用求积分法来积分一类非完整系统的运动方程

文献[1]指出,如果有n个自由度的Hamilton系统有n个独立的、处于相互内旋的第一积分,即Lie代数可交换,那么它可用求积分法被积分出来.本文研究一类特殊的非完整系统,这些系统的运动方程可变换为Hamilton正则方程的形式.寻求系统的足够数量的第一积分,如果这些积分是独立的,并且是相互内旋的,那么上述用于研究完整系统的结果可应用于这类非完整系统,从而解决了一类非完整系统运动方程的求积分问题.

Conserved quantities from Lie symmetries for nonholonomic systems

This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

Dynamic modeling and analysis of 3-■RS parallel manipulator with flexible links

The dynamic modeling and solution of the 3-RRS spatial parallel manipulators with flexible links were investigated. Firstly, a new model of spatial flexible beam element was proposed, and the dynamic equations of elements and branches of the parallel manipulator were derived. Secondly, according to the kinematic coupling relationship between the moving platform and flexible links, the kinematic constraints of the flexible parallel manipulator were proposed. Thirdly, using the kinematic constraint equations and dynamic model of the moving platform, the overall system dynamic equations of the parallel manipulator were obtained by assembling the dynamic equations of branches. FtLrthermore, a few commonly used effective solutions of second-order differential equation system with variable coefficients were discussed. Newmark numerical method was used to solve the dynamic equations of the flexible parallel manipulator. Finally, the dynamic responses of the moving platform and driving torques of the 3-RRS parallel mechanism with flexible links were analyzed through numerical simulation. The results provide important information for analysis of dynamic performance, dynamics optimization design, dynamic simulation and control of the 3-RRS flexible parallel manipulator.

Equation of Motion of a Mass Point in Gravitational Field and Classical Tests of Gauge Theory of Gravity

A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton＇s second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.

Photo-Induced Ultrafast Electron Dynamics in Anatase and Rutile TiO_(2):Effects of Electron-Phonon Interaction

The photo-induced ultrafast electron dynamics in both anatase and rutile TiO_(2) are investigated by using the Boltzmann transport equation with the explicit incorporation of electron-phonon scattering rates.All structural parameters required for dynamic simulations are obtained from ab initio calculations.The results show that although the longitudinal optical modes significantly affect the electron energy relaxation dynamics in both phases due to strong Fr?hlich-type couplings,the detailed relaxation mechanisms have obvious differences.In the case of a single band,the energy relaxation time in anatase is 24.0 fs,twice longer than 11.8 fs in rutile.This discrepancy is explained by the different diffusion distributions over the electronic Bloch states and different scattering contributions from acoustic modes in the two phases.As for the multiple-band situation involving the lowest six conduction bands,the predicted overall relaxation times are about 47 fs and 57 fs in anatase and rutile,respectively,very different from the case of the single band.The slower relaxation in rutile is attributed to the existence of multiple rate-controlled steps during the dynamic process.The present findings may be helpful to control the electron dynamics for designing efficient TiO_(2)-based devices.

Envelope Solitons Perturbed by Stochastic Noise

We perform langevin dynamics simulation for envelope solitons in an FPU-β lattice,with the nearestneighborinteraction and quartic anharmonicity.We get the motion equations of our discrete system by adding noiseand damping to the set of deterministic motion equations.We define'half-time'as the time when the amplitude of theenvelope soliton decreases by half due to damping.And then the mass,center and half-time of the perturbed envelopesoliton are numerically simulated,beginning with the discrete envelope soliton at rest.Results show successfully hownoise affects behavior of the envelope soliton.

