This paper presents the integration methods for vacco dynmmies equations of nonlinear nonholononic system,First.vacco dynamies equations are written in the canonical form and the field form.second the gradient methods...This paper presents the integration methods for vacco dynmmies equations of nonlinear nonholononic system,First.vacco dynamies equations are written in the canonical form and the field form.second the gradient methods the single-componentmethods and the field method are used to integrate the dynamics equations of the corresponding holonomic system respectively.And considering the restriction of nonholonomic construint to the initial conditions the solutions of Vacco dynamics cquations of nonlinear nonholonomic system are obtained.展开更多
The present article is concerned with the implementation of a recent semi-analytical method referred to as fractional reduced differential transform method （FRDTM） for computation of approximate solution of time-fra...The present article is concerned with the implementation of a recent semi-analytical method referred to as fractional reduced differential transform method （FRDTM） for computation of approximate solution of time-fractional gas dynamics equation （TFGDE） arising in shock fronts. In this approach, the fractional derivative is described in the Caputo sense. Four numeric experiments have been carried out to confirm the validity and the efficiency of the method. It is found that the exact or a closed approximate analytical solution of a fractional nonlinear differential equations arising in allied science and engineering can be obtained easily. Moreover, due to its small size of calculation contrary to the other analytical approaches while dealing with a complex and tedious physical problems arising in various branches of natural sciences and engineering, it is very easy to implement.展开更多
In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discreti...In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.展开更多
In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existe...In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.展开更多
Gas turbines play core roles in clean energy supply and the construction of comprehensive energy systems.The control performance of primary frequency modulation of gas turbines has a great impact on the frequency cont...Gas turbines play core roles in clean energy supply and the construction of comprehensive energy systems.The control performance of primary frequency modulation of gas turbines has a great impact on the frequency control of the power grid.However,there are some control difficulties in the primary frequency modulation control of gas turbines,such as the coupling effect of the fuel control loop and speed control loop,slow tracking speed,and so on.To relieve the abovementioned difficulties,a control strategy based on the desired dynamic equation proportional integral(DDE-PI)is proposed in this paper.Based on the parameter stability region,a parameter tuning procedure is summarized.Simulation is carried out to address the ease of use and simplicity of the proposed tuning method.Finally,DDE-PI is applied to the primary frequency modulation system of an MS6001B heavy-duty gas turbine.The simulation results indicate that the gas turbine with the proposed strategy can obtain the best control performance with a strong ability to deal with system uncertainties.The proposed method shows good engineering application potential.展开更多
In this paper, we propose a model based on dynamics equation for performance analysis and optimization for heterogeneous wireless networks （HWNs）. First, the channel occupation state with time of HWNs is modelled by...In this paper, we propose a model based on dynamics equation for performance analysis and optimization for heterogeneous wireless networks （HWNs）. First, the channel occupation state with time of HWNs is modelled by dynamics equation, in which users＇ mobility as an important factor affecting system performance is considered. Then the steady state probability distribution of channel occupation is derived. Based on the results, the expression of the throughput of HWNs is deduced, which includes a factor p which is the ratio of service arrival rate accessing one of the networks to the total service arrival rate in the overlapping area. And this paper proposes to maximize the throughput of the HWNs by optimizing the factor p to efficiently utilize the resources. Simulation results show that the proposed optimization method can effectively improve the throughput and in the meanwhile decrease the blocking probability of the whole system.展开更多
We propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics equations.By all regime,we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolve...We propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics equations.By all regime,we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolved discretization with respect to the Mach number M,i.e.such that the ratio between the Mach number M and the mesh size or the time step is small with respect to 1.The key idea is to decouple acoustic and transport phenomenon and then alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in term of M.This modified scheme is conservative and endowed with good stability properties with respect to the positivity of the density and the internal energy.A discrete entropy inequality under a condition on the modification is obtained thanks to a reinterpretation of the modified scheme in the Harten Lax and van Leer formalism.A natural extension to multi-dimensional problems discretized over unstructured mesh is proposed.Then a simple and efficient semi implicit scheme is also proposed.The resulting scheme is stable under a CFL condition driven by the(slow)material waves and not by the(fast)acoustic waves and so verifies the all regime property.Numerical evidences are proposed and show the ability of the scheme to deal with tests where the flow regime may vary from low to high Mach values.展开更多
Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp ra...Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple togeth- er the elementary uniform energy estimates of the global weak solutions and a well known Gronwall＇s inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980＇s to study the op- timal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay esti- mates with sharp rates of the global weak solutions of the Cauchy problems for n-dimensional incompressible Navier-Stokes equations, for the n-dimensional magnetohydrodynamics equations and for many other very interesting nonlin- ear evolution equations with dissipations can be established.展开更多
In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarant...In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.展开更多
We introduce adaptive moving mesh central-upwind schemes for one-and two-dimensional hyperbolic systems of conservation and balance laws.The proposed methods consist of three steps.First,the solution is evolved by sol...We introduce adaptive moving mesh central-upwind schemes for one-and two-dimensional hyperbolic systems of conservation and balance laws.The proposed methods consist of three steps.First,the solution is evolved by solving the studied system by the second-order semi-discrete central-upwind scheme on either the one-dimensional nonuniform grid or the two-dimensional structured quadrilateral mesh.When the evolution step is complete,the grid points are redistributed according to the moving mesh differential equation.Finally,the evolved solution is projected onto the new mesh in a conservative manner.The resulting adaptive moving mesh methods are applied to the one-and two-dimensional Euler equations of gas dynamics and granular hydrodynamics systems.Our numerical results demonstrate that in both cases,the adaptive moving mesh central-upwind schemes outperform their uniform mesh counterparts.展开更多
A tensor method for the derivation of the equations of rigid body dynamics, based on the concepts of continuum mechanics, is presented. The formula of time derivative of the inertia tensor with zero corotational rate ...A tensor method for the derivation of the equations of rigid body dynamics, based on the concepts of continuum mechanics, is presented. The formula of time derivative of the inertia tensor with zero corotational rate is used to prove the equivalences of five methods, namely, Lagrange's equations, Nielsen's equations, Gibbs-Appell's equations, Kane's equations and the generalized momentum type of Kane's equations. Some differential identities on angular velocity and angular acceleration are given.展开更多
The dot product of the bases vectors on the super-surface of the non-linear nonholonomic constraints with one order, expressed by quasi-coorfinates, and Mishirskiiequalions are regarded as the fundamental equations of...The dot product of the bases vectors on the super-surface of the non-linear nonholonomic constraints with one order, expressed by quasi-coorfinates, and Mishirskiiequalions are regarded as the fundamental equations of dynamics with non-linear andnon-holononlic constraints in one order for the system of the variable mass. From thesethe variant ddferential-equations of dynamics expressed by quasi-coordinates arederived. The fundamental equations of dynamics are compatible with the principle ofJourdain. A case is cited.展开更多
In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entrop...In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entropy solution in the limit if Courant number is less than or equal to 1.展开更多
In this paper, we study the initial-boundary value problem with rigid wall for the equations in combustion dynamics with largy parameter. Introducing variable scalar norms and two seminorms, making use of the vorticit...In this paper, we study the initial-boundary value problem with rigid wall for the equations in combustion dynamics with largy parameter. Introducing variable scalar norms and two seminorms, making use of the vorticity operator, overcome the difficulty from the large parameter. By energy estimation, the existence and unique theorems of local smooth solution is proved.展开更多
To determine the Earth＇s dynamics and their equations, which are crucial for Earth science research, this paper analyzes the interaction forces in the motion of a three-body system（namely, fixed, active, and passive...To determine the Earth＇s dynamics and their equations, which are crucial for Earth science research, this paper analyzes the interaction forces in the motion of a three-body system（namely, fixed, active, and passive points）, based on the orbital motion. The mathematical derivation has been conducted strictly according to trigonometric functions with time and space as variables. In spatial transformation, related data items are simplified and replaced reasonably and necessarily according to the physical phenomenon to conduct derivations of planar to spatial transformation, through which the motion point has universal significance. Moreover, the polynomial equation for the dynamics has been obtained. Results indicate that the polynomial expression for the dynamics comprises the tidal force, the powerful mid-latitude Force（PML Force）, and gravitation. Gravitation analysis shows that it is proportional to the dynamics quality, the size of the angular velocity of their deviation from the progenitor-paternal orbital plane＇s center position, and the square of the progenitor orbital plane＇s distance. However, it is inversely proportional to the distance of the paternal orbital plane and not related to another body＇s quality. Some past errors are addressed and some constructive conclusions are offered in the discussion of gravitation.展开更多
