ANALYSIS OF THE MOTION OF A GYRO-THEODOLITE

With the method of analytical mechanics,this paper studies the motions of a gyro-theodolite under the action of (1) the torque of gravity only,(2)the torque applied by theband suspension.(3)the torque of the band suspension with air damping considered,theequations of motion are then established and their solutions are found.Furthermore,analysis of the law of motion and the behaviour of gyro-theodolite during the orientation ismade.     

FLOW OF A TRAIN OF DEFORMABLE FLUID PARTICLES IN A TUBE

I.IntroductionWangandSkalakll]studiedforsolidspheresintubes.HymanandSkalak12--31studiedthemovementofacompactfluidspheres(non-deformable)intubes.Theyonlystudiedcompactdropswhoseradiusesarenotbiggerthan0.7.Pozrikidisl4]studiedthenlotiollofdeformabletluidparticlesintubes.Inthispaper,westudiedtwo-phasenowregime,consistingofaperiodictrainofequallyspacedliquidslugsmovingaxisymmetricallyinacontinuousliquidphasewhichisimmisciblewiththeslugphase(Fig.l(a)).Wereportnumericalsolutionsforthehydrodynamic…     

PROPERTIES OF A HALF SPACE INCLUDING A TWISTED SHAFT OF REVOLUTION

The properties of an elastic half space including a partly embedded twisting shaft of revolution are studied. Without knowing the exact solution of the torsion problem of agiven embedded shaft, these properties can indicate some features of thc displacement or stress field of the half space and can sometimes be used for checking a numerical sohttion. An example for checking the correct stress distribution on surfaces of twisted rigid cylindrical shaft embedded in a half space is given.     

MID-FACETS OF A SIMPLEX

The mid-facet of a simplex in n-dimensional Euclidean space which was introduced quite recently is an important geometric element. An analytic expression for the mid-facet area of a simplex is firstly given. In order to obtain the expression, the exterior differential method was presented. Furthermore, the properties of the mid-facets of a simplex analogous to median lines of a triangle ( such us for all mid-facets of a simplex,there exists another simplex such that its edge-lengths equal to these mid-facets area respectively, and all of the mid-facets of a simplex have a common point) were proved.Finally, by applying the analytic expression, a number of inequalities which combine edge-lengths, circumradius , median line, bisection area and facet area with the mid-facet area for a simplex were established.     

SUGGESTION OF A NEW DEFINITION OF ANGULAR STRAIN

A new definition of angular strain is put forward in this paper. Analogous to the definition of linear strain, angular strain is also defined as a rate of change (of angular displacement). It is verified that the new definition is equivalent to the original besides being more convenient for geometrical interpretations. Using this new definition we have deduced the transformation formulas for rotation of coordinate axes, established the strain tensor and proved the Hooke's law for shearing.     

ON GRAMMATICAL COMPLEXITY OF A CLASS OF ATTRACTORS

ＯＮＧＲＡＭＭＡＴＩＣＡＬＣＯＭＰＬＥＸＩＴＹＯＦＡＣＬＡＳＳＯＦＡＴＴＲＡＣＴＯＲＳＬｕＱｉｎｈｅ（卢钦和）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ．ＳｕｚｈｏｕＵｎｉｖｅｒｓｉｔ｝＇．Ｓｕｚｈｏｕ２１５００６．Ｐ．Ｒ．Ｃｈｉｎａ）Ａｂｓｔ...     

A METHOD OF DETERMINING BUCKLED STATES OF THIN PLATES AT A DOUBLE EIGENVALUE

A method of determining bifurcation directions at a double eigenvalue is presented by combining the finite element method with the perturbation method. By using the present method, the buckled states of rectangular plates at a double eigenvalue are numerically analyzed. The results show that this method is effective.     