Coupling Between Spin and Gravitational Field and Equation of Motion of Spin

In general relativity, the equation of motion of the spin is given by the equation of parallel transport, which is a result of the space-time geometry. Any result of the space-time geometry cannog be directly applied to gauge theory of gravity. In gauge theory of gravity, based on the viewpoint of the coupling between the spin and gravitational field, an equation of motlon of the spin is deduced. In the post Newtonian approximation, it is proved that this equation gives the same result as that of the equation of parallel transport. So, in the post Newtonian approximation, gauge theory of gravity gives out the same prediction on the precession of orbiting gyroscope as that of general relativity.

Various Extensions of Original Born-Kramers-Slater Model for Reactions Kinetics Based on Brownian Motion and Fokker-Plank Equation Including 1D, 2D, 3D, and Multi-dimensional Approaches

Different extensions, such as Transition State theory of Eyring-Polanyi-Evans model of the original Born-Kramers-Slater Model for the Velocity of Chemical Reactions are discussed based on Smoluchowski and Fokker-Plank equations with various properties of Brownian motion and including 1-, 2-, 3-, and multi- dimensional models with applications in Neuroscience.

Adiabatic Terminator for Fermionic Hierarchical Equations of Motion

The hierarchical equation of motion method has become one of the most popular numerical methods for describing the dissipative dynamics of open quantum systems linearly coupled to environment.However,its applications to systems with strong electron correlation are largely restrained by the computational cost,which is mainly caused by the high truncation tier L required to accurately characterize the strong correlation effect.In this work,we develop an adiabatic terminator by decoupling the principal dissipation mode with the fastest dissipation rate from the slower ones.The adiabatic terminator leads to substantially enhanced convergence with respect to L as demonstrated by the numerical tests carried out on a single impurity Anderson model.Moreover,the adiabatic terminator alleviates the numerical instability problems in the long-time dissipative dynamics.

Numerical Study of the Evaporation Effects on the Microdroplet Dynamics in Digital Microfluidic Biochips

In this paper, an electrohydrodynamic approach is used to model and study dynamics of evaporating microdroplets in digital microfluidic systems. A numerical eleetrohydrodynamic approach is used to calculate the driving force and shear force （due to the walls）. Effects of contact line pinning is considered by adding a three-phase contact line force, and also considering dynamic contact angle which modifies the mierodroplet boundary conditions. Since air is used as the filler fluid, the drag force is neglected. Although energy equation is not solved （constant temperature assumption）, effects of the evaporation is considered from two aspects： It is shown that an additional force is needed to balance the dynamic equation of the mierodroplet motion. Also, at each time step the microdroplet interface has to be deformed due to the change in the microdroplet radius. Important findings of the proposed model includes the transient velocity and displacement of the microdroplet as well as the driving and opposing forces acting on the microdroplet as functions of time. It is shown that mass loss due to evaporation tends to accelerate the droplet; whereas the competitive effect of the reduced driving force decelerates the droplet at the end of motion. The modeling results indicate that evaporation plays a crucial role in microdroplet motion by changing the force balance and the microdroplet boundary condition.

Quantum Entanglement of Parallel-Coupled Double Quantum Dots:a Theoretical Study Using the Hierarchical Equations of Motion Approach

Quantum dots comprise a type of quantum impurity system. The entanglement and co- herence of quantum states are significantly influenced by the strong electron-electron interactions among impurities and their dissipative coupling with the surrounding environment. Competition between many-body effects and transfer couplings plays an important role in determining the entanglement among localized impurity spins. In this work, we employ the hierarchical-equations-of-rnotion approach to explore the entanglement of a strongly correlated double quantum dots system. The relation between the total system entropy and those of subsystems is also investigated.

