Z = 8, Mr= 435.27, Dc = 1.480 g/cm3, /t= 0.923 mm^-1, Rint = 0.0900, F（000） = 1792, the final R= 0.0722 and wR = 0.0946 for 3641 observed reflections （I 〉 2tr（/））. Complex 1 exhibits a two-fold interpenetration 3D framework. As a single net of the 2-fold interpenetration structure, the L2- anion of complex 1, as a bridging ligand, connects the Co（Ⅱ） ion to form two-dimensional layers （Co3L3）n which are further linked to build a three-dimensional framework by bpy ligand.

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.

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.

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.

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.

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.

Deployment dynamics of a simplified spinning IKAROS solar sail via absolute coordinate based method

The spinning solar sail of large scale has been well developed in recent years. Such a solar sail can be considered as a rigid-flexible multibody system mainly composed of a spinning central rigid hub, a number of flexible thin tethers, sail membranes, and tip masses. A simplified interplanetary kite-craft accelerated by radiation of the Sun （IKAROS） model is established in this study by using the absolute-coordinate-based （ACB） method that combines the natural coordinate formulation （NCF） describing the central rigid hub and the absolute nodal coordinate formulation （ANCF） describing flexible parts. The initial configuration of the system in the second-stage deployment is determined through both dynamic and static analyses. The huge set of stiff equations of system dynamics is solved by using the generalized-alpha method, and thus the deployment dynamics of the system can be well understood.

A New Luminescent Cd(Ⅱ) Coordination Polymer Constructed with 2-(Carboxymethoxy) benzoic Acid

In this work, we synthesized a new Cd（Ⅱ） coordination polymer, [Cd（L）(cmb)H;O]· H;O（1）, by using mixed 2-（carboxymethoxy）benzoic acid（H2 cmb） and typical chelating N-donor ligands 2-（2-fluoro-6-fluorophenyl）-1 H-imidazo[4,5-f][1,10]phenanthroline ligand（L）. 1 crystallizes in monoclinic, space group P21/c with a = 17.6150（8）, b = 9.7811（4）, c = 18.1603（8） ?, β = 118.9150（10）o, V = 2738.9（2） ?;, Z = 4, C28 H20 CdF2 N4 O7, Mr = 674.88, Dc = 1.637 g/cm3, F（000） = 1352, μ（Mo Ka） = 0.865 mm–1, R = 0.0643 and w R = 0.1976. In 1, the cmb2– anions link neighboring Cd（Ⅱ） atoms in a bis-chelating mode, yielding a one-dimensional chain structure along the b axis. The L ligands are attached on one side of the chain through chelating the Cd（Ⅱ） atoms, and are stacked with those of an adjacent chain through π-π interactions to generate a one-dimensional double-chain structure. Furthermore, the one-dimensional double-chains are stacked by C–H???π interactions between the carbon atom of L ligand and the benzene ring of cmb2–ligand to give a layer structure. Moreover, the solid state luminescent property of 1 was also investigated at room temperature.

1D Lanthanide Coordination Polymers Based on 3-(Pyridin-4-yl)benzoic Acid: Syntheses, Structures and Luminescent Properties

ABSTRACT Four novel 1D lanthanide coordination polymers with formula [Ln（3,4-pybz）3（HzO）2. H2O]n （Ln = 1 Sm; 2 Eu; 3 Tb; 4 Dy, 3,4-Hpybz = 3-（pyridin-4-yl）benzoic acid） have been synthesized by hydrothermal reactions of lanthanide oxide and 3-（pyridine-4-yl） benzoic acid. Single-crystal X-ray diffraction shows that the four compounds are isostructural. They all crystallize in a monoelinic system, space group P1^-. They have a doubly carboxylate-bridged infinite-chain structure with alternating Ln-（carboxylate）2-Ln linkages and one chelating carboxylate group on each metal center. The Ln ion also combines to two water molecules to form an eight-coordinate square antiprismatic geometry. The pyridine nitrogen atoms of the ligand do not coordinate to the metal centers but direct the formation of a 3D network through hydrogen bonding with coordinated water molecules. The photoluminescent properties of 2 and 3 have been also studied.

Crystal Structure, Thermal Behavior and Luminescence of a New Copper Coordination Polymer Constructed with 4-(Carboxymethoxy)-benzoic Acid

A new Cu(Ⅱ) coordination polymer, [Cu(L1)(L2)](1), was synthesized under hydrothermal conditions(H_2L1 = 4-(carboxymethoxy)benzoic acid, L2 = 2-(4-fluorophenyl)-1 H-imidazo[4,5-f][1,10]phenanthroline). Crystallographic data for 1: triclinic, space group P1 with a = 9.750(5), b = 10.148(5), c = 12.869(5) ?, α = 104.904(5), β = 102.133(5), γ = 95.219(5)°, V = 1188.7(10) ?~3, Z = 2, C_(28)H_(17)FN_4O_5Cu, Mr = 572.01, D_c = 1.598 g/cm^3, F(000) = 582, μ(MoKa) = 0.977 mm^(-1), R = 0.0474 and w R = 0.1144. The TGA behaviors and luminescence of 1 have been studied in detail. The L1 dianions link neighboring Cu(Ⅱ) atoms in a bis-chelating mode, yielding a one-dimensional chain structure along the b axis. The L2 ligands are attached on one side of the chain through chelating the Cu(Ⅱ) atoms, and are stacked with those of an adjacent chain through π-π interactions, yielding a layer structure. Additionally, the N–H???O hydrogen bonds further stabilize the structure of 1.

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.

