Attraction property of a gimbal gyro with an electric motor

We consider an unbalanced gimbal gyro with vertical outer suspension axis mounted on an immovable base in the gravity field and supplied with an electric motor. The equations of motion of such a system admit a family of solutions describing its steady-state motions (regular precessions and rotor uniform rotations). We show that, in the case of an isolated minimum of the reduced potential energy, the perturbed motions tend in the course of time to steady-state motions in the same family (even in the critical cases of stability).     

Motion of a three-degree-of-freedom gyro with an electric spring and with zero angular momentum

We consider the motion of a three-degree-of-freedom gyro with an electric spring and with zero angular momentum mounted on a fixed base. The gimbal rotation angles are constrained by an elastic ring that is attached to the base and confines a rod attached to the internal gimbal. The equations of motion of the gyro are supplemented with equations allowing for the delay in the response of the gyro feedback circuit. By numerical integration we find a steady-state mode of the gyro motion, in which the rod alternately slides along the ring and moves in the interior of the ring. This motion can be used to check the gyro performance after launching a spacecraft to a near-Earth orbit by comparing the gyro motions in ground tests and on the orbit.     

分离摆式积分陀螺加速度计外环摩擦试验研究

为分离摆式积分陀螺加速度计外环摩擦力,提出一种在高精度三轴转台上测试摆式积分陀螺加速度计的新试验方法。该试验采用三轴转台中环转动速度随动摆式积分陀螺加速度计外环进动角速度,从而分离仪表外环轴摩擦力的方案。为研究三轴转台存在的动不平衡对摆式积分陀螺加速度计测试试验的影响,建立了三轴转台的动不平衡模型,分析了三轴转台的动不平衡对转台定位精度的影响,并通过提高三轴转台的带宽和改变工作点来获得高的定位精度,消除三轴转台的动不平衡扰动影响,完成分离摆式积分陀螺加速度计的外环摩擦力的试验。通过对试验数据进行分析,得出外环摩擦力的存在影响了摆式积分陀螺加速度计精度,为进一步改进仪表结构以提高仪表的精度提供了试验研究基础。     

Stability of a surface-charged viscous jet in an electric field

The stability of a surface-charged cylindrical jet in a longitudinal uniform electric field with respect to capillary pertubations is investigated in the linear approximation. The evolution of both axisymmetric and azimuthal-periodic perturbations is analyzed. In the latter case the first two modes among the azimuthal wavenumbers — bending and Bohr — are considered. Axisymmetric and bending instabilities lead to the transverse disintegration of the jet into individual drops and the Bohr mode to the longitudinal separation of the input jet into two parts. It is found that the axisymmetric and bending instabilities, respectively, can be completely suppressed and significantly attenuated by means of an external longitudinal field. In this case the role of the Bohr mode becomes more important leading under certain conditions to longitudinal longwave jet splitting. Events which can be interpreted as manifestations of longitudinal partition of the jet (dumbbell-like cross-section, branching nodes) are observed in experiments with evaporating polymer-solution microjets. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 29–40, March–April, 1998. The work was carried out with support from the Russian Foundation for Fundamental Research (project No. 97-01-00153).     

提高永磁陀螺电机效率的方法

永磁陀螺电机是一种取电机绕组反电势作为位置信号的无刷直流电机,通过锁相伺服电路的控制完成启动加速和恒速运行。首先推导了反电势控制的三相永磁陀螺电机电流、转矩、功率和效率等参数的计算公式,在此基础上说明了导通角的位置和大小对各种参数的影响,特别指出导通角(起始角～关断角)对电机效率有着非常明显的影响,然后提出用恒流源供电比用恒压源供电更有利于这种陀螺电机提高效率。最后以一个实际电机为例说明在导通角相同的条件下,恒流源供电较恒压源供电的电机效率提高10%,可达到98%以上。     

Stability of a stationary front of an exothermic reaction in the gas phase

The influence of the diffusion coefficient on the stability of a stationary front is investigated in the present piper on the assumption that the dependence of the reaction rate on the temperature is piecewise constant.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 14–16, July–August, 1987.     

Stability of Cosserat fluid motions

We obtain criteria of stability of the unsteady motion of an incompressible Cosserat fluid in an arbitrary time-dependent domain, employing a general energy method due to J. Serrin. It is shown that the original motion is stable if R _e ² 80 + 12800 C ₀ or if R _e80 + 6400 C ₀. The quantities R _e and C ₀ are the Reynolds number and Cosserat number, respectively, and - is the lower bound for the eigenvalues of the strain rate tensor D _ij.The theorems established for the stability criteria are universal in the sense that they do not depend either on the shape of the domain or on the distribution of the basic field variables. Finally an experimental scheme is proposed to determine the upper bound of the Cosserat number and consequently the characteristic length of a Cosserat fluid.     

