Special Lie symmetry and Hojman conserved quantity of Appell equations for a Chetaev nonholonomic system

A special Lie symmetry and Hojman conserved quantity of the Appell equations for a Chetaev nonholonomic system are studied. The differential equations of motion and Appell equations of the Chetaev nonholonomic system are established. Under the special Lie symmetry group transformations in which the time is invariable, the determining equation of the special Lie symmetry of the Appell equations for a Chetaev nonholonomic system is given, and the expression of the Hojman conserved quantity is deduced directly from the Lie symmetry. Finally, an example is given to illustrate the application of the results.     

Systematization of relaxation gas dynamics equations. A review

The phenomenological theory of relaxation gas dynamics equations is outlined for laminar flows of multicomponent reacting gases in an approximation analogous to the Navier-Stokes approximation. A system of general equations of relaxation gas dynamics including the level kinetics equations for all excited internal degrees of freedom is formulated on the basis of notions of continuum mechanics. A procedure of going over to particular cases characterized by certain relations between the relaxation times is described and examples of the corresponding closed systems of gas dynamics equations including systems containing the balance equations of the level or mode approximations for the vibrational energy levels of molecules of a gas mixture are given. A method of constructing a database of the models of the rate constants of physicochemical processes as coefficients in the source terms of the balance equations is considered.     

Influence of an Extraneous Electric Current on the Stress State of an Annular Plate of Variable Rigidity

Two-dimensional magnetoelastic equations are derived and an algorithm is proposed to solve a boundary-value problem for an annular plate of variable rigidity under the action of an extraneous electric current. A numerical example is given     

On the problem of crack system with an elliptic hole

The problem of cracks with an elliptic hole in an infinite plane is investigated. By introducing the fictitious loads on the hole edge and using the Muskhelishvili method, the problem is reduced to solving a system of mixed-type integral equations in which some are Fredholm equations but others Cauchy-type singular ones. A numerical method is suggested and can be used for the treatment of other similar equations. The numerical results for some typical examples are given, showing that the method is really effective.     

刚弹耦合的机器人机构动力学方程及其解

本文给出了一般开链弹性机器人机构动力学方程。该方程是由关节广义坐标和杆件模态坐标联立的非线性微分方程组。对方程的刚性性质作了讨论,根据Rosenbrock的二级二阶半隐式Runge—Kutta公械,导出了一种求解弹性机器人机构动力学方程的算法。对一平面二杆操作手机构作了计算。对该例同时也用Gill方法作了计算,验证了上述算法的精度和效率。     

Vortex motions of liquid in a narrow channel

Quasi-linear integrodifferential equations that describe vortex flows of an ideal incomparessible liquid in a narrow curved channel in the Eulerian-Lagrangian coordinate system are considered. The necessary and sufficient conditions for hyperbolicity of the system of equations of motion are obtained for flows with a monotonic velocity depth profile. The propagation velocities of the characteristics and the characteristic form of the system are calculated. A particular solution is given in which the system of integrodifferential equations changes type with time. The solution of the Cauchy problem is given for linearized equations. An example of initial data for which the Cauchy problem is ill-posed is constructed. Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 38–49, July–August, 1998.     

存在相关约束Euler-Lagrange 方程解的存在唯一性

 Euler-Lagrange方程是多体系统动力学的重要数学模型之一. 对存 在诸如包含平行机构的多体系统，采用绝对坐标建模时，系统动力学约束 方程往往是一组相关约束方程. 本文讨论了存在相关约束的Euler-Lagrange 方程解的存在唯一性条件，给出了一个解的存在唯一性定理. 定理中不再 要求满秩，但针对常秩的情形, 对于变秩的情形，通过注释的形式给出了 定理的使用方式.     

Damage evolution in an expanding/contracting hollow sphere at large strains

A generalization of one of the classical problems of plasticity theory, expansion/contraction of a hollow sphere, is proposed assuming that the conventional constitutive equations for rigid plastic, hardening material are supplemented with an arbitrary ductile damage evolution law. No restriction is imposed on the hardening law in the analytic part of the solution. The initial/boundary value problem is reduced to two equations in characteristic coordinates. A numerical scheme to solve these equations is proposed. An illustrative example is given.     

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.     

