Gauss Principle of Least Compulsion for Relative Motion Dynamics and Differential Equations of Motion

This paper focuses on Gauss principle of least compulsion for relative motion dynamics and derives differential equations of motion from it. Firstly, starting from the dynamic equation of the relative motion of particles, we give the Gauss principle of relative motion dynamics. By constructing a compulsion function of relative motion, we prove that at any instant, its real motion minimizes the compulsion function under Gaussian variation, compared with the possible motions with the same configuration and velocity but different accelerations. Secondly, the formula of acceleration energy and the formula of compulsion function for relative motion are derived because the carried body is rigid and moving in a plane. Thirdly, the Gauss principle we obtained is expressed as Appell, Lagrange, and Nielsen forms in generalized coordinates. Utilizing Gauss principle, the dynamical equations of relative motion are established. Finally, two relative motion examples also verify the results' correctness.

Conformal invariance and conserved quantities of dynamical system of relative motion

This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.

Special Lie symmetry and Hojman conserved quantity of Appell equations in a dynamical system of relative motion

Special Lie symmetry and the Hojman conserved quantity for Appell equations in a dynamical system of relative motion are investigated. The definition and the criterion of the special Lie symmetry of Appell equations in a dynamical system of relative motion under infinitesimal group transformation are presented. The expression of the equation for the special Lie symmetry of Appell equations and the Hojman conserved quantity, deduced directly from the special Lie symmetry in a dynamical system of relative motion, are obtained. An example is given to illustrate the application of the results.

Poisson theory and integration method for a dynamical system of relative motion

This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if （2n-1） first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.

Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints

Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.

Mei symmetry and Mei conserved quantity of the Appell equation in a dynamical system of relative motion with non-Chetaev nonholonomic constraints

The Mei symmetry and the Mei conserved quantity of Appell equations in a dynamical system of relative motion with non-Chetaev nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and the criterion of the Mei symmetry,and the expression of the Mei conserved quantity deduced directly from the Mei symmetry for the system are obtained.An example is given to illustrate the application of the results.

Brine-freeze-thaw Durability and Crack Density Model of Concrete in Salt Lake Region

The brine-freeze-thaw durability (defined as the durability under freeze-thaw cycles in Qinghai salt lake brine) of concrete (ordinary Portland cement concrete (OPC), high performance concrete (HPC-a), high performance concrete with steel fiber (HPC-b), and high performance concrete with high Young's modulus polyethylene fiber (HPC-c)) was systematically investigated by the relative dynamic elastic modulus, the relative mass, the appearance, the scanning electron microscopy, and the X-ray diffraction. In addition, the low-temperature physical and chemical corrosion mechanism and a crack density model after the modified relative dynamic elastic modulus being taken into consideration were proposed. The results show that the deterioration of OPC is the severest, followed by HPC-a, HPC-c and HPC-b. The admixture or the fiber is mixed into concrete, which can improve the brine-freeze-thaw durability of concrete. The critical mass growth of the failure of concrete is 3.7%. The cause of the deterioration of concrete under the brine-freeze-thaw cycles is physical and chemical corrosion, not freezing and thawing. The crack density model can effectively describe the deterioration evolution of concrete.

Evaluating Deterioration of Concrete by Sulfate Attack

Effects of factors such as water to cement ratio, fly ash and silica fume on the resistance of concrete to sulfate attack were investigated by dry-wet cycles and immersion method. The index of the resistance to sulfate attack was used to evaluate the deterioration degree of concrete damaged by sulfate. The relationship between the resistance of concrete to sulfate attack and its permeability/porosity were analyzed as well as its responding mechanism. Results show that the depth of sulfate crystal attack from surface to inner of concrete can be reduced by decreasing w/c and addition of combining fly ash with silica fume. The variation of relative elastic modulus ratio and relative flexural strength ratio of various specimens before and after being subjected to sulfate attack was compared.