Stability of the stationary motion of a spherical pendulum interacting with a string

The equation of motion of a spherical pendulum suspended at some point of a horizontal string is derived using a hybrid model of this mechanical system. The conditions for the asymptotic stability of the stationary motion of the spherical pendulum interacting with the elastic string are established     

Similarity in stationary motions of gas and two-phase medium with incompressible component

In this paper we suggest the transformation between the equations for a perfect gas and the equations describing in one-velocity approach the two-phase medium with any volume occupied by the incompressible phase. It is proved that the motion of a two-phase medium in the transformed coordinate system is similar with certain accuracy to that of a perfect gas. It means that the solutions obtained for perfect gas can be used to solve wave problems for media with incompressible component. There is no necessity directly to solve the problem for medium with incompressible component, and it is only sufficient to transform the known solution of the similar problem for a homogeneous medium. Thus, the solutions of many hydrodynamic problems for multi-component media with incompressible phase can be obtained without solving the original set of equations. The scope for the suggested transformation is demonstrated by reference to the strong explosion in a two-phase medium.     

Stability of the stationary motion of a double pendulum interacting with a string

The equation of in-plane vertical motion of a double pendulum suspended at some point of a horizontal elastic string is derived using a hybrid model of this mechanical system. The conditions for the asymptotic stability of the stationary motion of the pendulum interacting with the string are established     

Stability of axisymmetric motions in a rotating inviscid atmosphere

Summary We study the set of ordinary differential equations representing the truncation of the spectral vorticity equation in spherical geometry for two-dimensional, non divergent motions in a homogeneous, inviscid rotating atmosphere. The set of included spectral components represent an arbitrary axisymmetric field of motion (zonal flow) interacting with a couple of non zonal, wave-like perturbations. We analize the stability of the equilibrium configuration described by purely zonal flow, by an esplicit representation of the linear and non-linear parameters which characterize the unstable oscillations induced by perturbations of the equilibrium.

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Sommario Si studiano le soluzioni di un sistema di equazioni differenziali ordinarie che rappresentano il troncamento a poche componenti di Fourier dell'equazione di conservazione della vorticità per moti bidimensionali, non divergenti in una atmosfera rotante, inviscida e omogenea. Tale troncamento include tutte le componenti spettrali che rappresentano flussi a simmetria assiale (moti zonali) in interazione non lineare con una coppia di componenti asimmetriche che rappresentano flussi ondulatori. Si studia la stabilità della configurazione di equilibrio caratterizzata da moto zonale stazionario, analizzando i parametri lineari e non lineari che descrivono le oscillazioni instabili di ampiezza finita del campo di flusso che nascono da condizioni iniziali nell'intorno dell'equilibrio.

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This work was supported by the C.N.R. through the Gruppo Nazionale per la Fisica Matematica.     

Stability of a falling conducting liquid film in an alternating electric field

The flow of a thin viscous conducting liquid film falling along one of the plates of a vertically positioned plane capacitor is studied. The capacitor is connected to an alternating current power supply. It is shown that the presence of the electric field leads to flow destabilization; moreover, the parametric resonance of capillary waves is observed.     

Stability of a stationary steam-water front in a porous medium

The instability of a plane front between two phases of the same fluid (steam and water) in a porous medium is considered. The configuration is taken to be initially stationary with the more dense phase overlying the less dense phase. The frontal region is assumed sharp, so that macroscopic boundary conditions can be utilized. This assumption precludes the existence of dispersion instabilities. The stabilizing influence of phrase transition as well as the implication of different macroscopic pressure boundary conditions on the stability of the front are discussed and illustrated.     

Stability analysis of steady rotations of a rigid body bearing two-degree-of-freedom control moment gyros with dissipation in gimbal suspension axes

To study the stability of steady rotations of a control moment gyro system with internal dissipation, we use the Barbashin-Krasovskii theorem and the relation, established in [1], between the Lyapunov function and steady motions. Taking into account the special properties of the original problem, we reduce it to a lower-dimensional problem.We give a detailed presentation of an algorithm for analyzing the stability of steady motions of a gyrostat and use this algorithm to perform a complete study for two systems consisting, respectively, of one and two gyros whose gimbal axes are parallel to the principal axis of inertia of the system. Each steady motion is identified as either asymptotically stable or unstable. We find periodic motions that exist only in the presence of dynamic symmetry and which are regular precessions. For the system with two gyros, we prove the asymptotic stability of quiescent states and prove that in the angular momentum range where these states are defined the system does not have any other stable motions.     

陀螺电机动压气体轴承刚度测试方法改进（英文）

动压气体轴承陀螺电机的气膜刚度是评价轴承承载能力的关键指标。针对H型动压气体轴承陀螺电机气膜刚度测试方法存在测量精度和重复性差的问题,提出了刚度测试工装是保证刚度测试重复性精度的一个重要方面,刚度测试工装的加工和装配精度、材料的热变性和应力变形都是影响气膜刚度测试准确性的主要因素,在设计时必须考虑。通过对现有刚度测试工装材料、结构和方法的优化改进和仿真分析,验证了采用改进后的刚度测试工装和方法更有利于提高了轴承刚度测试的重复性精度。     

Stability of high-frequency periodic motions of a heavy rigid body with a horizontally vibrating suspension point

The motion of a heavy rigid body one of whose points (the suspension point) executes horizontal harmonic high-frequency vibrations with small amplitude is considered. The problem of existence of high-frequency periodic motions with period equal to the period of the suspension point vibrations is considered. The stability conditions for the revealed motions are obtained in the linear approximation. The following three special cases of mass distribution in the body are considered; a body whose center of mass lies on the principal axis of inertia, a body whose center of mass lies in the principal plane of inertia, and a dynamically symmetric body.