Prediction of Aircraft＇s Longitudinal Motion Based on Aerodynamic Coefficients and Derivatives by Surrogate Model Approach

The accuracy of a flight simulation is highly dependent on the quality of the aerodynamic database and prediction accuracies of the aerodynamic coefficients and derivatives. A surrogate model is an approximation method that is used to predict unknown functions based on the sampling data obtained by the design of experiments. This model can also be used to predict aerodynamic coefficients/derivatives using several measured points. The objective of this paper is to develop an efficient digital flight simulation by solving the equation of motion to predict the aerodynamics data using a surrogate model. Accordingly, there is a need to construct and investigate aerodynamic databases and compare the accuracy of the surrogate model with the exact solution, and hence solve the equation of motion for the flight simulation analysis. In this study, sample datas for models are acquired from the USAF Stability and Control DATCOM, and a database is constructed for two input variables （the angle of attack and Mach number）, along with two derivatives of the X-force axis and three derivatives for the Z-force axis and pitching moment. Furthermore, a comparison of the value predicted by the Kriging model and the exact solution shows that its flight analysis prediction ability makes it possible to use the surrogate model in future analyses.

Dynamic Analysis of aSelected Spatial One-DOF Linkage Mechanism with Friction in Joints

The dynamic analysis of a one-DOF RSRRR spatial linkage mechanism, including four rotational joints R and one spherical joint S, is presented in the paper. It is assumed that friction occurs in the rotational joints, whereas a spherical joint can be treated as an ideal one. The mechanism in the form of a closed-loop kinematic chain was divided by cut joint technique into two open-loop kinematic chains in place of the spherical joint. Joint coordinates and homogeneous transformation matrices were used to describe the geometry of the system. Equations of the chains＇ motion were derived using formalism of Lagrange equations. Cut joint constraints and reaction forces, acting in the cutting place---i.e, in the spherical joint, have been introduced to complete the equations of motion. As a consequence, a set of differential-algebraic equations has been obtained. In order to solve these equations, a procedure based on differentiation twice of the formulated constraint equations with respect to time has been applied. In order to determine values of friction torques in the rotational joints in each integrating step of the equations of motion, joint forces and torques were calculated using the recursive Newton-Euler algorithm taken from robotics. For the requirements of the method, a model of a rotational joint has been developed. Some examples of results of the numerical calculations made have been presented in the conclusions of the paper.

Quantum Transport Theory for Fusion Plasmas

Fundamental quantum transport equation for impact-ionization processes in fusion plasmas is formulated in the actor-spectator description. The density-matrix formulism is adopted to treat both coherent and incoherent effects in a unified fashion. Quantum electrodynamic effects are also considered for high-temperature scenarios. Electron-impact ionization of uranium ion U91＋ and proton-impact ionization of hydrogen are given as examples.

Breather Dynamics of the Sine-Gordon Equation

This paper studies the adiabatic dynamics of the breather soliton of the sine-Gordon equation. The integrals of motion are found and then used in soliton perturbation theory to derive the differential equation governing the soliton velocity. Time-dependent functions arise and their properties are studied. These functions are found to be bounded and periodic and affect the soliton velocity. The soliton velocity is numerically plotted against time for different combinations of initial velocities and perturbation terms.

A CFD/CSD model for aeroelastic calculations of large-scale wind turbines

In this paper,a CFD/CSD model coupling N-S equations and structural equations of motion in the time domain is described for aeroelastic analysis of large wind turbines.The structural modes of blades are analyzed with one-dimensional beam models.By combining point matched sliding grid for wind turbine rotation and deforming grid for structural vibrations,a hybrid dynamic grid strategy is designed for the multi-block structured grid system of a wind turbine.The dual time-stepping approach and finite volume scheme are applied to the three-dimensional unsteady preconditioned N-S equations,and DES approach is employed to simulate the unsteady massively separated flows.A modal approach is adopted to calculate the structural response,and a predictor-corrector scheme is used to solve the structural equations of motion.CFD and CSD solvers are tightly coupled via successive iterations within each physical time step.As a result,a time-domain CFD/CSD model for aeroelastic analysis of a large wind turbine is achieved.The presented method is applied to the NH1500 large wind turbine under the rated condition,and the calculated aeroelastic characteristics agree well with those of the prescribed vortex wake method.