A STUDY OF J-INTEGRAL OF THE ORTHOTROPIC COMPOSITE MATERIAL

ＡＳＴＵＤＹＯＦＪ－ＩＮＴＥＧＲＡＬＯＦＴＨＥＯＲＴＨＯＴＲＯＰＩＣＣＯＭＰＯＳＩＴＥＭＡＴＥＲＩＡＬＷａｎｇＡｉ－ｑｉｎ（王蔼勤）；ＦｅｎｇＢａｏ－ｌｉａｎ（冯宝莲）；ＹａｎｇＷｅｉ－ｙａｎｇ（杨维阳）（ＴａｉｙｕａｎＨｅａｖｙＭａｃｈｉｎｅｒｙ．...     

THE ASYMPTOTIC SOLUTION OF A KIND OF STEFAN PROBLEM

In this paper,a kind of Stefan problem subject to general initial condition is studied.The slab considered is divided into three regions.There is a different time scale in each one.By means of PLK method or like multi-scales method,the asympto-tic solution of each one is obtained.Finally we discuss the asymptotic solution and draw some conclusions.     

A CLASS OF ALTERNATING GROUP METHOD OF BURGERS' EQUATION

IntroductionWeconsiderthefollowingnonlinearBurgers’equation : u t u u x=ε 2 u x2 ,　　 0 0 ,( 1 )withtheinitialandtheboundaryconditions　　　　　u(x,0 ) =f(x) ,　　 0 相似文献   

The theory of relativistic analytical mechanics of the rotational systems

I'IntroductionThespinningmotionisintrinsicattributeofmicroscopicparticle.In1979,R.BengtssonandS.Frauendorfaccuratlymeasuredthemaximumvolumesofthespinningrotativevelocityof14kindsofnucleons,andtheresultsshowedthatthemaximumvolumesofthespinningrotativevelocityofeachnucleonaredifferent[ll.Withthede\'elopingofmodernscienceandtechnology,moreandmoreexperimentalfactsrelatedtothehighspeedrotationquestions,theEinstein'srelativitytheoryandtherotationaltheoryofclassicalmechanicsarenotsuitabletothesepro…     

Exact solution of the Boltzmann equation

We build up immediate connection between the nonlinear Boltzmann transport equation and the linear AKNS equation, and classify the Boltzmann equation as the Dirac equation by a new method for solving the Boltzmann equation out of keeping with the Chapman, Enskog and Grad’s way in this paper. Without the effect of other external fields, the exact solution of the Boltzmann equation can be obtained by the inverse scattering method.     

粘弹性固体的精细积分有限元算法

粘弹性固体本构方程的数学表达式分为微分型和积分型两种，其数值求解主要是时域上离散计算。文中从微分型表达式出发导出其状态空间方程的数学表达式，通过严格推导论证了它与微、积分型表达式的等价性；引入状态空间方程，从而利用精细积分格式来求解粘弹性固体本构方程；给出了粘弹性固体本构方程的精细积分有限元算法，为求解粘弹性固体本构方程的数值解提供了一个新的途径，具有计算简便，求解精度高等优点。     

Nonlinear natural frequency of shallow conical shells with variable thickness

IntroductionTheplatesandtheshellswithvariablethicknessarewidelyusedinengineering .Theproblemaboutstaticshasbeenstudiedbymanyscholars;therearemanyRefs .[1 -4 ]inthisfield .Papersaboutnonlineardynamicsaremuchless[5 ,6 ].Inthispaper,selectingthemaximumamplitudeinthecenterofshallowconicalshellswithvariablethicknessasperturbationparameter,thenonlinearnaturalfrequencyofshallowconicalshellswithvariablethicknessisobtainedbymethodgiveninRef.[7] .Thenonlinearnaturalfrequencyisnotonlyconnectedwiththeva…     

COMPARISON OF STABILITY BETWEEN NAVIER-STOKES AND EULER EQUATIONS

The stability about Navier-Stokes equation and Euler equation was brought into comparison. And by taking their typical initial value problem for example, the reason of leading to the difference in stability between Navier-Stokes equation and Euler equation was also analyzed.     

