Amplitude-frequency analysis of the earth polar oscillation process

The dynamic analysis of the Earth pole oscillatory motion is used to study the gravitational-tidal mechanism of formation of the annual component of the process. The results of an analysis of the interaction between the fine resonance structure of the long-period perturbation and the diurnal and semidiurnal tides are used to derive equations for the amplitude and phase of the oscillatory process of six-year pole wobble.     

Fluctuations of pole oscillations of deformable earth under nonstationary perturbations

An approach of celestial mechanics is used to consider variations in the tensor of inertia due to elastic deformations arising under the action of the centrifugal potential. The effects of influence of random actions are investigated in an example of fluctuation-dissipative perturbations of geophysical nature. A combined model of the Earth rotation fluctuations permits taking into account the stochastic components of the pole tide. It is shown that small irregular perturbations in tidal processes generate variations in the Chandler component of the pole oscillations.     

Oscillatory-rotational processes in the Earth motion about the center of mass: Interpolation and forecast

The celestial-mechanics approach (the spatial version of the problem for the Earth-Moon system in the field of gravity of the Sun) is used to construct a mathematical model of the Earth’s rotational-oscillatory motions. The fundamental aspects of the processes of tidal inhomogeneity in the Earth rotation and the Earth’s pole oscillations are studied. It is shown that the presence of the perturbing component of gravitational-tidal forces, which is orthogonal to the Moon’s orbit plane, also allows one to distinguish short-period perturbations in the Moon’s motion. The obtained model of rotational-oscillatory motions of the nonrigid Earth takes into account both the basic perturbations of large amplitudes and the more complicated small-scale properties of the motion due to the Moon short-period perturbations with combination frequencies. The astrometric data of the International Earth Rotation and Reference Systems Service (IERS) are used to perform numerical simulation (interpolation and forecast) of the Earth rotation parameters (ERP) on various time intervals.     

Gravitational-Tidal Model of Oscillations of Earth’s Poles

Based on the analysis of solar and lunar gravitational momentum, a viscoelastic Euler- Liouville model of the Earth’s pole oscillations is constructed. The model is based on taking into account the data on Earth’s shape and physical processes and does not involve the use of mathematical fitting methods, for example, based on polynomials. Within the framework of the model, the chandler frequency has themeaning of the fundamental frequency of the oscillations of the mechanical system, and the annual frequency is interpreted as the frequency of the compelling force. A delicate mechanism of oscillation excitation is found, based on a combination of eigenfrequencies and forced frequencies. The model has only six parameters, found from the experimental data of the least-squares method. The received forecast has high accuracy on an interval of several years.     

Rotational-oscillational motions of the nonrigid Earth about the center of mass

We use the model of a nearly axisymmetric viscoelastic rigid body to study perturbed rotational-oscillational motions of the Earth’s pole. We point out that the Chandler component of oscillations is of celestial-mechanics nature and is caused by the gravitational-tidal actions of the Sun and the Moon. We analyze the pole oscillation excitation mechanism at a frequency close to the Chandler frequency and show that the undamped pole oscillations are caused by the resonance harmonic of the external perturbation at a frequency close to the free nutation frequency. We discuss whether it is possible to solve the problem of constructing a short-term forecast of the pole motion on the basis of a polynomial filter obtained by the least-squares method without taking into account small-scale oscillations caused by wide-band random factors of arbitrary physical nature. In the present paper, we perform numerical simulation of tidal inhomogeneities in the Earth’s axial rotation. Attention is mainly paid to the analysis of day length variations on short time intervals with periods less than or equal to one year (interannual oscillations) and to their forecast.     

To Calculations of the Free Fall Acceleration on the Earth Surface

We obtain computational expressions for determining the generalized free fall acceleration at any point on the Earth surface depending on the terrestrial, solar, and lunar gravities, height above sea level, season, and diurnal time. The acceleration components due to the solar gravity and the Earth revolution around the Sun take sign-alternating values in the period of 24 hours. The greatest influence of the Sun on the free fall acceleration is in perihelion with the maximal diurnal amplitude of oscillations up to 55.34mGal, while the influence of the lunar gravity is negligible and takes sign-alternating values (up to 3–4mGal).We determine the maximum and minimum values of the acceleration on the Earth surface (983229.81 and 976073.25mGal) and also note the possibility of influence of accelerations due to centrifugal forces on the human organism.     

A dynamic model of diurnal irregularity in the nonrigid earth rotation

The previously constructed mathematical model of the Earth’s axial rotation irregularity is refined with the methods of celestial mechanics by considering secondary terms in the expansion of the lunisolar gravitational tidal torque and by using corrections (residuum) for zonal tidal perturbations. The diurnal and sub-diurnal variations in the Earth’s axial rotation were investigated; namely, a celestial mechanics model adequately describing the observation data and revealing the cause of the diurnal and sub-diurnal oscillations of the angular velocity of the Earth’s rotation was constructed. Some examples of predicting the Earth’s axial rotation are given.     

