Mass Moment Research Articles

Energy attenuation of seismic metamaterials composed of a periodic array of coated elliptical cylinders

Abstract We present a numerical study on energy attenuation of seismic metamaterials consisting of a periodic array of coated elliptical cylinders. The aim is to perceive the effect of aspect ratio for different wave modes so that the metamaterials can interact with the incoming wave causing them to interfere with each other destructively, especially for low-frequency seismic waves with relatively wide bandgap. Previous studies mainly focused on the configuration of coated circular cylinders or spheres, in which the metamaterial is composed of a hard inclusion surrounded by a soft coating layer and dispersed within a hard matrix. Here we utilize numerical simulations based on finite element calculation to analyze the local fields within the unit cell. Effective mass density, mass moment of inertia and shear modulus are analyzed through a homogenization procedure to characterize the macroscopic behavior of the effective medium. The effective behavior will be dependent for different aspect ratios and for different types of wave motions. To verify the effectiveness of energy attenuation, a full-scale model is adopted. Specifically, to identify optimal energy attenuation configurations, we illustrate the attenuation effects of elliptical metamaterials under longitudinal and shear horizontal types of waves. The present study demonstrates that elliptical metamaterials will have more reflexibilities to tune with the aspect ratio of the elliptical geometry as well as the directionality of incidence waves. Based on our simulations, we show the ability of the designed configuration in tuning local resonance frequencies and bandwidths for real implementations and applications of seismic metamaterials.

Forced oscillation of planetary mechanism synchronizer for spindle drive

The article is devoted to the results of a theoretical and experimental study of forced oscillation of the epi-hypocyclic planetary mechanism synchronizer used to drive the spindles of the cotton machine apparatus. Spectrum of natural oscillation frequency of synchronizer is determined and mass moment of their inertia is set for stability in operating mode when satellite comes in and out of gear engagement of planetary mechanism. Periodic nature of system oscillations under action of external forces of satellite is considered. The graph of oscillations of actual excitation of the synchronizer in the form of a pulse semi-sinusoidal curve is obtained. The beam diagram is built that allows you to make delaminations from the resonant modes of operation of the synchronizer.

Про стійкість обертання вільної системи двох пружно зв’язаних твердих тіл

The equations of rotation of the free system of two rigid bodies connected by an elastic spherical joint or a Hook joint are derived. Assuming that the center of mass of the rigid bodies is located on the third main axis of inertia, the equations of the disturbed motion of the mechanical system under consideration are written in the form of eight ordinary differential equations with periodic coefficients. In the case of two Lagrangian gyroscopes, a characteristic equation of the fourth order is obtained. On the basis of the Lénar-Schipar criterion, written in innor form, the necessary conditions for the stability of uniform rotations of Lagrange gyroscopes in the form of a system of three inequalities are obtained. Analytical studies of these stability conditions were carried out. It is proved that the first inequality is always satisfied. It follows from the third inequality that when gyroscopes have equal axial moments of inertia and rotate with the same angular velocities in different directions or there is no elasticity in the hinge, then the characteristic equation has multiple roots and the question of stability requires additional research. The conditions of stability with respect to kinetic moments are written and it is shown that the older coefficients of these two inequalities are positive, from which it follows that stability will always be possible with sufficiently large values of one of the two kinetic moments. Similar conclusions were obtained in the case of Hook's hinge, and it was also shown that when the gyroscopes are the same, the characteristic equation breaks down into two equations. The first and second equations describe the steady free rotation of one gyroscope on which the restoring moment acts, only in one of the equations it is necessary to add the mass moment of the second gyroscope to the equatorial moment. In the absence of elasticity in the joint, multiple zero roots appear and the question of stability requires additional research.

