Helicoseir as Shape of a Rotating String (I): 2D Theory and Simulation Using ANCF

A physically simple but mathematically cumbersome problem of rotating heavy string with one fixed top point was studied. A nonlinear equation of its two-dimensional shapes of relative equilibrium was obtained and solved numerically. A linear case of small displacements was analyzed in terms of Bessel functions. The qualitative and quantitative behavior of the problem is discussed with the help of a bifurcation diagram. Dynamics of the two-dimensional model near the equilibrium positions were studied with the help of a simulation using the absolute nodal coordinate formulation (ANCF); the equilibriums were found to be instable. The reason for instability is explained using a variational principle. The outlines for further full three-dimensional analysis are briefly proposed in this paper, and the full derivation will be explained in the next paper.     

Navigation of a Mobile System with Parametrically Uncertain State Vector

Navigation of a mobile system with parametrically uncertain state vector is studied. The required navigation accuracy is attained through orientation control of the gyrostabilized platform and identification of the parameters of the model of the platform drift. A wide range of functionals that depend on the a posteriori distribution density can be used as the optimization criteria since the solution is general. In the numerical example, the Shannon criterion is used as the optimization criterion.     

Application of Cayley-Klein parameters in the problem of strapdown navigation system stochastic state vector synthesis for a self-contained space vehicle

The state vector and observer equations are obtained for a strapdown (gimballess) navigation system with three accelerometers, three angular rate sensors, and a barometric altimeter. These equations are based on the nonlinear filtration methods that ensure required estimation accuracy under arbitrary space maneuver of a vehicle.     

The impact of sensor parameters on the accuracy of a strapdown inertial vertical gyroscope

The major factors affecting the accuracy and performance of any measuring system are the errors of embedded sensors. In this paper we analyze the impact of sensor parameters on the characteristics of an inertial vertical gyroscope based on the Wiener filter.     

轴流风机叶尖泄漏流动的大涡模拟（英文）

本文采用大涡模拟(LES)的方法研究了在基于外壳直径的雷诺数为9.36×105条件下5叶片的轴流式风扇的流动特性,并且着重分析了叶尖泄漏的流动现象。本文使用了基于有限体积法和分层笛卡尔网格的可压流求解器进行数值计算,并应用了体积守恒的切割网格方法处理风扇几何结构的浸入式边界。同时开发了用于笛卡尔网格的旋转周期性边界条件,这样只需分析由2.5亿网格构造的包含一片叶片的72°区域。该研究首先对网格质量进行了分析,之后讨论了瞬态和时均流场的特性,并与使用RANS的5叶片模拟结果进行了对比。RANS和LES模拟结果的主要不同之处体现在叶尖泄漏涡尾流中的湍流动能。本文进而研究了叶尖间隙对叶尖泄漏涡的影响。研究表明,间隙的大小会影响叶尖泄漏涡的大小形状。此外,间隙中更多的分离现象和反向旋转涡会导致较低的湍流动能。     

Features in the propagation of a supersonic fan-shaped jet

We present a scheme for the calculation of a fan-shaped jet formed on collision of supersonic oppositely directed underexpanded jets. A comparison with experiment is offered.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 16, No. 6, pp. 1106–1109, June, 1969.     

The use of Gaussian approximation for the solution of suboptimal control of radio system state vector problem

The problem of optimal non-linear stochastic systems control on the basis of information criteria use is solved. A theorem is introduced proving the possibility of reducing partial derivatives equation solution to the integration of common differential equations. On the example of Shannon criterion the control of a dynamic object is synthesized. Numerical results are obtained illustrating the efficiency of the suggested approach practical use.     

Field enhancement factor and field emission from a hemi-ellipsoidal metallic needle

We present an exact solution for the electrostatic field between a metallic hemi-ellipsoidal needle on a plate (as a cathode) and a flat anode. The basic idea is to replace the cathode by a linearly charged thread in a uniform electric field and to use a set of “image” charges to reproduce the anode. We calculate the field enhancement factor on the needle surface and ponderomotive force acting on the needle. Using the Fowler–Nordheim theory we obtain an exact analytical formula for the total current.