Boussinesq方程的发展形式与Airy波理论差异性研究

应用势流理论，采用递推函数方法推导出一个新形式的Ｂｏｕｓｉｎｅｓｑ方程。通过对新方程的参数设置，可以讨论出Ｂｏｕｓｓｉｎｅｓｑ方程发展趋势和不同的发展形式。对浅水波动的描述方程，Ｂｏｕｓｓｉｎｅｓｑ方程的发展趋势为适用水深范围的拓展。拓展应用范围的大小则由其方程频散特征向Ａｉｒｙ波频散解逼近程度来决定。而Ｂｏｕｓｉｎｅｑ方程又不同于Ａｉｒｙ波，主要原因是Ｂｏｕｓｓｉｎｅｓｑ方程中含有线性频散项，Ａｉｒｙ波则只是长波首项近似，无线性频散项。其频散特征为精确的线性频散解。对实际水波传播而言，Ａｉｒｙ波理论的局限性是不言而喻的。     

Asymptotic Stability of N-Solitary Waves of the FPU Lattices

We study stability of N-solitary wave solutions of the Fermi-Pasta-Ulam (FPU) lattice equation. Solitary wave solutions of the FPU lattice equation cannot be characterized as critical points of conservation laws due to the lack of infinitesimal invariance in the spatial variable. In place of standard variational arguments for Hamiltonian systems, we use an exponential stability property of the linearized FPU equation in a weighted space which is biased in the direction of motion. The dispersion of the linearized FPU equation balances the potential term for low frequencies, whereas the dispersion is superior for high frequencies.We approximate the low frequency part of a solution of the linearized FPU equation by a solution to the linearized Korteweg-de Vries (KdV) equation around an N-soliton solution. We prove an exponential stability property of the linearized KdV equation around N-solitons by using the linearized Bäcklund transformation and use the result to analyze the linearized FPU equation.     

Characteristic solutions of scalar newton equations in one space dimension

Newton equations are dynamical systems on the space of fields. The solutions of a given equation which are curves of characteristic fields for its force are planar and have constant angular momentum. Separable solutions are characteristic with angular momentum equal to zero. A Newton equation is separable if and only if its characteristic equation is homogeneous. Separable equations correspond to invariants of homogeneous ordinary differential equations, and those associated with a given homogenous equation correspond to its generalized dilation symmetries. A Newton equation is compatible with the characteristic condition if and only if its characteristic equation is linear. Such equations correspond to invariants of linear ordinary differential equations. Those associated with a given linear equation correspond to the central force problems on its solution space. Regardless of compatibility, any Newton equation with a plane of characteristic fields has non-separable characteristic solutions.     

Anisotropic elastic materials capable of a three-dimensional deformation (static or dynamic) with only one displacement component and uncoupling of all three displacement components

It is shown that there are anisotropic elastic materials that are capable of a non-uniform three-dimensional deformation with only one displacement component. For wave propagation, the equation of motion can be cast in the form of the differential equation for acoustic waves. For elastostatics, the equation of equilibrium reduces to Laplace’s equation. The material can be monoclinic, orthotropic, tetragonal, hexagonal or cubic. There are also anisotropic elastic materials that uncouple all three displacement components. The governing equation for each of the uncoupled displacement can be cast in the form of the differential equation for acoustic waves in the case of dynamic or Laplace’s equation in the case of static. The material can be orthotropic, tetragonal, hexagonal or cubic.     

Integral theory for the dynamics of nonlinear nonholonomic system in noninertial reference frames

This paper establishes the integral theory for the dynamics of nonlinearnonholonomic system in noninertial reference frame.Firstly,based on the Routhequation of the relative motion of nonlinear nonholonomic system gives the firstintegral of the system.Secondly,by using cyclic integral or energy integral reduces theorder of the equation and obtains generalized Routh equation and Whittaker equationrespectively.Thirdly,derives canonical equation and variation equation and by usingthe first integral constructs integral invariant.And then,establishes the basic integralvariants and the integral invariant of Poincare-Cartan type.Finally,we give a series ofdeductions.