Operational Evaluation of the Quantitative Precipitation Estimation by a CINRAD-SA Dual Polarization Radar System

In this paper,a quantitative precipitation estimation based on the hydrometeor classification(HCA-QPE)algorithm was proposed for the first operational S band dual-polarization radar upgraded from the CINRAD/SA radar of China.The HCA-QPE algorithm,localized Colorado State University-Hydrometeor Identification of Rainfall(CSUHIDRO)algorithm,the Joint Polarization Experiment(JPOLE)algorithm,and the dynamic Z-R relationships based on variational correction QPE(DRVC-QPE)algorithm were evaluated with the rainfall events from March 1 to October 30,2017 in Guangdong Province.The results indicated that even though the HCA-QPE algorithm did not use the observed rainfall data for correction,its estimation accuracy was better than that of the DRVC-QPE algorithm when the rainfall rate was greater than 5 mm h-1;and the stronger the rainfall intensity,the greater the QPE improvement.Besides,the HCA-QPE algorithm worked better than the localized CSU-HIDRO and JPOLE algorithms.This study preliminarily evaluated the improved accuracy of QPE by a dual-polarization radar system modified from CINRAD-SA radar.

Attitude control of spacecraft during propulsion of swing thruster

As for orbit transfer vehicle (OTV) with multiple satellites/payloads carried,the release of each payload will bring serious change to the mass center of OTV and the thrust produced by the swing thruster will form a rather large disturbance to the attitude of OTV. Steering the nozzle to track the estimated center of mass (ECM) of OTV can reduce but not remove the disturbance due to the difference between the ECM and the practical mass center (PCM) of OTV. The practical propelling direction will change with the internal motion during the propulsion process and attitude control system should be enabled to guarantee that the propelling direction is collinear with the command. Since the structural parameters have changed,which is due to internal motion and fuel consumption,the dynamic model have to be formulated to determine these time-varying parameters and the required attitude of OTV should be determined as well. Modulating attitude quaternion results in quasi Euler angles. Based on the resulting quasi Euler angles,a novel attitude switching control law is introduced to control the variable-mass OTV. Simulation results show that,even in the case of structural asymmetry,control torque matrix asymmetry,attitude disturbance and strong coupling between the channels,the attitude of OTV can be controlled perfectly,and the proposed attitude control law is effective for the variable-mass OTV with swing thruster.

Test on dynamic characteristics of subgrade of heavy-haul railway in cold regions

Dynamic characteristics of heavy-haul railway subgrade under vibratory loading in cold regions are investigated via low-temperature dynamie triaxial tests with multi-stage eyelic loading process. The relationship between dynamic shear stress and dynamic shear strain of frozen soil of subgrade under train loading and the influence of freezing temperatures on dynamic constitutive relation, dynamic shear modulus and damping ratio are observed in this study. Test results show that the dynamic constitutive relations of the frozen soils with different freezing temperatures comply with the hyperbolic model, in which model parameters a and b decrease with increasing freezing temperature. The dynamic shear modulus of the frozen soils decreases with increasing dynamic shear strains initially, followed by a relatively smooth attenuation tendency, whereas increases with decreasing freezing temperatures. The damping ratios decrease with decreasing freezing temperatures. Two linear functions are defined to express the linear relationships between dynamic shear modulus （damping ratio） and freezing temperature, respectively, in which corresponding linear coefficients are obtained through multiple regression analysis of test data.

AXIAL HEAT CONDUCTION MODEL TO PREDICT MAXIMUM HEAT REMOVE OF MINIATURE HEAT PIPE BASED ON GREY MODEL THEORY

Computer chip is always accompanied by the increase of heat dissipation and miniaturization. The miniature heat pipes are widely used in notebook computer to resolve the heat dissipation problems. Maximum heat removed model of miniature heat pipes building by grey model is presented. In order to know the foundation for modeling, the smooth grade of error examination is inquired and the accuracy of grey relational grade is verified. The model can be used to select a suitable heat pipes to solve electric heat problems in the future. Final results show that the grey model only needs four experiment data and its error value is less than 10%, further, it is better than computational fluid dynamics （CFD） model.