Simulation and analysis of the Earth’s polar oscillations

The fundamental model considered in [2–9] is used to interpolate and forecast the polar motion by the least-squares method applied to IERS data [1]. On the basis of the fundamental model, we consider an extended model of the Earth’s polar motion taking into account oscillations due to lunar influence. It is established that high-frequency lunar oscillations can occur on the beats period and one can interpolate them on a short time interval. A comparative analysis of models taking into account the month and two-week frequencies is performed.     

Pendulum motions of extended lunar space elevator

In the usual everyday life, it is well known that the inverted pendulum is unstable and is ready to fall to “all four sides,” to the left and to the right, forward and backward. The theoretical studies and the lunar experience of moon robots and astronauts also confirms this property. The question arises: Is this property preserved if the pendulum is “very, very long”? It turns out that the answer is negative; namely, if the pendulum length significantly exceeds the Moon radius, then the radial equilibria at which the pendulum is located along the straight line connecting the Earth and Moon centers are Lyapunov stable and the pendulum does not fall in any direction at all. Moreover, if the pendulum goes beyond the collinear libration points, then it can be extended and manufactured from cables. This property was noted by F. A. Tsander and underlies the so-called lunar space elevator (e.g., see [1]). In the plane of the Earth and Moon orbits, there are some other equilibria which turn out to be unstable. The question is, Are there equilibria at which the pendulum is located outside the orbital plane? In this paper, we show that the answer is positive, but such equilibria are unstable in the secular sense. We also study necessary conditions for the stability of lunar pendulum oscillations in the plane of the lunar orbit. It was numerically discovered that stable and unstable equilibria alternate depending on the oscillation amplitude and the angular velocity of rotation. The study of the lunar elevator dynamics originates in [2]. The concept of lunar elevator was developed in detail in [3, 4]. Several classes of equilibria with the finiteness of the Moon size taken into account were studied in [5]. The possibility of location of an orbital station fixed to the Moon surface by a pair of tethers was investigated in [6]. The problem of orientation of the terminal station of the lunar space elevator was studied in [7]. The influence of the tether length variations on the motion of the lunar tether system was considered in [8]. The alternation of stable and unstable flat oscillations is well known in the problem of satellite oscillations in a circular orbit [9, 10].     

基于伪地球坐标系的捷联惯导全球动基座初始对准算法

由捷联惯导系统建模原因造成的导航误差随纬度升高会被急剧放大,是实现惯导系统全球初始对准所面临的主要问题之一,且现有多种编排方案共存的全球初始对准算法也不利于初始对准算法在全球范围内统一。另一方面,极地地区越来越小的地球自转水平分量,使得极点及其附近的静态自对准是无法实现的,且动基座初始对准也有利于提高导航系统的快速反应能力。基于此,提出了采用伪地球坐标系惯导编排来实现惯导系统的全球动基座初始对准,消除由惯导建模造成对全球初始对准性能的影响,并期望探索一种统一导航编排的全球初始对准算法。最后通过仿真证明了该算法的可行性。     

Density-contrast instabilities in finite element modelling of slow viscous flow

Finite element methods are often used to model Earth processes involving slow viscous or viscoelastic flow. Inertial terms of the Navier-Stokes equations are neglected in very slow flows, so timestep size is not limited by the Courant instability. However, where there is advection of density contrasts in a gravitational field, over-advection can lead to numerically induced flow oscillations. We derive analytic results for the maximum stable timestep size in two cases: a free surface over a fluid of uniform density, and a free surface kept level by sedimentation/erosion, but with a density gradient in the underlying medium. Using parameters appropriate to the Earth's crust we show that the density-contrast instability occurs for timesteps larger than 3000 years for the constant-density case. For a fluid with a density gradient of 10 kg/m³ per km the solution is stable for timesteps up to about 200,000 years if full erosion/sedimentation is implemented.     

Studying the Complex Oscillations of a Star in the Field of a Galaxy

The oscillations of a star in the filed of a galaxy are studied. Initial energy conditions are established under which regular and complex oscillations occur. The latter are different from regular oscillations by the presence of saddle solutions in the trajectory. Unstable oscillations are due to only saddle solutions, with the trajectory tending to infinity     

端部切向载荷作用下的压杆失稳分析及其应用

细直杆件在压应力作用下会产生横向屈曲即失稳．直杆撞击刚性平面或拉断卸载后将形成压缩波，因承载压缩载荷的长度增加可以引起失稳．冲击速度转换的压应力沿着杆件切线方向，该处弯矩和剪力为零；而众多文献设定的失稳段固支边界条件并不准确．基于精确的杆件变形曲率方程得到端部载荷指向杆件中固定点时的受压失稳条件，得到其极限状态即载荷沿杆端切向作用时失稳长度相当于两端简支的1.5 倍．对于钢丝绳拉断形成的冲击失稳，载荷恒定而长度增加，可以产生高阶屈曲即在侧向出现多次曲折，并基于尼龙-橡胶带的模拟试验给出了定性说明．     

