Rotation Law Research Articles

The formation of multiples in small-N subclusters

Abstract We explore the relative percentages of binary systems and higher-order multiples that are formed by pure stellar dynamics, within a small subcluster of N stars. The subcluster is intended to represent the fragmentation products of a single isolated core, after most of the residual gas of the natal core has dispersed. Initially the stars have random positions, and masses drawn from a log-normal distribution. For low-mass cores spawning multiple systems with Sun-like primaries, the best fit to the observed percentages of singles, binaries, triples and higher-order systems is obtained if a typical core spawns on average between N = 4.3 and 5.2 stars, specifically a distribution of N with mean $\mu _{_{N}}\sim 4.8$ and standard deviation $\sigma _{_N}\sim 2.4$. This fit is obtained when $\sim 50\%$ of the subcluster’s internal kinetic energy is invested in ordered rotation and $\sim 50\%$ in isotropic Maxwellian velocities. There is little dependence on other factors, for example mass segregation or the rotation law. Whilst such high values of N are at variance with the lower values often quoted (i.e. N = 1 or 2), very similar values (N = 4.3 ± 0.4 and N = 4.5 ± 1.9) have been derived previously by completely independent routes, and seem inescapable when the observed distribution of multiplicities is taken into account.

Design of optimum spacecraft reorientation control with a combined criteria of quality based on the quaternions

Specifical original problem of attitude controlling for spacecraft was proposed in this paper. Problem of optimal rotation from a known initial state in a prescribed spatial orientation was studied in detail (turnaround time is not fixed). Design of optimal program of reorientation is based on new indicator of quality that combines energy costs including the contribution of controlling torques and integral of rotary energy (in a known proportion) and reorientation time; presence of duration factor bounds time of rotation finish. To construct an optimal control of angular momentum changing, quaternionic method and the maximum principle were applied. Differential equation that relates spacecraft angular momentum and quaternion of spacecraft orientation is a base to obtain analytic solution to a problem. We reveal the properties of optimum control program analytically, and study key features of optimum motion in details. Also, we write the formalized equations, mathematical formulas to design optimal law for change of spacecraft’s angular momentum. Analytic relations and equations are given for finding the optimal solution. Control law (in as explicit dependence between phase variables and con-trolling variables has been formulated. Main relations determining optimum values of parameters for rotation control algorithm were given. The closed-form law for rotation was obtained for dynamically symmetric solids. Numerical example as well as results of mathematical modeling of spacecraft motion that formed using optimum control are presented. This data as addition to the made theoretic descriptions shows reorientation process (in virtual form) and demonstrates practical feasibility of the developed control method. A designed algorithm for optimal control of rotation improves an efficiency of attitude system, and originates more economical performing of space vehicle during its flight along orbit.

Test on progressive collapse of steel moment-resisting frame with upper-and-lower flange angle steel connection

Both of test and numerical simulation methods are employed to study the vertical progressive collapse and collapse assessment methods of steel frame under accidental loads. Firstly, a steel frame collapse test model with a geometric similarity ratio of 1:1.5 is designed and manufactured. The ends of column of test model is fixed. The upper and lower flange angle steel connection is used. The far end of the beam is constrained by a controllable sliding hinge support. The various stages of vertical progressive collapse of structures are simulated by a large displacement loads applied at the far end of the beam. The main focus of the testing is to examine the stress and deformation of beam and joint at various stages, particularly the development of stress and deformation in the angle steel attached to the beam-column connection. The development law of collapse load-displacement curve, joint rotation, beam strain, and angle steel strain are analyzed. The structural resistance mechanism and the transformation relationship between resistance mechanisms during collapse are studied. Subsequently, the relationship between the structural dynamic increase factor curve and the structural collapse process is analyzed using finite element method. The results show that the strain of angle steels can better reflect the destruction and deformation process of substructure during the collapse, the collapse resistance mechanism of structure, and the transition between resistance mechanisms.With the help of the characteristic points on the structural dynamic increase factor curve, the collapse limit state of structure can be reliably determined.

