完整力学系统的高阶运动微分方程

从质点系的牛顿动力学方程出发,引入系统的高阶速度能量,导出完整力学系统的高阶Lagrange方程、高阶Nielsen方程以及高阶Appell方程,并证明了完整系统三种形式的高阶运动微分方程是等价的.结果表明,完整系统高阶运动微分方程揭示了系统运动状态的改变与力的各阶变化率之间的联系,这是牛顿动力学方程以及传统分析力学方程不能直接反映的.因此,完整系统高阶运动微分方程是对牛顿动力学方程及传统Lagrange方程、Nielsen方程、Appell方程等二阶运动微分方程的进一步补充. 关键词： 高阶速度能量 高阶Lagrange方程 高阶 Nielsen方程 高阶Appell方程     

Equations of motion in unified five-dimensional geometrized theory

The equations of motion in unified five-dimensional theory of gravitation, electromagnetism, and scalar field are considered. It is shown that some of the equations of the theory follow from the rest as equations of motion. In the classical limit of the theory, the equations of motion are found, which coincide with the related equations of general relativity. The similarity of the classical limit of the five-dimensional theory and of the Brans-Dicke theory is noted.     

Equations of motion of particle in circular accelerator with general field

Lagrange equations of motion are derived for a particle in a circular accelerator with arbitrarily spatially variable guiding magnetic field describing the motion of a particle by means of dimensionless deviations of the particle from a circle as the reference curve. The author also derives linearized equations of motion (so-called equations of perturbations used in stability investigations according to the Ljapunov method of the 1st approximation). The equations are given in the closed form and are thus quite exact.     

Extraction of the spurious states from the solution of the motion equation within the random phase approximation

The general form of nuclear Hamiltonian equation of motion is derived within the Random Phase Approximation (RPA). The connection between the Goldstone modes of motion (spurious states) and the equations of motion is shown. The general method of extraction of spurious states from the solution of the RPA equations of motion is proposed.     

Post-post-Newtonian equations of motion for point particles in the general theory of relativity

The post-post-Newtonian equations of motion for point particles are derived from the Einstein gravitational field equations by using the Einstein-Infeld-Hoffmann method with the help of the energy-momentum tensor proposed by Infeld and Plebanski [5, 6]. The obtained equations of motion coincide with the equations derived by Kopeikin [10] by using the Fock method.     

An alternative approach for the analysis of nonlinear vibrations of pipes conveying fluid

Based on a novel extended version of the Lagrange equations for systems containing non-material volumes, the nonlinear equations of motion for cantilever pipe systems conveying fluid are deduced. An alternative to existing methods utilizing Newtonian balance equations or Hamilton's principle is thus provided. The application of the extended Lagrange equations in combination with a Ritz method directly results in a set of nonlinear ordinary differential equations of motion, as opposed to the methods of derivation previously published, which result in partial differential equations. The pipe is modeled as a Euler elastica, where large deflections are considered without order-of-magnitude assumptions. For the equations of motion, a dimensional reduction with arbitrary order of approximation is introduced afterwards and compared with existing lower-order formulations from the literature. The effects of nonlinearities in the equations of motion are studied numerically. The numerical solutions of the extended Lagrange equations of the cantilever pipe system are compared with a second approach based on discrete masses and modeled in the framework of the multibody software HOTINT/MBS. Instability phenomena for an increasing number of discrete masses are presented and convergence towards the solution for pipes conveying fluid is shown.     

Equations of motion of a solid in a circular orbit at fast relative motion of its carried material point

An approximated set of equations of motion of a solid with respect to its center of mass is obtained. The estimate from which the solutions of rough equations approximate the solutions of an exact set of equations of motion is determined.     

Integrability of Nonlinear Equations of Motion on Two-Dimensional World Sheet Space-Time

The integrability character of nonlinear equations of motion of two-dimensional gravity with dynamical torsion and bosonic string coupling is studied in this paper. The space-like and time-like first integrals of equations of motion are also found.     

On similarity criteria at the experimental modeling of the flying vehicles motion with the aid of small-scale models

The equations of the longitudinal motion of flying vehicles at their steady and unsteady motion are considered. The nondimensionalization of equations has been carried out, and the similarity criteria have been obtained. The capabilities of the experimental modeling of the unsteady motion of flying vehicles are illustrated with the aid of small-scale models.     

Mechanics of a particle near the center of a rotating ring

The equations of motion of a test particle moving near the center of a massive rotating ring are derived up to the post-post-Newtonian order of approximation, by using the metric tensor for many body system which is Minkowskian at spatial infinity. Logarithmic divergences due to self-interaction of the ring appear in the equations of motion. These divergences can be removed by the procedure which is similar to the renormalization method in particle physics. In the equations of motion there appears a force directing to the rotation axis and depending on the angular velocity of the ring. This force vanishes when the magnitude of the gravitational constant times the mass of the ring divided by the radius of the ring is about one tenth of the square of the velocity of light. Under this condition it is shown that the relative magnitude of the Coriolis force to the centrifugal force in the equations of motion agrees with the expected one from the equations of motion in a rotating reference frame.     

