NOETHER’S THEORY FOR NONHOLONOMIC DYNAMICAL SYSTEMS RELATIVE TO NON-INERTIAL REFERENCE FRAME

The new variational principle of Gauss’s form of nonlinear nonholonomicnonpotential system relative to non-inertial reference frame is established byconstructing generalized inertial potentials.Noether’s theorem and Noether’s inversetheorem of the system above is presented and proved.Finally,one example is given toillustrate the application.     

NOETHER’S CONSERVATION LAWS OF HOLONOMIC NONCONSERVATIVE DYNAMICAL SYSTEMS IN GENERALIZED MECHANICS

ＮＯＥＴＨＥＲ’ＳＣＯＮＳＥＲＶＡＴＩＯＮＬＡＷＳＯＦＨＯＬＯＮＯＭＩＣＮＯＮＣＯＮＳＥＲＶＡＴＩＶＥＤＹＮＡＭＩＣＡＬＳＹＳＴＥＭＳＩＮＧＥＮＥＲＡＬＩＺＥＤＭＥＣＨＡＮＩＣＳＱｉａｏＹｏｎｇ－ｆｅｎ（乔永芬）ＹｕｅＱｉｎｇ－ｗｅｎ（岳庆文）（Ｎｏ...     

GENERALIZED NOETHER’S THEOREM OF NONHOLONOMIC NONPOTENTIAL SYSTEM IN NONINERTIAL REFERENCE FRAMES

The new Lagrangian of the relative motion of mechanical system is constructed,thevariational principles of Jourdain’s form of nonlinear nonholonomic nonpotential system innoninertial reference frame are established,the generalized Noether’s theorem of thesystem above is presented and proved,and the conserved quantities of system are studied.     

EIGEN THEORY OF VISCOELASTIC DYNAMICS BASED ON THE KELVIN-VOIGT MODEL

Using the eigen theory of solid mechanics, the eigen properties of anisotropic viscoelastic bodies with Kelvin-Voigt model were studied, and the generalized Stokes equation of anisotropic viscoelastic dynamics was obtained, which gives the three-dimensional pattern of viscoelastical waves. The laws of viscoelastical waves of different anisotropical bodies were discussed. Several new conclusiones are given.     

ON LIAPOUNOFF’S METHOD IN THE THEORY OF STABILITY OF LAMINAR FLUID FLOWS

In[1]Zhou extended some Liapounoff‘s theorems of the theory of stability in the case of plane laminar fluid flows.In[2]Zhou and Li investigated the eigenvalue problem and expansion theorems associated with Orr-Sommerfeld equation,and obtained some new results.In this paper,based on the results of[1]and[2]we shall prove:(1)For the linearized problem the definition of stability according to the eigenvalues of Orr-Sommerfeld equation and that according to the perturbation.energy are equivalent;(2)The method of linearization is admissible for the stability pro-blem of plane laminar fluid flows for sufficiently small initial disturbance.     

COMPREHENSIVE MATHEMATICAL MODEL OF MICROCIRCULATORY DYNAMICS (Ⅰ)——BASIC THEORY

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｂａｓｉｃｆｕｎｃｔｉｏｎｏｆｔｈｅｍｉｃｒｏｃｉｒｃｕｌａｔｉｏｎｉｓｔｏａｌｌｏｗｒａｐｉｄｅｘｃｈａｎｇｅｏｆｗａｔｅｒ，ｇａｓｅｓ，ｎｕｔｒｉｅｎｔｓａｎｄｗａｓｔｅｐｒｏｄｕｃｔｓｂｅｔｗｅｅｎｔｈｅｂｌｏｏｄａｎｄｔｉｓｓｕｅｃｅｌｌｓ．Ａｍｉｃｒｏｃｉｒｃｕｌａｔｉｏｎｕｎｉｔｔｈｅｒｅｆｏｒｅｃｏｎｓｉｓｔｓｏｆｍｉｃｒｏｖｅｓｓｅｌｓ（ａｒｔｅｒｉｏｌｅｓ，ｃａｐｉｌｌａｒｉｅｓ，ｖｅｎｕｌｅｓ，ｔｈｏｒｏｕｇｈｆａｒｅｓａｎｄａｒｔｅｒｉｏｌｅ＿…     

COMPREHENSIVE MATHEMATICAL MODEL OF MICROCIRCULATORY DYNAMICS (Ⅰ)——BASIC THEORY

Under the basis of physiological data, a nonlinear and unsteady comprehensive mathematical model of microcirculatory dynamics with distributed parameters is developed. Hemodynamics, interstitium dynamics, lymph dynamics, dynamics of protein transport, oxygen dynamics, dynamics of heat transfer, and myogenic and metabolic regulation procedures are included. The interactions between these factors were comprehensively exhibited. The influences of arteriolar vasomotion and nonlinear viscoelasticity of blood in arteriole are considered. A simplified vessel network consisting of arteriole, open and reserved capillaries, venule, initial lymphatics and arteriole-venule anastomose is adopted as the geometrical model. This kind of comprehensive mathematical model is helpful in analyzing clinical data and developing a “numerical experiment method” in microcirculation research.     