Synthesis, Structure and Photoluminescence of a New Cd(Ⅱ) Coordination Polymer Based on 4-(Carboxymethoxy)-benzoic Acid and 1,10-Phenanthroline Derivative

A new ID coordination polymer, [Cda（L1）2（L2）2].H2O （1, H2L1 = 4-（carboxy- methoxy）benzoic acid and L2 = 2-（4-fluorophenyl）-I H-imidazo[4,5-f][1,10]phenanthroline）, has been hydrothermally synthesized and characterized by elemental analysis and single-crystal X-ray diffraction. It crystallizes in triclinic, space group P1 with a = 9.985（5）, b = 10.768（5）, c = 12.512（5） A, a = 68.959（5）, β = 80.354（5）, γ = 79.663（5）°, V= 1227.4（10） A3, Z = 1, C56H36Cd2F2N8O11, Mr = 1259.73, Dc = 1.704 g/cm3, F（000） = 630, μ（MoKa） = 0.949 mm-1, R = 0.0261 and wR = 0.0655. The L1 anions link the neighboring Cd（II） atoms to form a 1D double chain structure. The L2 ligands are alternately located on both sides of the double chains. More interestingly, the lateral L2 ligands from adjacent double chains are paired to furnish strong π-π interactions, yielding a 2D supramolecular layer. N-H...O, O-H...N and O-H...O hydrogen bonds further stabilize the structure of 1. The luminescent property of 1 was studied in solid state at room temperature.

A New Cadmium(Ⅱ) Coordination Polymer Constructed by 2-(2-Chloro-6-fluorophenyl)-1H-imidazo[4,5-f][1,10]phenanthroline and 1,2,3-Benzenecarboxylate: Synthesis, Structure and Luminescence

A new Cd（II） coordination polymer, namely, [Cd3（1,2,3-BTC）2（L）2]·2.25H2O （1, L = 2-（2-chloro-6-fluorophenyl）-1H-imidazo[4,5-A][1,10]phenanthroline and 1,2,3-BTC = 1,2,3-ben- zenetricarboxylate）, has been synthesized under hydrothermal conditions. The compound was characterized by single-crystal X-ray diffraction. It crystallizes in triclinic, space group Pī with α = 11.650（2）, b = 12.240（2）, c = 19.760（4） A, α = 72.01（3）, β = 77.11（3）, γ = 83.48（3）°, V = 2609.4（9） A3, Z = 2, C56H31Cd3Cl2F2N8O14.25, Mr = 1489.99, Dc = 1.896 g/cm3, F（000） = 1466, μ（MoKa） = 1.401 mm^-1, R = 0.0401 and wR = 0.1104. Compound 1 shows a 1D chain structure, and the neigh- boring 1D chains of 1 are joined together by π···π interactions to result in a 2D supramolecular layer. In addition, the luminescent property of 1 has been studied in the solid state at room temperature.

Starting flow in a rotating parallel plate channel

The starting flow due to a suddenly applied pressure gradient in a parallel plate channel which is rotating as a system is studied. Exact analytic series solutions to the unsteady Navier-Stokes equations are found by both the Laplace transform method and the separation of parameters method, the latter is shown to be superior. Rotation not only induces a secondary transverse flow but also alters the character of the transient flow rate and velocity profiles. Back flow and inertial oscillations occur, especially at higher rota- tion rates.

A New Co(Ⅱ) Coordination Polymer Based on a Flexible 1,4-Cyclohexanedicarboxylic Acid: Synthesis, Structure and Thermal Behavior

A new Co（Ⅱ） coordination polymer, [Co（1,4-chdc）（L）（H2O）]n（1）, was synthesized under hydrothermal condition（1,4-H2chdc = 1,4-cyclohexanedicarboxylic acid, L = 2-（4-fluoro-phenyl）-1 H-imidazo[4,5-f][1,10]phenanthroline）. Its crystal structure was determined by single-crystal X-ray diffraction. 1 crystallizes in triclinic, space group P1 with a = 8.790（5）, b = 10.486（5）, c = 13.305（5） ?, α = 87.391（5）, β = 82.925（5）, γ = 81.841（5）o, V = 1204.2（10） ?3, Z = 2, C27H23FN4O5Co, Mr = 561.42, Dc = 1.548 g/cm3, F（000） = 578, μ（Mo Ka） = 0.769 mm-1, R = 0.0415 and wR = 0.1043. In 1, each 1,4-chdc anion bridges two neighboring Co（Ⅱ） atoms to give a chain structure. The L ligands are attached on one side of the chain through chelating the Co（Ⅱ） atoms, and are stacked with those of an adjacent chain through π-π interactions, yielding a double-chain structure. The double-chain structures are linked into a supramolecular layer structure through N–H···O hydrogen-bonding interactions between the adjacent double-chain structures. Moreover, the thermal behavior of 1 was also studied.

The Coupling Coordination Evolution Research of Economy - Ecology - Society System in Xinjiang：Based on the Interaction Perspective of Water Resources

Under the water resources perspective,coupling coordination of economy-ecology-society system in Xinjiang was taken as the research object. By building the coupling evaluation index system of the water resources-economy-ecology-society system,quantitative evaluation and analysis of the coupling coordination of the water resources-economy-ecology-society system from 2001 to 2014 were conducted. The results showed that benefit indexes of economic system and social system grew rapidly,while benefit indexes of water resources system and ecosystem fluctuated smoothly from 2001 to 2014; coupling state of the whole system was at rival stage,and coupling coordination was reluctant coordination type,and the coupling index was slightly higher than the coupling coordination index. Moreover,it showed that the more the coupling systems,the lower indices of coupling and the coupling coordination.