Lie Symmetries and Conserved Quantities of Systems of Relative Motion Dynamics

Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equaiton of the Lie symmetries for the dynamical equationS of relative motion is established.The structure quation and the form conserved quantities are obtained. An example iD illustrate the application of the result is given.

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.

Perturbation to Symmetries and Adiabatic Invariants of Nonholonomic Dynamical System of Relative Motion

Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic dynamical system of relative motion are studied. The perturbation to symmetries for the nonholonomic dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.

Noether Symmetry and Noether Conserved Quantity of Nielsen Equation for Dynamical Systems of Relative Motion

Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given. Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained. Finally, an example is given to illustrate the application of the results.

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.

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.

Effect of carbonation-drying-wetting on durability of coral aggregate seawater concrete

Based on the drying-wetting cycles experiment and the carbonation-drying-wetting cycles experiment for coral aggregate seawater concrete(CASC)with different strength grades,the effects of carbonation-drying-wetting on the durability of CASC are studied with the surface state,mass loss rate,relative dynamic elastic modulus,ultrasonic wave velocity and cube compressive strength as indices.Results show that the mass loss rate of CASC increases gradually with the increase in cycle times in the drying-wetting and carbonation-drying-wetting cycles.The mass loss rate increases relatively slowly at the initial stage but it increases remarkably after 10 cycles.The relative dynamic elastic modulus and ultrasonic wave velocity decrease gradually with the increase in cycle times.After 6 cycles,the decrease rate of the relative dynamic elastic modulus and ultrasonic wave velocity of CASC tends to be flat and the surface is slightly damaged.Compared with the initial 28 d cube compressive strength,the cube compressive strength of CASC decreases by 8.8%to 11.0%.Drying-wetting cycles and carbonation can accelerate seawater erosion on CASC,and drying-wetting cycles result in salting-out and accelerate the destruction of concrete.Therefore,the carbonation-drying-wetting accelerates the destruction of CASC.

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.

Mechanical properties of cement mortar in sodium sulfate and sodium chloride solutions

To investigate the mechanical properties of cement mortar in sodium sulfate and sodium chloride solutions, uniaxial compression test and ultrasonic test were performed. Test results show that the relative dynamic elastic modulus, the mass variation,and the compressive strength of cement mortar increase first, and then decrease with increasing erosion time in sodium sulfate and sodium chloride solutions. The relative dynamic elastic moduli and the compressive strengths of cement mortars with water/cement ratios of 0.55 and 0.65 in sodium sulfate solution are lower than those in sodium chloride solution with the same concentration at the420 th day of immersion. The compressive strength of cement mortar with water/cement ratio of 0.65 is more sensitive to strain rate than that with water/cement ratio of 0.55. In addition, the strain-rate sensitivity of compressive strength of cement mortar will increase under attacks of sodium sulfate or sodium chloride solution.

Relative Attitude Dynamics and Control of Spacecraft Formation Flying Considering Flexible Panels

As a key technology for orbital applications, researches on spacecraft formation flying(SFF) attract more attention. However, most of existing researches about dynamics and control of SFF focus on rigid spacecrafts without considering the effect of flexible attachments(such as flexible panels). In this paper, relative attitude dynamics and active control of SFF for a flexible spacecraft(follower spacecraft) and a rigid spacecraft(target spacecraft) are investigated. Firstly, a dynamic model of the flexible spacecraft is established by the principle of angular momentum. Then, the equation of relative attitude dynamics between the flexible spacecraft and the rigid spacecraft is derived by the quaternion to represent the attitude relation of the two spacecrafts. Finally,an attitude feedback controller is designed for the SFF system, and its stability is proved by the Lyapunov stability theory. Simulation results indicate that the panel flexibility has an obvious influence on the dynamic behaviour of the system, the designed controller can effectively control the attitude of the two spacecrafts to achieve synchronization, and the elastic vibration of the panels may be suppressed simultaneously.

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.