Moments Of Perturbations Research Articles

Studying the vibrational motion of a rotating symmetrically charged solid body subjected to external forces and moments

This paper studies the rotatory vibrating motion of a dynamically symmetric charged solid body (SB) connected with a spring around a fixed point as a novel model. The body is assumed to be influenced by a Newtonian force field (NFF) besides extrinsic moments like perturbing, restoring, and gyrostatic moment (GM). These moments are guided along the body’s principal axes of inertia. The body is assumed to have a high starting angular velocity in the direction of the dynamic symmetry axis, and the perturbing moments (PM) are thought to be less than the restoring moment. These assumptions provide us with a tiny parameter, to use the averaging technique (AT), and to acquire the averaging system of the regulating one. Several applications are introduced to achieve the solutions of this system separately. These solutions are graphed to reveal the positive influences of the body’s numerical values on the behavior of the body, taking into account the various impacts of the applied moments, the electromagnetic field, and the Newtonian one for all examined applications. The obtained results are considered a generalization of those which were obtained in related previous works. For the projections of the body angular velocity, the proportion of differences as a function of the investigated parameters varies between 17% and 35%, whereas the other parameters are varied between 0.0011% and 0.37%, respectively. Therefore, these outcomes are considered to be significant due to their applications in life specially that based on the theory of vibrating systems in physics and engineering fields.

Modeling and analysis of the nonlinear rotatory motion of an electromagnetic gyrostat

This paper investigates the three-dimensional rotary motion of a charged rigid body (gyrostat) about a fixed point close to the case of Lagrange. We mainly consider the motion under the influence of some forces and moments, on the gyrostat, such as a Newtonian force field in addition to perturbing, gyrostatic, and restoring moments. The body is assumed to have an initially extremely large angular velocity along the direction of the axis of dynamical symmetry and the perturbing moments are smaller than the moment of restoring. Next, the averaging method is used to obtain the averaging system of motion in view of these conditions. The angles of precession and nutation are evaluated asymptotically as new aspects of the orientation of the body at any instant. The graphical performance of these angles is plotted to display the good influence of the applied moments on the motion. In addition, the Runge-Kutta method of fourth-order is applied to get the numerical results of the governing system of motion and these results are represented in other plots. The significance of the current work is due to its various implementations in the theory of gyroscopic motion especially in the design of aircraft, spaceships, and submarines because they are mainly responsible for directing these vehicles.

Direct and inverse secondary resonance effects in the spherical motion of an asymmetric rigid body with moving masses

Secondary resonance effects in the spherical motion of a heavy asymmetrical rigid body with moving masses are reviewed in the case close to the Lagrange top. It is known that perturbations acting on the body, particularly a small displacement of the center of mass with respect to axis of symmetry and a small perturbing moment in a connected system of coordinates, lead to non-resonant evolutions of angular velocity. These evolutionary phenomena are called direct secondary resonance effects. They are visible in a dynamic system consisting of an asymmetric rigid body and several masses fixed relative to the body. However, the presence of moving masses connected to a rigid body by springs may lead to the stabilization of the angular velocity of the body. This dynamic phenomenon should be attributed to the inverse secondary resonance effect. The aim of this paper is to study the characteristic direct and inverse secondary resonance effects in a perturbed spherical motion of a rigid body with fixed and moving masses. The method of integral manifolds and the averaging method are used for the asymptotic analysis of the secondary resonance effects. The paper presents the numerical results of modeling the direct and inverse resonance effects.