Realistic models of general-relativistic differentially rotating stars

ABSTRACT General-relativistic equilibria of differentially rotating stars are expected in a number of astrophysical scenarios, from core-collapse supernovae to the remnant of binary neutron-star mergers. The latter, in particular, have been the subject of extensive studies where they were modelled with a variety of laws of differential rotation with varying degree of realism. Starting from accurate and fully general-relativistic simulations of binary neutron-star mergers with various equations of state and mass ratios, we establish the time when the merger remnant has reached a quasi-stationary equilibrium and extract in this way realistic profiles of differential rotation. This allows us to explore how well traditional laws reproduce such differential-rotation properties and to derive new laws of differential rotation that better match the numerical data in the low-density Keplerian regions of the remnant. In this way, we have obtained a novel and somewhat surprising result: the dynamical stability line to quasi-radial oscillations computed from the turning-point criterion can have a slope that is not necessarily negative with respect to the central rest-mass density, as previously found with traditional differential-rotation laws. Indeed, for stellar models reproducing well the properties of the merger remnants, the slope is actually positive, thus reflecting remnants with angular momentum at large distances from the rotation axis, and hence with cores having higher central rest-mass densities and slower rotation rates.

Mechanism of principal stress rotation and deformation failure behavior induced by excavation in roadways

The failure modes of rock after roadway excavation are diverse and complex. A comprehensive investigation of the internal stress field and the rotation behavior of the stress axis in roadways is essential for elucidating the mechanism of roadway failure. This study aimed to examine the spatial relationship between roadways and stress fields. The law of stress axis rotation under three-dimensional (3D) stress has been extensively studied. A stress model of roadways in the spatial stress field was established, and the far-field stress state at different spatial positions of the roadways was analyzed. A mechanical model of roadways under a 3D stress state was established using far-field stress solutions as boundary conditions. The distribution of principal stresses σ1, σ2 and σ3 around the roadways and the variation of the stress principal axis were solved. It was found that the stability boundary of the stress principal axis exhibits hysteresis when compared with that of the principal stress magnitudes. A numerical analysis model for spatial roadways was established to validate the distribution of principal stress and the mechanism of principal axis rotation. Research has demonstrated that the stress axis undergoes varying degrees of spatial rotation in different orientations and radial depths. Based on the distribution of principal stress and the rotation law of the stress principal axis, the entire evolution mechanism of the two stress adjustments to form the final failure form after roadway excavation has been revealed. The on-site detection results also corroborate the findings presented in this paper. The results provide a basis for the analysis of the failure mechanism under a 3D stress state.

A Multiscale Method to Develop Three-Dimensional Anisotropic Constitutive Model for Soils

A multiscale method is presented to develop a constitutive model for anisotropic soils in a three-dimensional (3D) stress state. A fabric tensor and its evolution, which quantify the particle arrangement at the microscale, are adopted to describe the effects of the inherent and induced anisotropy on the mechanical behaviors at the macroscale. Using two steps of stress mapping, the deformation and failure of anisotropic soil under the 3D stress state are equivalent to those of isotropic soil under the triaxial compression stress state. A series of discrete element method (DEM) simulations are conducted to preliminarily verify this equivalence. Based on the above method, the obtained anisotropic yield surface is continuous and smooth. Then, a fabric evolution law is established according to the DEM simulation results. Compared with the rotational hardening law, the fabric evolution law can also make the yield surface rotate during the loading process, and it can grasp the microscopic mechanism of soil deformation. As an example, an anisotropic modified Cam-clay model is developed, and its performance validates the ability of the proposed method to account for the effect of soil anisotropy.

Rotating neutron stars in the first-order post-Newtonian approximation

We study models of uniformly and differentially rotating neutron stars in the framework of the first-order post-Newtonian approximation in general relativity as established by Chandrasekhar. In particular, we adopt the polytropic equation of state in order to derive the appropriate hydrodynamic equations and a rotation law based on the generalized Clement’s model. To compute equilibrium configurations at the mass-shedding limit, i.e. at critical angular velocity (equivalently, Keplerian angular velocity), we develop an iterative numerical method, belonging to the category of the well-known “self-consistent field methods”, with two perturbation parameters: the “rotation parameter” ῡ and the “gravitation or relativity parameter” σ̄. These two parameters represent the effects of rotation and gravity on the configuration. We investigate the validity and the limits of our method by comparing our results with respective results of other computational methods and public domain codes. As it turns out, our method can derive satisfactory results for general-relativistic polytropic configurations at critical rotation.