To analyze the attitude errors of vertical docking test system of small satellite,the static error and kinematic error of test system are considered.The working principle of test system and coordinate of actuator are ...To analyze the attitude errors of vertical docking test system of small satellite,the static error and kinematic error of test system are considered.The working principle of test system and coordinate of actuator are introduced.The model of friction torque on the joints and torque on docking mechanism are built.Dynamics equation of actuator is built by the Lagrange equation and the Nielsen equation.Under the condition of 24 different angle groups,the calculation of dynamics equation is built by using MATLAB/SIMULINK platform and the kinematic errors of actuator are obtained.The attitude error models of docking mechanism are built.Results shows that the main angle error sources of yaw,row,pitch are not identical.The attitude error of yaw angle can be decreased by compensating the angle error around xaxis.The attitude error of row angle mainly originates in the system error,and it can be eliminated by adjusting non-orthogonal degree.展开更多
： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati tech...： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.展开更多
This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequal...This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.展开更多
A new averaged general dynamic equation （GDE） for nanoparticles in the turbulent flow is derived by considering the combined effect of convection, Brownian diffusion, turbulent diffusion, turbulent coagulation, and ...A new averaged general dynamic equation （GDE） for nanoparticles in the turbulent flow is derived by considering the combined effect of convection, Brownian diffusion, turbulent diffusion, turbulent coagulation, and fluctuating coagulation. The equation is solved with the Taylor-series expansion moment method in a turbulent pipe flow. The experiments are performed. The numerical results of particle size distribu- tion correlate well with the experimental data. The results show that, for a turbulent nanoparticulate flow, a fluctuating coagulation term should be included in the averaged particle GDE. The larger the Schmidt number is and the lower the Reynolds number is, the smaller the value of ratio of particle diameter at the outlet to that at the inlet is. At the outlet, the particle number concentration increases from the near-wall region to the near-center region. The larger the Schmidt number is and the higher the Reynolds num- ber is, the larger the difference in particle number concentration between the near-wall region and near-center region is. Particle polydispersity increases from the near-center region to the near-wall region. The particles with a smaller Schmidt number and the flow with a higher Reynolds number show a higher polydispersity. The degree of particle polydispersity is higher considering fluctuating coagulation than that without considering fluctuating coagulation.展开更多
First,screw theory,product of exponential formulas and Jacobian matrix are introduced.Then definitions are given about active force wrench,inertial force wrench,partial velocity twist,generalized active force,and gene...First,screw theory,product of exponential formulas and Jacobian matrix are introduced.Then definitions are given about active force wrench,inertial force wrench,partial velocity twist,generalized active force,and generalized inertial force according to screw theory.After that Kane dynamic equations based on screw theory for open-chain manipulators have been derived. Later on how to compute the partial velocity twist by geometrical method is illustrated. Finally the correctness of conclusions is verified by example.展开更多
文摘This paper presents the integration methods for vacco dynmmies equations of nonlinear nonholononic system,First.vacco dynamies equations are written in the canonical form and the field form.second the gradient methods the single-componentmethods and the field method are used to integrate the dynamics equations of the corresponding holonomic system respectively.And considering the restriction of nonholonomic construint to the initial conditions the solutions of Vacco dynamics cquations of nonlinear nonholonomic system are obtained.
文摘The present article is concerned with the implementation of a recent semi-analytical method referred to as fractional reduced differential transform method （FRDTM） for computation of approximate solution of time-fractional gas dynamics equation （TFGDE） arising in shock fronts. In this approach, the fractional derivative is described in the Caputo sense. Four numeric experiments have been carried out to confirm the validity and the efficiency of the method. It is found that the exact or a closed approximate analytical solution of a fractional nonlinear differential equations arising in allied science and engineering can be obtained easily. Moreover, due to its small size of calculation contrary to the other analytical approaches while dealing with a complex and tedious physical problems arising in various branches of natural sciences and engineering, it is very easy to implement.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035,11171038,and 10771019)the Science Reaearch Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region,China (Grant No. NJZZ12198)the Natural Science Foundation of Inner Mongolia Autonomous Region,China (Grant No. 2012MS0102)
文摘In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.
基金supported by the National Natural Science Foundation of China(12071491,12001113)。
文摘In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.
基金supported by Science and Technology Project of Jiangsu Frontier Electric Technology Co.,Ltd. (Grant Number KJ202004),Gao A.M. (author who received the grant).