WONDER BEYOND EXPECTATION: NOETHER’S THEOREM IN MECHANICS

诺特(Noether) 定理建立了对称性与守恒定律之间的联系,是现代物理学与力学的基石之一。文中介绍了诺特定理提出的起因、定理的内涵及相关逸闻,说明了固体力学中J 积分、艾西比(Eshelby) 张量与诺特定理的关系。     

A THEORY OF CLASSICAL SPACETIME (Ⅱ)——EDDINGTON’S IDENTIFICATION

Based on the SU(2)-structure, the identification procedures of Eddington and Weyl are followed in order to see what logical conclusions these two schemes lead to.     

EXTENSION OF POINCARE’S NONLINEAR OSCILLATION THEORY TO CONTINUUM MECHANICS (I)-BASIC THEORY AND METHOD

In this paper we extend Poincare’s nonlinear oscillation theory of discrete system to continuum mechanics. First we investigate the existence conditions of periodic solution for linear continuum system in the states of resonance and non-resonance. By applying the results of linear theory, we prove that the main conclusion of Poincare’s nonlinear oscillation theory can be extended to continuum mechanics. Besides, in this paper a new method is suggested to calculate the periodic solution in the states of both resonance and nonresonance by means of the direct perturbation of partial differential equation and weighted integration.     

The integration methods of Vacco dynamics equation of nonlinear nonholonomic system

ＴＨＥＩＮＴＥＧＲＡＴＩＯＮＭＥＴＨＯＤＳＯＦＶＡＣＣＯＤＹＮＡＭＩＣＳＥＱＵＡＴＩＯＮＯＦＮＯＮＬＩＮＥＡＲＮＯＮＨＯＬＯＮＯＭＩＣＳＹＳＴＥＭＬｕｏＳｈａｏｋａｉ（罗绍凯）（ＲｃｅｅｉｖｅｄＡｕｇ．２．１９９３：ｃｏｍｍｕｎｉｃａｔｅｄｂｙＷａｎ...     

非完整非保守系统在相空间的Noether定理及其逆定理

本文根据动力学系统在相空间的作用积分在无穷小群变换下的变换性质，得到了非完整非保守系统在相空间的Ｎｏｅｔｈｅｒ定理和逆定理。并举例说明。     

关于经典非完整力学的一个争议

本文对文献[4]的论断提出不同意见。同时对传统的 Gauss-Appell- 非完整动力学理论和 Vacco 动力学理论的特征给出评价。     

On the classic nonholonomic dynamics

For first-order nonlinear nonholonomic systems, the present paper proves that thed-δ operations are commutative and derives the equation of motion without making use of the additional Appell-Chetaev condition. This equation of motion coincides with the equation of “Vacco dynamics”. Project supported by the Science-Technology Foundation for Universities     

Noether's theory of mechanical systems with unilateral constraints

Ｎｏｅｔｈｅｒ’ｓｔｈｅｏｒｅｍｒｅｖｅａｌｓｔｈｅｉｎｎｅｒｃｏｎｎｅｃｔｉｏｎｂｅｔｗｅｅｎｔｈｅｃｏｎｓｅｒｖａｔｉｏｎｌａｗｓａｎｄｔｈｅｄｙｎａｍｉｃａｌｓｙｍｍｅｔｒｙｏｆｄｙｎａｍｉｃａｌｓｙｓｔｅｍｓ．Ｉｎｔｈｅｒｅｃｅｎｔｔｗｅｎｔ...     

关于经典非完整力学

对一阶非线性非完整系统,本文证明了,d-δ运算是可交换的,并且不必附加条件推导出运动方程,这个运动方程和“Vacco动力学”方程一致。     

Kinetic theory molecular dynamics; numerical considerations

Typical numerical simulations of dense plasmas are limited by either an inability to treat the dynamical quantum evolution of the electrons or a difficulty with strongly-coupled ions. Yet these different physics problems are individually well-treated by particular approximations. Kinetic theory molecular dynamics (KTMD) is a hybrid approach that treats electrons via kinetic theory (KT) and ions with molecular dynamics (MD). We present a derivation suitable for classical plasmas and specialize to the Vlasov or mean-field case. In addition, we consider the limit of adiabatic electron dynamics, where the problem reduces to the Poisson–Boltzmann (PB) equations coupled to MD. An exploration of practical ways to implement KTMD within an existing MD framework. The initial goal is to develop computationally efficient solutions of the PB problem, suitable for large-scale PB or Thomas-Fermi MD simulations.     

Noether's theorem for nonholonomic systems of non-Chetaev's type with unilateral constraints in event space

Ｔｈｅｓｔｕｄｙｏｆｃｏｎｓｅｒｖａｔｉｏｎｌａｗｓｏｆｄｙｎａｍｉｃａｌｓｙｓｔｅｍｉｓａｓｉｇｎｉｆｉｃａｎｔａｓｐｅｃｔｏｆｍｏｄｅｒｎａｎａｌｙｔｉｃａｌｍｅｃｈａｎｉｃｓ.Ｉｎ1918,ｕｓｉｎｇｔｈｅｉｎｖａｒｉａｎｃｅｏｆＨａｍｉｌｔｏｎａｃｔｉｏｎｕｎｄｅｒｔｈｅｉｎｆｉｎｉｔｅｓｉｍａｌｔｒａｎｓｆｏｒｍａｔｉｏｎｓ,Ｎｏｅｔｈｅｒ[1]ｓｔｕｄｉｅｄｃｏｎｓｅｒｖａｔｉｏｎｌａｗｓｏｆｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍａｎｄｐｒｅｓｅｎｔｅｄｔｈｅｆａｍｏｕｓＮｏｅｔｈｅｒ’ｓｔｈｅｏｒ…