The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integ...The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integrating factors is given, and the necessary conditions for the existence of the conserved quantities are studied in detail. Then, the conservation theorem and its inverse of system are established. Finally, an example is given to illustrate the application of the result.展开更多
In this paper the conservation theorems of the constrained Birkhoffian systems are studied by using the method of integrating factors. The differential equations of motion of the system are written. The definition of ...In this paper the conservation theorems of the constrained Birkhoffian systems are studied by using the method of integrating factors. The differential equations of motion of the system are written. The definition of integrating factors is given for the system. The necessary conditions for the existence of the conserved quantity for the system are studied. The conservation theorem and its inverse for the system are established. Finally, an example is given to illustrate the application of the results.展开更多
The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are g...The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.展开更多
According to the theory of the transport and vorticity dynamics,the paper establishes the theory of vorticity flux and the conservation theorem between the vorticity flux and vortex strength in a plane flow.The theory...According to the theory of the transport and vorticity dynamics,the paper establishes the theory of vorticity flux and the conservation theorem between the vorticity flux and vortex strength in a plane flow.The theory of vorticity flux is a basic one in research on turbulence.展开更多
For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the paramet...For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the parametric equations of the system. First, the parametric equations of the Birkhoffian system in the event space are established, and the definition of integrating factors for the system is given; second the necessary conditions for the existence of conservation laws are studied in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the results.展开更多
The new Lagrangian of the relative motion of mechanical system is constructed, the varialional principles oj Jourdain's form of nonlinear nonlwlonomic nonpotential system in noninertial reference frame are establi...The new Lagrangian of the relative motion of mechanical system is constructed, the varialional principles oj Jourdain's form of nonlinear nonlwlonomic nonpotential system in noninertial reference frame are established, the generalized Noether's theorem of the system above is presented and proved, and the conserved quantities of system are studied.展开更多
This paper presents a linear microdilation microcontinuum theory in which the microconstituents have only one unknown degree of freedom,volumetric strain or a quantity proportional to volumetric strain,and have three ...This paper presents a linear microdilation microcontinuum theory in which the microconstituents have only one unknown degree of freedom,volumetric strain or a quantity proportional to volumetric strain,and have three known rigid rotational degrees of freedom defined by the classical rotations.In this microdilation theory,the microconstituents,the medium as well as the interaction of the microconstituents all have thermoelastic deformation physics.Additionally,the microconstituents can experience rigid rotations.Due to deformable microconstituents,we begin the derivation with the microconstituent conservation and balance laws using classical continuum mechanics,followed by integral-average definitions that facilitate derivation of macro conservation and balance laws.This microdilation theory is completely different than Eringen’s microstretch theory;the differences are discussed in the paper.It is shown that the approach of using smoothing weight functions in deriving macro balance of linear momenta,macro balance of angular momenta and the new balance law proposed for closure of the mathematical model in Eringen’s work is neither needed nor used in the present work and is not supported by thermodynamics.All constitutive theories are derived using representation theorem and integrity,hence mathematically consistent and complete.The linear microdilation theory presented in this paper for thermoelastic solids is shown to be thermodynamically and mathematically consistent.展开更多
基金The project supported by Natural Science Foundation of Heilongjiang Province of China under Grant No. 9507
文摘The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integrating factors is given, and the necessary conditions for the existence of the conserved quantities are studied in detail. Then, the conservation theorem and its inverse of system are established. Finally, an example is given to illustrate the application of the result.
基金Project supported by the Heilongjiang Natural Science Foundation of China （Grant No 9507）
文摘In this paper the conservation theorems of the constrained Birkhoffian systems are studied by using the method of integrating factors. The differential equations of motion of the system are written. The definition of integrating factors is given for the system. The necessary conditions for the existence of the conserved quantity for the system are studied. The conservation theorem and its inverse for the system are established. Finally, an example is given to illustrate the application of the results.
基金The project supported by the Natural Science Foundation of Heilongjiang Province of China under Grant No. 9507
文摘The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.
文摘According to the theory of the transport and vorticity dynamics,the paper establishes the theory of vorticity flux and the conservation theorem between the vorticity flux and vortex strength in a plane flow.The theory of vorticity flux is a basic one in research on turbulence.
基金the Natural Science Foundation of Higher Education Institution of Jiangsu Province of China under Grant Nos.04KJA130135 and 08KJB13002
文摘For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the parametric equations of the system. First, the parametric equations of the Birkhoffian system in the event space are established, and the definition of integrating factors for the system is given; second the necessary conditions for the existence of conservation laws are studied in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the results.
文摘The new Lagrangian of the relative motion of mechanical system is constructed, the varialional principles oj Jourdain's form of nonlinear nonlwlonomic nonpotential system in noninertial reference frame are established, the generalized Noether's theorem of the system above is presented and proved, and the conserved quantities of system are studied.
文摘This paper presents a linear microdilation microcontinuum theory in which the microconstituents have only one unknown degree of freedom,volumetric strain or a quantity proportional to volumetric strain,and have three known rigid rotational degrees of freedom defined by the classical rotations.In this microdilation theory,the microconstituents,the medium as well as the interaction of the microconstituents all have thermoelastic deformation physics.Additionally,the microconstituents can experience rigid rotations.Due to deformable microconstituents,we begin the derivation with the microconstituent conservation and balance laws using classical continuum mechanics,followed by integral-average definitions that facilitate derivation of macro conservation and balance laws.This microdilation theory is completely different than Eringen’s microstretch theory;the differences are discussed in the paper.It is shown that the approach of using smoothing weight functions in deriving macro balance of linear momenta,macro balance of angular momenta and the new balance law proposed for closure of the mathematical model in Eringen’s work is neither needed nor used in the present work and is not supported by thermodynamics.All constitutive theories are derived using representation theorem and integrity,hence mathematically consistent and complete.The linear microdilation theory presented in this paper for thermoelastic solids is shown to be thermodynamically and mathematically consistent.