文摘Gas turbines play core roles in clean energy supply and the construction of comprehensive energy systems.The control performance of primary frequency modulation of gas turbines has a great impact on the frequency control of the power grid.However,there are some control difficulties in the primary frequency modulation control of gas turbines,such as the coupling effect of the fuel control loop and speed control loop,slow tracking speed,and so on.To relieve the abovementioned difficulties,a control strategy based on the desired dynamic equation proportional integral(DDE-PI)is proposed in this paper.Based on the parameter stability region,a parameter tuning procedure is summarized.Simulation is carried out to address the ease of use and simplicity of the proposed tuning method.Finally,DDE-PI is applied to the primary frequency modulation system of an MS6001B heavy-duty gas turbine.The simulation results indicate that the gas turbine with the proposed strategy can obtain the best control performance with a strong ability to deal with system uncertainties.The proposed method shows good engineering application potential.
基金supported by the National Natural Science Foundation of China (61372125)the National Basic Research Program of China (2013CB329104)the open research fund of National Mobile Communications Research Laboratory, Southeast University (2013D01)
文摘In this paper, we propose a model based on dynamics equation for performance analysis and optimization for heterogeneous wireless networks （HWNs）. First, the channel occupation state with time of HWNs is modelled by dynamics equation, in which users＇ mobility as an important factor affecting system performance is considered. Then the steady state probability distribution of channel occupation is derived. Based on the results, the expression of the throughput of HWNs is deduced, which includes a factor p which is the ratio of service arrival rate accessing one of the networks to the total service arrival rate in the overlapping area. And this paper proposes to maximize the throughput of the HWNs by optimizing the factor p to efficiently utilize the resources. Simulation results show that the proposed optimization method can effectively improve the throughput and in the meanwhile decrease the blocking probability of the whole system.
文摘We propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics equations.By all regime,we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolved discretization with respect to the Mach number M,i.e.such that the ratio between the Mach number M and the mesh size or the time step is small with respect to 1.The key idea is to decouple acoustic and transport phenomenon and then alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in term of M.This modified scheme is conservative and endowed with good stability properties with respect to the positivity of the density and the internal energy.A discrete entropy inequality under a condition on the modification is obtained thanks to a reinterpretation of the modified scheme in the Harten Lax and van Leer formalism.A natural extension to multi-dimensional problems discretized over unstructured mesh is proposed.Then a simple and efficient semi implicit scheme is also proposed.The resulting scheme is stable under a CFL condition driven by the(slow)material waves and not by the(fast)acoustic waves and so verifies the all regime property.Numerical evidences are proposed and show the ability of the scheme to deal with tests where the flow regime may vary from low to high Mach values.
文摘Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple togeth- er the elementary uniform energy estimates of the global weak solutions and a well known Gronwall＇s inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980＇s to study the op- timal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay esti- mates with sharp rates of the global weak solutions of the Cauchy problems for n-dimensional incompressible Navier-Stokes equations, for the n-dimensional magnetohydrodynamics equations and for many other very interesting nonlin- ear evolution equations with dissipations can be established.
基金Supported by Russian Fund of Fund amental Investigations(Pr.990101064)and Russian Minister of Educatin
文摘In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.
基金The work of A.Kurganov was supported in part by the National Natural Science Foundation of China grant 11771201by the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design(No.2019B030301001).
文摘We introduce adaptive moving mesh central-upwind schemes for one-and two-dimensional hyperbolic systems of conservation and balance laws.The proposed methods consist of three steps.First,the solution is evolved by solving the studied system by the second-order semi-discrete central-upwind scheme on either the one-dimensional nonuniform grid or the two-dimensional structured quadrilateral mesh.When the evolution step is complete,the grid points are redistributed according to the moving mesh differential equation.Finally,the evolved solution is projected onto the new mesh in a conservative manner.The resulting adaptive moving mesh methods are applied to the one-and two-dimensional Euler equations of gas dynamics and granular hydrodynamics systems.Our numerical results demonstrate that in both cases,the adaptive moving mesh central-upwind schemes outperform their uniform mesh counterparts.
文摘A tensor method for the derivation of the equations of rigid body dynamics, based on the concepts of continuum mechanics, is presented. The formula of time derivative of the inertia tensor with zero corotational rate is used to prove the equivalences of five methods, namely, Lagrange's equations, Nielsen's equations, Gibbs-Appell's equations, Kane's equations and the generalized momentum type of Kane's equations. Some differential identities on angular velocity and angular acceleration are given.
文摘The dot product of the bases vectors on the super-surface of the non-linear nonholonomic constraints with one order, expressed by quasi-coorfinates, and Mishirskiiequalions are regarded as the fundamental equations of dynamics with non-linear andnon-holononlic constraints in one order for the system of the variable mass. From thesethe variant ddferential-equations of dynamics expressed by quasi-coordinates arederived. The fundamental equations of dynamics are compatible with the principle ofJourdain. A case is cited.