THE STABILIZATION ACCURACY OF THE PHASE POSITION OF THE WORKING BODY OF THE ROBOTICS COMPLEX

To stabilize the phase position of the working body of the robotics complex a single-circuit precision electric drive system was developed based on the principle of phase-locked loop. The direct-driven electric drive is made on the basis of brushless direct current motor, which is switched to synchronous mode with minimal discrepancy between the phases of the reference signals and the pulse speed sensor. The phase error signal is fed to the input of the PID controller, which controls the pulse width modulation of the impulses controlling the operation of the power transistors of the autonomous voltage inverter. In a static mode, the control system of the autonomous voltage inverter implements a sinusoidal law of the pulse width modulation of the output pulses. The PID controller and the control system of the autonomous voltage inverter are programmatically implemented on the basis of the controller.
 In the process of analysing of the stabilization accuracy, the synchronous motor is represented by a second-order linear link, which establishes a relation between the phase deviations of the motor rotor and the stator magnetic field. The autonomous voltage inverter is represented by a zero-order hold whose coefficient of amplification on amplitude is found by the results of the approximation of its output voltage using the Walsh-Fourier series.
 The analysis of the phase stabilization process is performed on the basis of the state variables method taking into account the perturbations at the moment of load using the program which implements the recurrent procedure.
 The settings of the PID controller are determined by the variation results when the moment of load changes. Their initial values ​​are determined as a result of optimizing the system in terms of operation speed considering the condition of finite duration processes. It is assumed that there is no moment of load perturbation.
 The procedure for setting the PID controller parameters to the optimal operation speed mode can also be performed on the basis of neural networks.
 As a result of the calculations, it was found that with an increase of the load moment by 5%, the maximum deviation of the rotor phase was 0.22 us and 0.03 us of minimum deviation respectively.

Results of engineless studies of power plant supports for machine-tractor units operation

When using a machine-tractor unit, external conditions of its operation change in a wide range. It results in frequent changes in the parameters of speed and load modes of its power plant. Resulting vibrations and oscillations in addition to discomfort and excessive loads on components and mechanisms of the power plant also cause fuel overspending and power losses. To reduce negative vibration impact on effective performance of the power plant creation of supports with adjustable characteristics is suggested. Both internal unbalance of the power plant itself and external influence of variable moment of resistance and impulses of supports themselves are considered perturbing moments. Changes in rigidity and damping coefficients of relevant supports can reduce the amplitude of oscillations of the power plant in variable operating modes, which will improve its utilization indicators.

Spatiotemporal perturbations in paced finger tapping suggest a common mechanism for the processing of time errors

Paced finger tapping is a sensorimotor synchronization task where a subject has to keep pace with a metronome while the time differences (asynchronies) between each stimulus and its response are recorded. A usual way to study the underlying error correction mechanism is to perform unexpected temporal perturbations to the stimuli sequence. An overlooked issue is that at the moment of a temporal perturbation two things change: the stimuli period (a parameter) and the asynchrony (a variable). In terms of experimental manipulation, it would be desirable to have separate, independent control of parameter and variable values. In this work we perform paced finger tapping experiments combining simple temporal perturbations (tempo step change) and spatial perturbations with temporal effect (raised or lowered point of contact). In this way we decouple the parameter-and-variable confounding, performing novel perturbations where either the parameter or the variable changes. Our results show nonlinear features like asymmetry and are compatible with a common error correction mechanism for all types of asynchronies. We suggest taking this confounding into account when analyzing perturbations of any kind in finger tapping tasks but also in other areas of sensorimotor synchronization, like music performance experiments and paced walking in gait coordination studies.

PREVENTIVE „NON-EXISTENT ANIMAL" DRAWING FOR THE STUDY OF AGGRESSION IN CHILDREN OF PRIMARY SCHOOL AGE BY DECIMATING THE SYMPTOMS ACCOMPANYING „COGNITIVE DISMODERATE INTERCOURSE”

The studied students are from the fourth grade, the town of Kyustendil. The drawing of the "Non-existent animal" aims to prevent the essence of the problem of working at the level of primary prevention of aggression in children of primary school age. The following criteria are distinguished in order to analyze the symptom of the "non-existent animals" depicted by children: the preventive symbolic meaning of the depicted objects; preventative importance of colors; degree of aggression; the presence of decorative details. The preventative approach in the drawing is based on the stage in which children painting the non-existent animal, drawing themselves in situations of social communication. When children accumulate in their minds subjective, emotional estimates of their intercourse with their peers, they as a result of cognitive psychological stress sharpen their feelings of being suppressed. Students begin to experience inwardly negative feelings, as a result of which they push these experiences unconsciously and at a conflict moment of perturbation from the external environment with which they communicate, these emotions of emotion in the children are unleashed. At such times, children with lower self-control outweigh the aggressive manifestation of a calm reaction that avoids the aggressive outburst. There are situations where the propensity of children to irritable behavior leads to behavioral deficits in my forms of communication with others. When there is an unfavorable relationship between children, they start distancing and non-acceptance of the other's point of view, and then begin to feel lonely as a factor in „cognitive dismoderate intercourse". Incomplete interactions between children help to ignore the essential moments of communication between children; in practice, incorrect feedback is broken in the course of cognitive processes in communication. There is a distance, not a clarification of the relationship. A small percentage of children start sharing their emotions even with their loved ones. In practice, children do not clarify their positions and relationships with peers and those with whom they have problematic interactions. In this way, children reconstruct in their minds subjective assumptions about the actual irritants leading to aggressive manifestations. Children begin to get angry at themselves and the people they communicate with on every occasion, even with the most common remark. These children are predominantly irritable, especially among the students, which contributes to the escalation of their aggressive behavior. Children do not realize what behavior they actually have and how it affects the people they communicate with. They lack the proactive behavioral standard. Subsequently, there is an imbalance between perceptual views of children and their classmates about attitudes related to problematic issues. In practice, there is an incorrect refraction of the feedback in the process of communication between children, and the focus on their own perceptual attitudes comes to the fore. Emphasizing on one's own views and neglecting the corrective preventive attitude of adult authority on the problematic situation only reinforces the process of „cognitive dismoderate intercourse", among children.

