The model of the differential steering system(DSS) of electric vehicle with motorized wheels and the three-degree-of-freedom dynamic model of vehicle are built.Based on these models,the concepts and quantitative expre...The model of the differential steering system(DSS) of electric vehicle with motorized wheels and the three-degree-of-freedom dynamic model of vehicle are built.Based on these models,the concepts and quantitative expressions of steering road feel,steering portability and steering stability are proposed.Through integrating the Monte Carlo descriptive sampling,elitist non-dominated sorting genetic algorithm(NSGA-II) and Taguchi robust design method,the system parameters are optimized with steering road feel and steering portability as optimization targets,and steering stability and steering portability as constraints.The simulation results show that the system optimized based on quality engineering can improve the steering road feel,guarantee steering stability and steering portability and thus provide a theoretical basis for the design and optimization of the electric vehicle with motorized wheels system.展开更多
The Hamilton-Jacobi method for solving ordinary differential equations is presented in this paper. A system of ordinary differential equations of first order or second order can be expressed as a Hamilton system under...The Hamilton-Jacobi method for solving ordinary differential equations is presented in this paper. A system of ordinary differential equations of first order or second order can be expressed as a Hamilton system under certain conditions. Then the Hamilton-Jacobi method is used in the integration of the Hamilton system and the solution of the original ordinary differential equations can be found. Finally, an example is given to illustrate the application of the result.展开更多
This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differenti...This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system.展开更多
The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation metho...The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.展开更多
By using the precise integration method, the numerical solution of linear quadratic Gaussian (LQG) optimal control problem was discussed. Based on the separation principle, the LQG central problem decomposes, or separ...By using the precise integration method, the numerical solution of linear quadratic Gaussian (LQG) optimal control problem was discussed. Based on the separation principle, the LQG central problem decomposes, or separates, into an optimal state-feedback control problem and an optimal state estimation problem. That is the off-line solution of two sets of Riccati differential equations and the on-line integration solution of the state vector from a set of time-variant differential equations. The present algorithms are not only appropriate to solve the two-point boundary-value problem and the corresponding Riccati differential equation, but also can be used to solve the estimated state from the time-variant differential equations. The high precision of precise integration is of advantage for the control and estimation. Numerical examples demonstrate the high precision and effectiveness of the algorithm.展开更多
Creative telescoping is the method of choice for obtaining information about definite sums or integrals. It has been intensively studied since the early 1990s, and can now be considered as a classical technique in com...Creative telescoping is the method of choice for obtaining information about definite sums or integrals. It has been intensively studied since the early 1990s, and can now be considered as a classical technique in computer algebra. At the same time, it is still a subject of ongoing research.This paper presents a selection of open problems in this context. The authors would be curious to hear about any substantial progress on any of these problems.展开更多
An important modern method in analytical mechanics for finding the integral, which is called the field-method, is used to research the solution of a differential equation of the first order. First, by introducing an i...An important modern method in analytical mechanics for finding the integral, which is called the field-method, is used to research the solution of a differential equation of the first order. First, by introducing an intermediate variable, a more complicated differential equation of the first order can be expressed by two simple differential equations of the first order, then the field-method in analytical mechanics is introduced for solving the two differential equations of the first order. The conclusion shows that the field-method in analytical mechanics can be fully used to find the solutions of a differential equation of the first order, thus a new method for finding the solutions of the first order is provided.展开更多
Magnetic measurement and diagnostics are critical for the operation of magnetic confinement experimental facilities and plasma analysis, while differential signals are mostly detected by a detector. For this, we have ...Magnetic measurement and diagnostics are critical for the operation of magnetic confinement experimental facilities and plasma analysis, while differential signals are mostly detected by a detector. For this, we have developed and designed a stable and reliable data integration system for HL-2M magnetic measurement and magnetic diagnostics. The system will be used for realtime control of HL-2M after the construction of HL-2M is completed. The system is built based on the PXI platform, and the software system is based on the LABVIEW platform. Key technologies realized by the system primarily include drift compensation, pulse data acquisition technology, multi-threading processing technology and transmission control communication protocol. Trials of the system were successfully carried out on HL-2A, and the results showed that the system could fully meet the construction needs of HL-2M.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 51005115 and 51005248)the Science Fund of State Key Laboratory of Automotive Safety and Energy (Grant No. KF11201)
文摘The model of the differential steering system(DSS) of electric vehicle with motorized wheels and the three-degree-of-freedom dynamic model of vehicle are built.Based on these models,the concepts and quantitative expressions of steering road feel,steering portability and steering stability are proposed.Through integrating the Monte Carlo descriptive sampling,elitist non-dominated sorting genetic algorithm(NSGA-II) and Taguchi robust design method,the system parameters are optimized with steering road feel and steering portability as optimization targets,and steering stability and steering portability as constraints.The simulation results show that the system optimized based on quality engineering can improve the steering road feel,guarantee steering stability and steering portability and thus provide a theoretical basis for the design and optimization of the electric vehicle with motorized wheels system.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10272021, 10572021） and the Doctoral Program Foundation of Institution of Higher Education of China （Grant No 20040007022）.