基金Supported in part by the National Natural Science of China, NSF Grant No. DMS-8657319.
文摘In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entropy solution in the limit if Courant number is less than or equal to 1.
文摘In this paper, we study the initial-boundary value problem with rigid wall for the equations in combustion dynamics with largy parameter. Introducing variable scalar norms and two seminorms, making use of the vorticity operator, overcome the difficulty from the large parameter. By energy estimation, the existence and unique theorems of local smooth solution is proved.
基金sponsored by the Project for Talent Employment by Educational Department of Guangdong Provincethe state key lab.of Oil and Gas Reservoir Geology and Exploitation
文摘To determine the Earth＇s dynamics and their equations, which are crucial for Earth science research, this paper analyzes the interaction forces in the motion of a three-body system（namely, fixed, active, and passive points）, based on the orbital motion. The mathematical derivation has been conducted strictly according to trigonometric functions with time and space as variables. In spatial transformation, related data items are simplified and replaced reasonably and necessarily according to the physical phenomenon to conduct derivations of planar to spatial transformation, through which the motion point has universal significance. Moreover, the polynomial equation for the dynamics has been obtained. Results indicate that the polynomial expression for the dynamics comprises the tidal force, the powerful mid-latitude Force（PML Force）, and gravitation. Gravitation analysis shows that it is proportional to the dynamics quality, the size of the angular velocity of their deviation from the progenitor-paternal orbital plane＇s center position, and the square of the progenitor orbital plane＇s distance. However, it is inversely proportional to the distance of the paternal orbital plane and not related to another body＇s quality. Some past errors are addressed and some constructive conclusions are offered in the discussion of gravitation.
基金supported by National Natural Science Foundation of China(No.51375125)the Foundation for Distinguished Young Scholars of Heilongjiang Province,China(No.JC201111)the Program for New Century Excellent Talents in University(No.NCET10-0146)
文摘To analyze the attitude errors of vertical docking test system of small satellite,the static error and kinematic error of test system are considered.The working principle of test system and coordinate of actuator are introduced.The model of friction torque on the joints and torque on docking mechanism are built.Dynamics equation of actuator is built by the Lagrange equation and the Nielsen equation.Under the condition of 24 different angle groups,the calculation of dynamics equation is built by using MATLAB/SIMULINK platform and the kinematic errors of actuator are obtained.The attitude error models of docking mechanism are built.Results shows that the main angle error sources of yaw,row,pitch are not identical.The attitude error of yaw angle can be decreased by compensating the angle error around xaxis.The attitude error of row angle mainly originates in the system error,and it can be eliminated by adjusting non-orthogonal degree.
基金Supported by the Scientific Research Fund of Hunan Provincial Education Department(09A082)
文摘： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.
基金Supported by the NNSF of China(11071222)Supported by the NSF of Hunan Province(12JJ6006)Supported by Scientific Research Fund of Education Department of Guangxi Zhuang Autonomous Region(2013YB223)
文摘This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.
基金Project supported by the National Natural Science Foundation of China(No.11132008)
文摘A new averaged general dynamic equation （GDE） for nanoparticles in the turbulent flow is derived by considering the combined effect of convection, Brownian diffusion, turbulent diffusion, turbulent coagulation, and fluctuating coagulation. The equation is solved with the Taylor-series expansion moment method in a turbulent pipe flow. The experiments are performed. The numerical results of particle size distribu- tion correlate well with the experimental data. The results show that, for a turbulent nanoparticulate flow, a fluctuating coagulation term should be included in the averaged particle GDE. The larger the Schmidt number is and the lower the Reynolds number is, the smaller the value of ratio of particle diameter at the outlet to that at the inlet is. At the outlet, the particle number concentration increases from the near-wall region to the near-center region. The larger the Schmidt number is and the higher the Reynolds num- ber is, the larger the difference in particle number concentration between the near-wall region and near-center region is. Particle polydispersity increases from the near-center region to the near-wall region. The particles with a smaller Schmidt number and the flow with a higher Reynolds number show a higher polydispersity. The degree of particle polydispersity is higher considering fluctuating coagulation than that without considering fluctuating coagulation.
文摘First,screw theory,product of exponential formulas and Jacobian matrix are introduced.Then definitions are given about active force wrench,inertial force wrench,partial velocity twist,generalized active force,and generalized inertial force according to screw theory.After that Kane dynamic equations based on screw theory for open-chain manipulators have been derived. Later on how to compute the partial velocity twist by geometrical method is illustrated. Finally the correctness of conclusions is verified by example.