Differential geometric modeling of guidance problem for interceptors

It is a comparatively convenient technique to investigate the motion of a particle with the help of the differential geometry the-ory,rather than directly decomposing the motion in the Cartesian coordinates.The new model of three-dimensional (3D) guidance problem for interceptors is presented in this paper,based on the classical differential geometry curve theory.Firstly,the kinematical equations of the line of sight (LOS) are gained by carefully investigating the rotation principle of LOS,the kinematic equations of LOS are established,and the concepts of curvature and torsion of LOS are proposed.Simultaneously,the new relative dynamic equations between interceptor and target are constructed.Secondly,it is found that there is an instan-taneous rotation plane of LOS (IRPL) in the space,in which two-dimensional (2D) guidance laws could be constructed to solve 3D interception guidance problems.The spatial 3D true proportional navigation (TPN) guidance law could be directly introduced in IRPL without approximation and linearization for dimension-reduced 2D TPN.In addition,the new series of augmented TPN (APN) and LOS angular acceleration guidance laws (AAG) could also be gained in IRPL.After that,the dif-ferential geometric guidance commands (DGGC) of guidance laws in IRPL are advanced,and we prove that the guidance commands in arc-length system proposed by Chiou and Kuo are just a special case of DGGC.Moreover,the performance of the original guidance laws will be reduced after the differential geometric transformation.At last,an exoatmospheric intercep-tion is taken for simulation to demonstrate the differential geometric modeling proposed in this paper.

From Dislocation Motion to an Additive Velocity Gradient Decomposition, and Some Simple Models of Dislocation Dynamics

A mathematical theory of time-dependent dislocation mechanics of unrestricted geometric and material nonlinearity is reviewed. Within a "small deformation" setting, a suite of simplified and interesting models consisting of a nonlocal Ginzburg Landau equation, a nonlocal level set equation, and a nonlocal generalized Burgers equation is derived.In the finite deformation setting, it is shown that an additive decomposition of the total velocity gradient into elastic and plastic parts emerges naturally from a micromechanical starting point that involves no notion of plastic deformation but only the elastic distortion,material velocity, dislocation density and the dislocation velocity. Moreover, a plastic spin tensor emerges naturally as well.

A two-dimensional numerical model coupled with multiple hillslope hydrodynamic processes and its application to subsurface flow simulation

A numerical hillslope hydrodynamic model is of great importance in facilitating the understanding of rainfall-runoff mechanism.However,most of the currently existing models do not consider the effect of coupled hydrodynamic processes as runoff,subsurface flow or groundwater flow.In this study,the Tsinghua Hillslope Runoff Model based on multiple hydrodynamic process,THRM model,is developed,which couples with Saint Venant equation for surface runoff and Richards equation for variably saturated soil water movement(including subsurface flow and groundwater flow).A finite difference scheme with improved boundary conditions is adopted in this research.It is revealed from the simulation that the THRM model has a high computational efficiency and stability in simulating subsurface flow of the experimental hillslope,which is valuable in assessing the hillslope runoff generation mechanism.A model based sensitivity analysis is also carried out.The impact of boundary condition,grid size and initial soil moisture on simulation result and model stability are revealed,which provides insightful references to understand the mechanism of subsurface flow.

Two-post-Newtonian approximation of the scalar-tensor theory with an intermediate-range force for general matter

Some future space missions measure distances of laser links and angles with unprecedented precision, allowing us to test theories of gravity up to the two-post-Newtonian （2PN） order. Besides, investigation of an intermediate-range force has been of considerable interests in gravitational experiments. Inspired by these ideas, within the framework of the scalar-tensor theory with an intermediate- range force, its 2PN approximation is obtained with Chandrasekhar＇s approach. It includes the 2PN metric and equations of motion for general matter without specific equation of state. The conserved quantities to the 2PN order are isolated with the aid of the energy-momentum complex. We also discuss the prospect of testing and distinguishing the intermediate-range force with the orbital motions of celestial bodies and spaeecrafts.