On the representation of the solutions of the equilibrium equations of a piezoelectric transversally-isotropic spherical shell

A method is proposed for constructing equilibrium equations for thickness-polarized transversally isotropic piezoceramic shells. The method is based on Fourier expanding the required functions in Legendre polynomials. The appropriate system of differential equations is formed for the expansion coefficients as functions of two independent variables. The equilibrium equations are given in particular for transversally isotropic spherical shells. A method is given for constructing the general solution in the first approximation. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 7, pp. 59–68, July, 1999.     

多柔体系统动力学方程一种数值求解方法

本文提出用含有二阶自校正功能的增广法和半隐式Runge-Kutta法相结合求解多柔体系统动力学中的微分-代数型方程。并给出了计算实例和实验验证。     

On CML model for study of spatiotemporal chaos

A new coupled map lattic(CML)model is given by using some stability analysis for the related difference equations.Numerical results show that the new model is.an effective one of studying spatiotemporal chaos,especially for strongly coupled systems.     

Preconditioned conjugate gradient methods for the incompressible Navier-Stokes equations

A robust technique for solving primitive variable formulations of the incompressible Navier-Stokes equations is to use Newton iteration for the fully implicit non-linear equations. A direct sparse matrix method can be used to solve the Jacobian but is costly for large problems; an alternative is to use an iterative matrix method. This paper investigates effective ways of using a conjugate-gradient-type method with an incomplete LU factorization preconditioner for two-dimensional incompressible viscous flow problems. Special attention is paid to the ordering of unknowns, with emphasis on a minimum updating matrix (MUM) ordering. Numerical results are given for several test problems.     

Stability for manifolds of equilibrium states of generalized Hamiltonian systems

For a generalized Hamiltonian system, stability for the manifolds of equilibrium states is presented based on Lyapunov’s stability theories. Equilibrium equations, perturbation equations and first approximate equations of the system are given. A theorem for the stability of manifolds of equilibrium states of general autonomous system is used to the generalized Hamiltonian system, and three propositions on the stability of manifolds of equilibrium states of the system are obtained. Two examples are given to illustrate application of the method and results.     

Exact solutions of the kinetic-moment equations of a mixture of monatomic gases

An extension is given of the class of exact solutions of the kinetic-moment equations for a monatomic gas in the absence of external forces [1] to the case of a mixture of monatomic Maxwellian gases with account for external forces. Very simple solutions of this class are obtained which are examples of the normal solutions of the Boltzmann equations in the Chapman-Enskog sense [2]. Conclusions are summarized concerning the applicability of the various methods of solving the Boltzmann equations and their properties, obtained on the basis of an analysis of the indicated exact solutions.The author wishes to thank M. N. Kogan and A. A. Nikol'skii for their interest in the study.     

Reduced equilibrium equations for perfectly elastic materials

Sufficient conditions are given on the coordinate systems which enable reduced equilibrium equations to be derived for perfectly elastic materials involving deformations which depend in an essential way only on two of the three coordinates. Reduced equilibrium equations given previously for plane and axially symmetric deformations are special cases of the equations given here. These equations considerably reduce the calculations involved in investigating possible solutions of finite elasticity, either exact semi-inverse solutions or approximate perturbation solutions. Moreover a formula for the pressure function appearing in the reduced equilibrium equations is given which relates to the corresponding pressure function associated with the inverse deformation. This formula is similar to one given previously for fully three dimensional deformations.     

Technical Stability of Forced Motion in Nonstationary Automatic-Control Systems of Variable Structure

Sufficient conditions of technical stability are established for nonstationary automatic-control systems of variable structure. The case is considered where for appropriate controls and for all admissible initial perturbations from a predefined measurable set of initial states, the nonstationary parameters of a process under external actions vary within given ranges. The control process depends on the mismatch signal and its derivatives up to an order that is less by one than the order of the equations of motion. The associated system of differential equations contains discontinuous time-dependent coefficients. A relationship is established between the eigenvalues of the quadratic forms of the given Lyapunov functions and the technical-stability criteria. It is shown that the technical-stability conditions do not depend on the sliding-mode conditions for variable-structure control processes     

The simulation of oscillatory pipe flow on an analogue computer

Summary A formulation of equations governing oscillatory flow of a fluid in a circular pipe is given. The equations are then cast in a form suitable for analogue computation and a corresponding programming diagram suitable for use with an EAI 680 Analogue Computer is provided. Results have been obtained forNewtonian flow for a range ofReynolds numbers and for combinations of the realReynolds number, and the ratio of elastic to viscous forces in the case of linear viscoelastic fluids.The displacement profiles given in this work do not depend upon specific rheological models and are therefore of universal validity for linear fluids.