Analysis of a class of undesired multimode oscillations

The behavior of a negative-resistance circuit in which the parameters permit self-sustained oscillations to occur is discussed. In such a circuit, undesired oscillations of higher frequency caused by parasitic elements can exist in addition to normal oscillations. Parasitic oscillations are described by second-order simultaneous non-linear differential equations, taking into account of existence of the shunt capacitance, lead inductance and resistance of a negative-resistance element. Assuming that the frequency of the parasitic oscillations is sufficiently high compared with that of the desired normal oscillations, the approximate periodic solutions are obtained by using a method of averaging. In addition, the theoretical results are compared with the observed behavior of an experimental oscillator having similar parameters.     

Map of regimes of pressure oscillations induced by absorption during gas jet injection through a submerged nozzle

Map of regimes of pressure oscillations induced by absorption during rapid injection of a soluble gas jet through a submerged nozzle into liquid, namely, oscillations during absorption, bubbling, internal chugging and small chugging, is suggested. Boundaries between various pressure oscillations regimes occurring when rapidly soluble gas is absorbed in water are investigated theoretically. It is showed that these boundaries are determined by four equations. It is showed that regime of high-frequency pressure oscillations during absorption occurs due to gas bubble oscillations, and other regimes of oscillations occur due to pressure oscillations in the whole system comprising the header, vent tubes and gas bubble. The conditions for excitation of high-frequency and low-frequency oscillations and boundaries between different regimes of pressure pulsations are determined. In a case when Henri's law for soluble gases is valid the developed model predicts that oscillations during absorption are not excited.     

Oscillations of liquid in a vessel in the form of a rectangular parallelepiped

We consider the forced and the free oscillations of a liquid partially filling a cavity in the form of a rectangular parallelepiped. The characteristics of these oscillations are studied for small deformations of the free surface. It is shown that for definite frequencies and amplitudes of two-dimensional translational motions of the parallelepiped the fundamental of the liquid oscillations is excited in the plane perpendicular to the plane of motion of the vessel. The effect of small linear damping of the liquid oscillations on the shape of the boundaries of the principal region of instability of the liquid oscillations is evaluated. Fairly large oscillations of a liquid in a cylinder were considered in [1]. The same problem for a cavity of arbitrary configuration was studied in [2]. We note also that the conclusions of the study presented here are in qualitative agreement with the basic results obtained by a somewhat different method in [3] for a cavity in the form of a right circular cylinder.     

Model for the Formation of Acoustic Self-Oscillations in a Chamber with a Jet Flowing Through its Nozzle

This paper describes free acoustic oscillations of gas in a chamber with a jet flowing through its nozzle in the case of nonstationary intensity component of vortex sheet flowing down from the edge of the nozzle. There is established feedback between acoustic oscillations and oscillations induced by a corresponding vortex sheet component. It is shown that, in the presence of given feedback, there could be instability of acoustic oscillations, which would result in acoustic self-oscillations in the chamber. The boundaries of the domain in which instability is formed are determined by developing a mathematical model of stable acoustic oscillations in the chamber with account for the influence of the vortex sheet.     

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利用有限元软件,通过对撑竿跳高过程的大变形动力学数值模拟,得到了不同材料 撑竿的变形过程、跳高成绩,以及能量的转化效率指标. 通过截面尺寸设计,预测了不同材 料撑竿所能达到的最大高度. 最后以布勃卡的体能参数为标准,为其设计能越过最大高度的 等截面和变截面碳纤维复合材料撑竿.     

各种极对数的高精度多级旋转变压器的轴角─—数字转换原理及软硬件实现

－国内国际常用的多级旋转变压器主要有１６对极，３０对极和３６对极几种。多级旋转变压器在导航设备中起着重要作用。本文叙述了其输出的高精度角度信号如何被计算机转换成数字信号，以便为主机显控提供数据，还从原理和软硬件实现方法上给出了一种实现方案。     

Simple models for the diurnal cycle and convectively coupled waves

This paper presents a study of the diurnal cycle of tropical precipitation and its interaction with convectively coupled waves in the context of simple models with crude vertical resolution. One and two baroclinic mode models are tested in both the context of a one-column model and the context of a full spatial dependency that permits waves to propagate and interact with the diurnal cycle. It is found that a one baroclinic mode model is capable of reproducing a realistic diurnal cycle of tropical precipitation both over land and over the ocean provided an adequate switch function is used to mimic the congestus preconditioning mechanism that operates in the multicloud model of Khouider and Majda. However, a full two baroclinic mode multicloud model is needed to capture the interaction of convectively coupled tropical waves with the diurnal cycle. In a more conventional mass flux parameterization framework, both one and two baroclinic mode models fail to capture the diurnal cycle of tropical precipitation.