Durability of Concrete with Different Improvement Measures and Its Ser-vice Life Prediction in Island and Reef Environment

To solve the durability of island and reef concrete engineering in the harsh environment of high temperature,high salt,high humidity and windy,the strength grade of concrete and the type of corrosion inhibitor were used as the influence factors,while the relative dynamic elastic modulus was used as the evaluation index.In addition,the law and time variability of the deterioration of concrete,the size effect,environmental similarity and the service life model were studied.The results showed that improving the strength grade of concrete could improve the durability of concrete,and corrosion inhibitor could slightly improve the durability of concrete.Time-varying law of the deterioration of concrete conformed to the univariate quadratic polynomial.Combined with the concrete damage equivalent theory,a size effect model based on the relative dynamic elastic modulus was proposed and verified,and the size effect coefficient was also given.An environmental similarity model between simulated and practical island and reef environment was proposed.Combined with the reliability theory and the first order second moment method,a new service life model of concrete structure was proposed.The authors were convinced that the research will be advantageous to researchers.

Dynamic Magma Conduit System Related to the Jinchuan Ni-Cu Sulfide Deposit,NW China

The Jinchuan Ni-Cu sulfide deposits,NW China,are hosted in small ultramafic intrusions that were emplaced into Paleoproterozoic metamorphic rocks. The ultramafic intrusions were previously thought to be the segments of a single elongate intrusion that was dismembered by late faults into eastern and western portions,each of which have distinct stratigraphic sequences.

Survey of orbital dynamics and control of space rendezvous

Rendezvous orbital dynamics and control （RODC） is a key technology for operating space rendezvous and docking missions. This paper surveys the studies on RODC. Firstly, the basic relative dynamics equation set is introduced and its improved versions are evaluated. Secondly, studies on rendezvous trajectory optimization are commented from three aspects： the linear rendez- vous, the nonlinear two-body rendezvous, and the perturbed and constrained rendezvous. Thirdly, studies on relative navigation are briefly reviewed, and then close-range control methods including automated control, manual control, and telecontrol are analyzed. Fourthly, advances in rendezvous trajectory safety and robust analysis are surveyed, and their applications in trajectory optimization are discussed. Finally, conclusions are drawn and prospects of studies on RODC are presented.

Freeze-thaw Resistance of Concrete in Seawater

The effect of freeze-thaw cycles in seawater on the performance of concrete was studied in this paper. Concrete samples with different water binder ratio and different component were prepared,and were then put into fresh water and synthesized seawater. After the experiments of freeze-thaw cycles,the mass loss,relative dynamic elastic modulus (RDEM) and compressive strength of each sample were tested. The results obtained reveal that with the increase of the water binder ratio,the resistance ability of freeze-thaw impact in seawater of concrete decrease dramatically. When the concrete contain 15% fly ash and 20% slag,its resistance ability to the freeze-thaw impact in seawater is the optimal. Compared to the seawater corrosion,the impact of freeze-thaw cycles to the properties of concrete is severer.

Dynamic compressive behavior and constitutive relations of lanthanum metal

The dynamic compressive behavior and constitutive relations of Lanthanum（La） metal was determined by using the first compression in split Hopkinson pressure bar（SHPB） tests at different strain rates and temperatures.The constitutive relation of La metal determined in a certain range of strains was employed and adjusted in numerically simulating large deformations of La metal specimens generated by multi-compression in SHPB tests and recorded by a high-speed camera.The dynamic compressive behavior and constitutive relations of La metal under multiple SHPB tests loading was also revealed.The results of scanning electron microscope（SEM） investigation of the recovered La metal specimens for typical tests showed that there was a variety of deformation microstructures depending on strain rate,temperature and stress state.