Equilibriums of extremely magnetized compact stars with force-free magnetotunnels

We present numerical solutions for stationary and axisymmetric equilibriums of compact stars associated with extremely strong magnetic fields. The interior of the compact stars is assumed to satisfy ideal magnetohydrodynamic (MHD) conditions, while in the region of negligible mass density the force-free conditions or electromagnetic vacuum are assumed. Solving all components of Einstein's equations, Maxwell's equations, ideal MHD equations, and force-free conditions, equilibriums of rotating compact stars associated with mixed poloidal and toroidal magnetic fields are obtained. It is found that in the extreme cases the strong mixed magnetic fields concentrating in a toroidal region near the equatorial surface expel the matter and form a force-free toroidal magnetotunnel. We also introduce a new differential rotation law for computing solutions associated with force-free magnetosphere, and present other extreme models without the magnetotunnel.

Effect of compaction parameter on aggregate particle migration and compaction mechanism using 2D image analysis

Pavement performance is not only affected by materials and production but also by compaction quality. This paper investigates the migration and rotation law of coarse aggregate during asphalt mixture compaction using the statistical means based on 2D image analysis. The variation of surface texture during compaction was extracted by laser scanner, and its anti-sliding performance was tested. The compaction mechanism was then discussed in combination with the Stribeck curve. The results show that mixtures with different gradations required different compaction energy during compaction, the AC-13 mixture was easier to compacted than the SMA-13. The aggregate contact developed rapidly in the early compaction stage in the horizontal direction but increased gradually in the vertical direction. With the compaction, the radial angle of the aggregate tended to be consistent in the horizontal direction and the major axis of the aggregate approached to the horizontal axis in the vertical direction. At the same time, the aggregates on the surface of the mixture were embedded with each other with compaction, and the surface structure gradually decreased. Combined with the aggregate contact, asphalt mortar viscosity and the Stribeck curve theory, the compaction process of asphalt mixture could be divided into pre-mixed lubrication dominated by asphalt lubrication and post-mixed lubrication dominated by aggregate contact. The research results offer a reliable basis for studying the compaction mechanism and improving the construction quality control of the asphalt pavement.

THE TRAJECTORIES CONSTRUCTION OF THE UNIVERSAL JOINT MOVEMENT IN THE CONFIGURATION SPACE IN ℝ3

In this paper, the study of the movement of the universal joint using the quaternion formalism was carried out, the law of movement of the cross of the universal joint was established with a known law of rotation of the drive shaft. A method of visual interpretation of the law of motion of the crosspiece is proposed, using the mapping of unit quaternions into a three-dimensional ball with radius 2π.

Validated analytical model for a cyclorotor wave energy device

We present a new analytical model for a horizontal axis cyclorotor-based wave energy converter (WEC). A number of cyclorotor-based WEC concepts and models, with different numbers of hydrofoils, have previously been studied. Our model is derived for a horizontal cyclorotor with 2 hydrofoils. The governing equations are optimised and converted to the polar coordinate system. The mechanical model is based on Newton's second law for rotation. Rotation is considered in two-dimensional potential flow, for both monochromatic and panchromatic waves, including waves generated by the rotating rotor, and viscous losses. The developed model is very convenient for modelling, analysis and control design for a cyclorotor based WEC.
 The authors of this work have derived new, exact, analytic functions for the free surface perturbation and induced fluid velocity field caused by hydrofoil rotation. These new formulae significantly decrease the model calculation time, compared to previous models, and increase the accuracy of the results. We present the results of free rotation simulations for the rotor in monochromatic and panchromatic waves obtained with the use of the newly derived equations.

Analytic model for photometric variation due to starspots on a differentially rotating star

Abstract We present an analytic model of the light-curve variation for stars with non-evolving starspots on a differentially rotating surface. The Fourier coefficients of the harmonics of the rotation period are expressed in terms of the latitude of the spot, ℓs, and the observer’s line-of-sight direction, ℓo, including the limb-darkening effect. We generate different realizations of multi-spots according to the model, and perform mock observations of the resulting light-curve modulations. We discuss to what extent one can recover the properties of the spots and the parameters for the differential rotation law from the periodogram analysis. Although our analytical model neglects the evolution of spots on the stellar surface (dynamical motion, creation, and annihilation), it provides a basic framework to interpret the photometric variation of stars, in particular from the existing Kepler data and the future space-born mission. It is also applicable to photometric modulations induced by rotation of various astronomical objects.