文摘The Hamilton-Jacobi method for solving ordinary differential equations is presented in this paper. A system of ordinary differential equations of first order or second order can be expressed as a Hamilton system under certain conditions. Then the Hamilton-Jacobi method is used in the integration of the Hamilton system and the solution of the original ordinary differential equations can be found. Finally, an example is given to illustrate the application of the result.
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)the Doctoral Programme Foundation of Institution of Higher Education of China (Grant No 20040007022)
文摘This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system.
文摘The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.
文摘By using the precise integration method, the numerical solution of linear quadratic Gaussian (LQG) optimal control problem was discussed. Based on the separation principle, the LQG central problem decomposes, or separates, into an optimal state-feedback control problem and an optimal state estimation problem. That is the off-line solution of two sets of Riccati differential equations and the on-line integration solution of the state vector from a set of time-variant differential equations. The present algorithms are not only appropriate to solve the two-point boundary-value problem and the corresponding Riccati differential equation, but also can be used to solve the estimated state from the time-variant differential equations. The high precision of precise integration is of advantage for the control and estimation. Numerical examples demonstrate the high precision and effectiveness of the algorithm.
基金supported by the National Natural Science Foundation of China under Grant No.11501552the President Fund of the Academy of Mathematics and Systems Science,CAS(2014-cjrwlzx-chshsh)+1 种基金a Starting Grant from the Ministry of Education of Chinasupported by the Austrian FWF under Grant Nos.F5004,Y464-N18,and W1214
文摘Creative telescoping is the method of choice for obtaining information about definite sums or integrals. It has been intensively studied since the early 1990s, and can now be considered as a classical technique in computer algebra. At the same time, it is still a subject of ongoing research.This paper presents a selection of open problems in this context. The authors would be curious to hear about any substantial progress on any of these problems.
基金Sponsored by the National Natural Science Foundation of China(10572021)
文摘An important modern method in analytical mechanics for finding the integral, which is called the field-method, is used to research the solution of a differential equation of the first order. First, by introducing an intermediate variable, a more complicated differential equation of the first order can be expressed by two simple differential equations of the first order, then the field-method in analytical mechanics is introduced for solving the two differential equations of the first order. The conclusion shows that the field-method in analytical mechanics can be fully used to find the solutions of a differential equation of the first order, thus a new method for finding the solutions of the first order is provided.
基金supported by National Natural Science Foundation of China(No.1157518)
文摘Magnetic measurement and diagnostics are critical for the operation of magnetic confinement experimental facilities and plasma analysis, while differential signals are mostly detected by a detector. For this, we have developed and designed a stable and reliable data integration system for HL-2M magnetic measurement and magnetic diagnostics. The system will be used for realtime control of HL-2M after the construction of HL-2M is completed. The system is built based on the PXI platform, and the software system is based on the LABVIEW platform. Key technologies realized by the system primarily include drift compensation, pulse data acquisition technology, multi-threading processing technology and transmission control communication protocol. Trials of the system were successfully carried out on HL-2A, and the results showed that the system could fully meet the construction needs of HL-2M.