Dynamics of systems of extended bodies in monad representation

A universal form proposed earlier by the author for the equations of motion is used to find a monad representation of the equations of motion of a system of N extended bodies in general relativity theory. An explicit form of the equations of motion in a fixed chronometric reference system is presented. It is shown that it differs from the known coordinate motion equations obtained by the Fock method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 72–78, January, 1995.     

相对运动动力学系统Nielsen方程的Lie对称性与Hojman守恒量

研究相对运动动力学系统Nielsen方程的Lie对称性和Lie对称性直接导致的Hojman守恒量.在群的无限小变换下,给出相对运动动力学系统Nielsen方程Lie对称性的定义和判据;得到相对运动动力学系统Nielsen方程Lie对称性的确定方程以及Lie对称性直接导致的Hojman守恒量的表达式.举例说明结果的应用. 关键词： 相对运动动力学 Nielsen方程 Lie对称性 Hojman守恒量     

THE PROBLEM OF MOTION IN THE KALUZA THEORY

It is shown that the equations of motion for a charged massive particle are consequences of the field equations in Kaluza unification theory of gravitation and electromagnetism, i.e., the equations of motion for the particle can be deduced from Kaluza field equations, just as that in Einstein's theory of motion of general relativity the equations of motion for a massive particle are consequences of the Einstein equations. Furthermore, the Lorentz equations for a particle maving in the Maxwell electromagnetic field on the Minkowskian space-time can also be obtained from the Maxwell equations by means of the Kaluze mechanism of the Maxwell theory.     

A variational principle for Newton-Cartan theory

In the framework of a space-time theory of gravitation a variational principle is set up for the gravitational field equations and the equations of motion of matter. The general framework leads to Newton's equations of motion with an unspecified force term and, for irrotational motion, to a restriction on the propagation of the shear tensor along the streamlines of matter. The field equations obtained from the variation are weaker than the standard field equations of Newton-Cartan theory. An application to fluids with shear and bulk viscosity is given.     

Nonlocal conserved quantities,balance laws,and equations of motion

A formalism is developed whereby balance laws are directly obtained from nonlocal (integrodifferential) linear second-order equations of motion for systems described by several dependent variables. These laws augment the equations of motion as further useful information about the physical system and, under certain conditions, are shown to reduce to conservation laws. The formalism can be applied to physical systems whose equations of motion may be relativistic and either classical or quantum. It is shown to facilitate obtaining global conservation laws for quantities which include energy and momentum. Applications of the formalism are given for a nonlocal Schrödinger equation and for a system of local relativistic equations of motion describing particles of arbitrary integral spin.     

Derivation of fluid dynamics from kinetic theory with the 14-moment approximation

We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains two approximations, the first being the so-called 14-moment approximation to truncate the single-particle distribution function. The second consists in the choice of equations of motion for the dissipative currents. Israel and Stewart used the second moment of the Boltzmann equation, but this is not the only possible choice. In fact, there are infinitely many moments of the Boltzmann equation which can serve as equations of motion for the dissipative currents. All resulting equations of motion have the same form, but the transport coefficients are different in each case.     

正则形式的QED约束关联动力学（Ⅱ）等时关联格林函数的运动方程与二体关联近似

本文把多时关联格林函数的运动方程转变成等时关联格林函数的运动方程，包括电子和光子的密度矩阵的运动方程以及等时顶点的运动方程，在二体关联截断近似下，给出运动方程，高斯定律及Ｗａｒｄ恒等式的明显表达式．     

正则形式的SU（N）规范理论的约束关联动力学（Ⅲ）等时关联Green函数的运动方程与二体关联近似

把多时关联Ｇｒｅｅｎ函数的运动方程转变成等时关联Ｇｒｅｅｎ函数的运动方程，其中包括夸克和胶子的密度矩阵的运动方程以及顶角函数的运动方程．在二体关联截断近似下，给出运动方程、高斯定律和Ｗａｒｄ恒等式的明显表达式．     

相对运动动力学系统Appell方程Mei对称性导致的Mei守恒量

研究相对运动动力学系统Appell方程的Mei对称性及其直接导致的Mei守恒量.在群的无限小变换下,给出相对运动动力学系统Appell方程Mei对称性的定义和判据;得到相对运动动力学系统Appell方程Mei对称性的结构方程以及Mei对称性直接导致的Mei守恒量的表达式.举例说明结果的应用. 关键词： 相对运动动力学 Appell方程 Mei对称性 Mei守恒量