Three-dimensional stress path in deep-sea sediment under the driving load of a nodule collector

The quasi-static method was used to study the internal stress path in deep-sea sediment under the driving load of a crawler-type nodule collector. First, the instantaneous stress state of a soil element was calculated according to the theory of elasticity and was compared with the results of a numerical simulation. Next, the relative positions of the load imposed by the nodule collector and the soil element were changed to simulate the driving of the nodule collector to obtain the full-time stress path in the soil. Finally, the stress path and rotation of the principal stress axes in the soil at typical positions were analysed. The results showed that the spatial position of the soil had a significant influence on the stress path. In addition, the stress, peak value of the time-history curve for the principal stress and rotation mode of the principal stress axes showed correlations with the spatial position. Therefore, the stress-loading scheme should be selected according to the actual conditions of a given position in a laboratory test. A method was developed for representing the three-dimensional (3D) rotation of the principal stress axes based on a spherical projection of the direction vector. The proposed method can intuitively show the rotation law of the principal stress axes at any position in the soil during the driving of the crawler.

Analysis of energy losses in electric transmis-sion taking into account the Sommerfeld – Kononenko effect

The use of an electric drive in modern vehicles allows solving a number of problems related to the issues of environmental and energy security of the country. However, this approach imposes a number of practical limitations. Among them there is such a significant factor as the limitation on the stored energy in the traction batteries and, as a consequence, the limitation of the mileage on one charge. One of the ways to solve this problem is to reduce mechanical losses associated with the appearance of resonance phenomena in rotating transmission elements and having an unbalanced mass. Goal. The goal is to assess the influence of the Sommerfeld – Kononenko effect on energy indicators during the transfer of rotation from the electric motor to the drive wheel of an electric vehicle.
 To achieve this goal, it is necessary to determine the law of motion of the rotor of an electric motor and a car wheel using the energy approach and a model of complex motion. Methodology. To solve the problem of determining the law of rotation of an electric motor rotor, a dynamic model of an eccentric vibrator is adopted. The study takes into account the fluctuations in the angular velocity of the shaft with Hooke's hinge when the shaft axis deviates from horizontal positions. It is proposed to apply an energy approach using a model of complex motion to determine the law of rotation of an electric motor rotor and a wheel. Results. The dependence of the speed of rotation of the wheel of an electric vehicle is determined in accordance with the dynamic model under the conditions of fluctuations in the angular speed of transmission elements with Hooke's hinge when the wheel axis deviates from the horizontal position. Practical value. An energy approach is proposed for finding losses in a complex motion model to determine the law of rotation of an electric motor rotor and a wheel.
 An analytical dependence of additional energy losses caused by wheel unbalance on vehicle mileage and wheel unbalance is found.

Models of binary neutron star remnants with tabulated equations of state

ABSTRACT The emergence of novel differential rotation laws that can reproduce the rotational profile of binary neutron star merger remnants has opened the way for the construction of equilibrium models with properties that resemble those of remnants in numerical simulations. We construct models of merger remnants, using a recently introduced 4-parameter differential rotation law and three tabulated, zero-temperature equations of state. The models have angular momenta that are determined by empirical relations, constructed through numerical simulations. After a systematic exploration of the parameter space of merger remnant equilibrium sequences, which includes the determination of turning points along constant angular momentum sequences, we find that a particular rotation law can reproduce the threshold mass to prompt collapse to a black hole with a relative difference of only $\sim 1{{\ \rm per\ cent}}$ with respect to numerical simulations, in all cases considered. Furthermore, our results indicate a possible correlation between the compactness of equilibrium models of remnants at the threshold mass and the compactness of maximum-mass non-rotating models. Another key prediction of binary neutron star merger simulations is a relatively slowly rotating inner region, where the angular velocity Ω (as measured by an observer at infinity) is mostly due to the frame dragging angular velocity ω. In our investigation of the parameter space of the adopted differential rotation law, we naturally find quasi-spherical (Type A) remnant models with this property. Our investigation clarifies the impact of the differential rotation law and of the equation of state on key properties of binary neutron star remnants and lays the groundwork for including thermal effects in future studies.