Influence of Transonic Flutter on the Conceptual Design of Next-Generation Transport Aircraft

Transonic aeroelasticity is an important consideration in the conceptual design of next-generation aircraft configurations. This paper develops a low-order physics-based flutter model for swept high-aspect-ratio wings. The approach builds upon a previously developed flutter model that uses the flowfield’s lowest moments of vorticity and volume-source density perturbations as its states. The contribution of this paper is a new formulation of the model for swept high-aspect-ratio wings. The aerodynamic model is calibrated using offline two-dimensional unsteady transonic computational-fluid-dynamics simulations. Combining that aerodynamic model with a beam model results in a low-dimensional overall aeroelastic system. The low computational cost of the model permits its incorporation in a conceptual design tool for next-generation transport aircraft. The model’s capabilities are demonstrated by finding transonic flutter boundaries for different clamped-wing configurations and investigating the influence of transonic flutter on the planform design of next-generation transport aircraft.

Physics-Based Low-Order Model for Transonic Flutter Prediction

This paper presents a physical low-order model for two-dimensional unsteady transonic airfoil flow, based on small unsteady disturbances about a known steady flow solution. This is in contrast to traditional small-disturbance theory, which assumes small disturbances about the freestream. The states of the low-order model are the flowfield’s lowest moments of vorticity and volume-source density perturbations, and their evolution equation coefficients are calibrated using off-line unsteady computational fluid dynamics simulations through dynamic mode decomposition. The resulting low-order unsteady flow model is coupled to a typical-section structural model, thus enabling prediction of transonic flutter onset for wings with moderate to high aspect ratios. The method is fast enough to permit incorporation of transonic flutter constraints in conceptual aircraft design calculations. The accuracy of this low-order model is demonstrated for forced pitching and heaving simulations of an airfoil in compressible flow. Finally, the model is used to describe the influence of compressibility on the flutter boundary, and its accuracy is demonstrated for the Isogai Case A classical flutter test case.

On the motion of a gyro in the presence of a Newtonian force field and applied moments

This work focuses on the motion of a dynamical model that consists of a symmetric rigid body (gyro) that rotates about a fixed point similar to Lagrange’s gyroscope. This body is acted upon by external forces represented by a Newtonian force field, gyro torques about the principal axes of inertia of the gyro and perturbing moments acting on the same axes. Assuming that, the gyro initially has a high angular velocity about the dynamic axis of symmetry. The averaging technique is used to obtain a more appropriate averaging system for the governing system of equations of motion in terms of a small parameter. Therefore, the analytical solutions of this system for two applications, depending on different forms of perturbing moments, are presented. These solutions are represented graphically to clarify the effectiveness of the different parameters of the body on the motion.

Geometrical measures of non-Gaussianity generated from single field inflationary models

We calculate the third-order moments of scalar curvature perturbations in configuration space for different inflationary models. We develop a robust numerical technique to compute the bispectrum for different models that have some features in the inflationary potential. From the bispectrum we evaluate moments analytically in the slow-roll regime while we devise a numerical mechanism to calculate these moments for non-slow-roll single-field inflationary models with a standard kinetic term that are minimally coupled to gravity. With the help of these third-order moments one can directly predict many non-Gaussian and geometrical measures of cosmic microwave background distributions in the configuration space. Thus, we devise a framework to calculate different third-order moments and geometrical measures, e.g. Minkowski functionals or the skeleton statistic, generated by different single-field models of inflation.