Analysis on non-stationary gyroscopes and their application in measurement technology

In this work, the main subjects of research are: 1) analysis of the process of rotation of a Chinese top on a flat surface, 2) analysis of the main dependencies and an explanation of the rise of the center of gravity of the top during rotation due to nonlinear friction and the resulting force of the overturning top on the upper axis. Also, an analytical study of the motion of the top along the plane and the laws of rotation was carried out, the rotation of the top was analyzed from the point of view of asymmetry during rotation. The top-top spinning top is an interesting case of raising the center of gravity during rotation. The simplest model of a Chinese top can be a dynamic symmetric inhomogeneous ball, the center of mass of which lies on the axis of dynamic symmetry, but does not coincide with its geometric center. The precession of the Chinese top is based on dry friction. The occurrence of a gyroscopic deflection moment is based on the frictional force. Considering the simplest top-type top, one can distinguish the main forces acting on this body, as well as its characteristics that determine the precession. Based on this fact, it is possible to propose the use of this body of revolution as a working medium for instruments such as tribometers and gravimeters. In the first case, this makes it possible to increase the accuracy of the device, in the second, to create a new scheme for measuring gravitational fields. The relevance of this work is the analysis of the rotation of the Chinese top and the possibility of its use in measuring instruments.

Research on reliable sealing technology of spacecraft rectangular hatch based on boundary control

In view of the large size of the sealing surface of the space large diameter rectangular cabin door, the large number of locking mechanisms and long service life, it is difficult to adjust the multi degree of freedom attitude in the assembly process, the complex assembly and adjustment of the mechanism, the synchronization accuracy is not easy to ensure, the consistency of the multi-point seal compression rate is high, and it is not easy to control. Based on the rotation law of the spatial linkage mechanism, the precise dimension chain control of the hatch is carried out, and the attitude of the multi degree of freedom linkage is adjusted to realize the synchronous compression of multiple compression units of the compression mechanism; Based on the minimum and maximum operating force as the boundary, through the sealing stress simulation, the “boundary control” coupling assembly and adjustment technology is proposed to optimize the sealing structure and realize rapid and efficient assembly. The results show that the vacuum leakage rate is still less than 2.5×10−3 PaL/s after 2000 door opening and closing tests and sealing compression ratio are better than 15%. The long-life test verifies the feasibility and effectiveness of this method, and forms a set of high reliable and long-life sealing assembly and adjustment method of space hatch, which provides technical guidance and reference for the subsequent assembly of similar space hatch mechanisms.

Chaotic Assessment of the Heave and Pitch Dynamics Motions of Air Cushion Vehicles

In this study, three degrees of freedom nonlinear air cushion vehicle (ACV) model is introduced to examine the dynamic behavior of the heave and pitch responses in addition to the cushion pressure of the ACV in both time and frequency domains. The model is based on the compressible flow Bernoulli's equation and the thermodynamics nonlinear isentropic relations along with the Newton’s second law of translation and rotation. In this study, the dynamical investigation was based on numerical simulation using the stiff ODE solvers of the Matlab software. The chaotic investigations of the proposed model is provided using the Fast Fourier Transform (FFT), the Poincaré maps, and the regression analysis. Three control design parameters are investigated for the chaotic studies. These parameters are: ACV mass (M), the mass flowrate entering the cushion volume (m ̇_in), and the ACV base radius (r). Chaos behavior was observed for heave, and pitch responses as well as the cushion pressure.

Chaotic Assessment of the Heave and Pitch Dynamics Motions of Air Cushion Vehicles

In this study, three degrees of freedom nonlinear air cushion vehicle (ACV) model is introduced to examine the dynamic behavior of the heave and pitch responses in addition to the cushion pressure of the ACV in both time and frequency domains. The model is based on the compressible flow Bernoulli's equation and the thermodynamics nonlinear isentropic relations along with the Newton’s second law of translation and rotation. In this study, the dynamical investigation was based on numerical simulation using the stiff ODE solvers of the Matlab software. The chaotic investigations of the proposed model is provided using the Fast Fourier Transform (FFT), the Poincaré maps, and the regression analysis. Three control design parameters are investigated for the chaotic studies. These parameters are: ACV mass (M), the mass flowrate entering the cushion volume (m ̇_in), and the ACV base radius (r). Chaos behavior was observed for heave, and pitch responses as well as the cushion pressure.

Applying No-z Approximation in Dynamo for Keplerian Rotation Law

Applying No-z Approximation in Dynamo for Keplerian Rotation Law