Deployable dynamic analysis and on-orbit experiment for inflatable gravity-gradient boom

Inflatable structures have numerous advantages, such as small folding size, high deployable reliability, and low cost. This paper accomplishes several tasks with a focus on the gravity-gradient boom of microsatellite. An inflatable boom model balanced by inflatable deployment and delaminating resistance is presented. A system is established to simulate agravic deployment. The inflatable deployment of a tip mass has been tested with the aid of a 3.0m rolled deployable boom. The perturbation moment during the inflatable deployment is analyzed. Three inflatable booms are tested in a thermal vacuum chamber further. Based on the tests and analyses, the microsatellite which carried an inflatable gravity-gradient boom was launched into orbit successfully in November 2012. After being stored on-orbit for 6months, the inflatable method was applied to the inflatable boom to unfold the 2.0kg tip mass steadily at a distance 3.0m away from the microsatellite in May 2013. This work completes the test of inflatable on-orbit deployment on the base of microsatellite for the first time internationally.

Monoaxial electrodynamic stabilization of earth satellite in the orbital coordinate system

Consideration was given to the Earth satellite moving along a circular arbitrarily inclined orbit. The possibility of using the electrodynamic control system for monoaxial stabilization of the satellite in an indirect position in the orbital coordinate system was analyzed. An extension of the concept of electrodynamic control including a solution of the problem of electrodynamic compensation of the perturbing moment was suggested. Conditions were established for solution of the formulated problem with the use of the electromagnetic control in the presence of perturbing action of the gravitational moment. Sufficient conditions for asymptotic stability of the satellite equilibrium were established for the nonlinear statement of problem.

Fully coupled hydrogeophysical inversion of a laboratory salt tracer experiment monitored by electrical resistivity tomography

We perform a salt tracer experiment, monitored by time‐lapse electrical resistivity tomography, in a quasi‐two‐dimensional sandbox with the aim of determining the hydraulic conductivity distribution in the domain. We use sodium chloride as a tracer, together with cochineal red for visual monitoring. The time series of observed resistance for each electrode configuration is characterized by its temporal moments. We invert the mean arrival time of electrical potential perturbations and a few steady state hydraulic head measurements using the fully coupled hydrogeophysical approach recently introduced by Pollock and Cirpka (2010). This is the first application of the approach to experimental data. The results obtained show a reasonable agreement between the estimated hydraulic conductivity field and the pattern of the actual sandbox filling. Using this estimation, a transient simulation is performed to compute the propagation of the salt tracer plume through the sandbox. The latter is compared to pictures taken during the experiment. These results show an even better agreement, indicating that the lenses of different sand types are not entirely homogeneous and some unexpected preferential flow paths are present. We conclude that temporal moments of potential perturbations obtained during salt tracer tests provide a good basis for inferring the hydraulic conductivity distribution by fully coupled hydrogeophysical inversion.

The localized role of base level lowering on channel adjustment of tributary streams in the Trinity River basin downstream of Livingston Dam, Texas, USA

The purpose of this study is to describe and explain river channel cross-sectional change in tributary streams within the 60-km scour zone of the Trinity River, Texas, downstream of Livingston Dam. This study investigates changes within the tributary systems to base level changes triggered by incision, associated with scour and channel migration within the dammed trunk stream. The dam represents a precise moment and place of a system perturbation and therefore represents an opportunistic geomorphic experiment. Geomorphological effects of the lower Trinity River tributaries were investigated through three different types of data: resurveys of bridge cross sections, planform change as measured from aerial photographs, and field mapping of changes in channel geometry using fallen trees, undercut banks, and other geomorphic indicators of change. While field evidence of channel change was found at sites well upstream of tributary confluences with the Trinity, these were not consistent with responses to lower base level. Downcutting and lateral changes in response to lowered base level were confined to lower tributary reaches. This suggests distance decay and lag times in transmission of responses upstream and/or masking of dam-induced effects by other processes and controls. The most dynamic locations of geomorphic change are near the confluences of the tributaries with the Trinity River, where the response to dam-induced incision is strongly influenced by local trunk stream morphology, indicating a high degree of historical and geographical contingency.

Global attractivity of the almost periodic solution of a delay logistic population model with impulses

In this paper, we study the existence of almost periodic solutions of a delay logistic model with fixed moments of impulsive perturbations. By using a comparison theorem and constructing a suitable Lyapunov functional, a set of sufficient conditions for the existence and global attractivity of a unique positive almost periodic solution is obtained. As applications, some special models are studied; our new results improve and generalize former results.

Fully coupled hydrogeophysical inversion of synthetic salt tracer experiments

We present a method for the determination of hydraulic conductivity from monitoring of salt tracer tests by electrical resistivity tomography (ERT). To ensure that the underlying principles of flow, transport, and geoelectrics are obeyed in the inversion, we perform a fully coupled hydrogeophysical analysis using temporal moments of electrical potential perturbations. In the predictive mode, we use moment‐generating equations with corresponding adjoint equations for the evaluation of sensitivities. For inversion, we apply the quasi‐linear geostatistical inversion approach. The method is tested in a synthetic case study mimicking a laboratory‐scale quasi two‐dimensional sandbox, in which 48 electrodes and 8 piezometers are used. The hydraulic conductivity field is estimated from the mean arrival times of electrical potential perturbations and hydraulic heads. The estimated hydraulic conductivity field reproduces most features with, however, a loss of variability. Even though only the temporal moments of the electrical signals are used for inversion, the transient behavior is satisfactorily recovered. Also, the spatial patterns of concentration arrival times in the true and estimated cases are in good agreement, so that the propagation of the tracer plume can be followed fairly accurately. We test the effects of large measurement errors and erroneous prior information on the performance of the inversion. While prior statistical parameters are of minor importance in detecting the major pattern of hydraulic conductivity, a large measurement error could have an important impact on the solution. Also, the choice of electrode configurations appears to be important. In particular, strictly surface‐based geoelectrical surveys do not seem to be very suitable for identifying spatial patterns of hydraulic conductivity by ERT monitoring of salt tracer tests within aquifers.

Modeling a Multi-Agents System as a Network

The article presents an empirically oriented investigation on the dynamics of a specific case of a multi-agents system, the stock market. It demonstrates that S&P500 market space can be described using the geometrical and topological characteristics of its dynamics. The authors proposed to measure the coefficient R, an index providing information on the evolution of a manifold describing the dynamics of the market. It indicates the moments of perturbations, proving that the dynamics is driven by shocks and by a structural change. This dynamics has a characteristic dimension, which also allows for a description of its evolution. The consequent description of the market as a network of stocks is useful for the identification of patterns that emerge from multi-agent interaction, and defines our research, as it is derived from a system of measure and it is part of the logic of a defined mathematics.

Perturbing moments in a floating gyroscope with elastic device housing on a vibrating base in the case of a nonsymmetric end outflow

The influence of elastic compliance of the float housing on the vibration perturbing moment in gyros with cylindrical floating suspension in the case of symmetric fluid outflow was studied in [1, 2]. It was shown that, for a sufficiently thick float housing made of a material of small density and large Young modulus, the influence of elastic compliance can be neglected, and one can assume that the float housing is absolutely rigid. In the case of collet fixation of the gyro at the working position, to ensure the heat withdrawal to the end faces, the device housing is constructed as an elastic cylindrical shell with rigid attachment on the end faces. The influence of the device housing elasticity in the case of symmetric fluid outflow through the end faces was considered in [3], and the influence of the nonsymmetric fluid outflow through the end faces for the case of a rigid device housing was studied in [4]. We consider the influence of the perturbing moment of the floating gyroscope with elastic device housing in the case of nonsymmetric fluid outflow through the ends on a vibrating base in the case of translational and angular vibrations of the base. We show that the elasticity of the device housing and the nonsymmetry of the fluid outflow significantly affect the hydrodynamic perturbing moment.

Spatial chaotic vibrations when there is a periodic change in the position of the centre of mass of a body in the atmosphere

The spatial chaotic motion of a blunt body in the atmosphere when there is a periodic change in the position of the centre of mass is considered. A restoring moment, described by a biharmonic dependence on the spatial angle of attack, a small perturbing moment, due to the periodic change in the position of the centre of mass, and also a small damping moment, acts on the body. The motion when the velocity head remains constant is investigated. When there are no small perturbations, the phase portrait of the system can have points of stable and unstable equilibrium. The behaviour of the system in the neighbourhood of the separatrice is investigated using Mel’nikov's method. An analytic solution of the equation of the body motion along the separatrice is obtained. The criteria for the occurrence of chaos are obtained and the results of numerical modelling, which confirm the correctness of the solutions obtained, are presented.