COMPARATIVE ANALYSIS OF THE BEARING CAPACITY OF PLANETARY MECHANISMS FORMED ON THE BASIS BY TWO SIMPLE JAMES PLANETARY MECHANISMS, ACCORDING TO SEQUENTIAL NON-LOOP AND CLOSED KINEMATIC SCHEMES WITH ONE LOOP

The article presents a method for comparative analysis of the bearing capacity of planetary mechanisms of various kinematic schemes using several CAD/CAE software environments. To implement the method of comparative analysis, the KOMPAS-3D and SolidWorks software environments were used. In the first environment, calculations were performed according to the method of the GOST 21354-87 standard. The initial data and results of calculations performed by the KOMPAS-GEARS software package are stored in the appropriate files. In the second environment, a parametric 3D geometric solid model of the kinematic scheme of the planetary mechanism was created. According to this model, such characteristics of gears as mass and axial moment of inertia were determined. These characteristics are used to perform optimization calculations of the mass and speed of the designed planetary mechanism. The study of the speed of the planetary mechanism can be carried out in SolidWorks Motion. The overall dimensions of the model allow the designer to assess the acceptability of the design constraints for given dimensions to the specified requirements. According to the method, a study was made of the suitability of gear designs that were designed for a closed planetary mechanism as gears of an open-loop sequential planetary mechanism. The closed planetary gear is formed by two simple James planetary gears. The circuities planetary gear is formed by the series connection of the same simple planetary gears. Two cases of loading gears for a given kinematic scheme of the planetary mechanism were studied. Keywords: simple James planetary mechanism (mechanisms type ); closed planetary mechanism; contourless planetary gear; moment of inertia of gear-wheel; gear mass; planetary gear mass; contact strength of the gearing; bending strength of the gearing; toothing resource; 3D geometric solid model of the kinematic scheme of the planetary mechanism

Numerical modeling of geological sequestration of brine wastewater due to coal mining in the Ordos Basin, China

The coal resources play an indispensable role in the development of heavy industry in China, and coal mining activity leads to brine wastewater drainage, causing major risks for the aquatic environmental system. Thus, the effective and economic treatment of coal mine wastewater is vital to mitigate the environmental burdens, and geological sequestration by deep-well injection is a promising treatment technique. This study elucidates the physical and geochemical processes of coal mine wastewater transport in deep reservoirs and proposes an optimized injection scheme to satisfy environmental and economic benefits simultaneously in the Ordos Basin, China. First, a variable density and variable parameter groundwater reactive transport model is constructed to simulate the long-term process of deep-well injection for coal mine wastewater treatment. Then, the environmental metrics, i.e., the percentage of permeability reduction, the total mass and spatial second moment of the wastewater plume, and the economic metric defined as achieving a higher concentration at a higher injection rate are proposed to evaluate the performance of the injection scheme. The simulation results show that the secondary mineral anhydrite dominates the reduction of reservoir permeability due to the precipitation reactions with SO42− in the brine wastewater, and the permeability in the reaction zone decreases by 0.66 % ~ 1.26 % after 10 years in the basic scenario. Moreover, higher concentrations negatively affect reservoir permeability and increase total dissolved solids, while higher injection rates decrease reservoir permeability and increase the brine wastewater plume. The study also identifies promising schemes that can achieve an optimal trade-off between the conflicting metrics. Based on the economic and environmental benefits demanded in this study, an injection scenario with a concentration of C4 and an injection volume of 800 m3/d is recommended to maximize environmental benefits. Overall, this numerical study offers significant implications for designing an economically and environmentally sustainable treatment injection scheme for coal mining wastewater drainage.

A longer Achilles tendon moment arm length is not associated with superior hopping performance.

Variability in musculoskeletal and lower leg structure has the potential to influence hopping height. Achilles tendon moment arm length and plantarflexor muscle strength can influence ankle joint torque development and, consequently, hopping performance. While most studies have examined the connection of the Achilles tendon moment arm with hopping performance including the resting length, in this study we attempted to explore how the changes in Achilles tendon moment arm are related to hopping performance. Therefore, the purpose of this study was to test for correlations between foot and lower leg muscle structure parameters (i.e., muscle mass, volume, cross-sectional area and Achilles tendon moment arm length) and hopping height performance in relation to changes in Achilles tendon moment arm length. Eighteen participants (10 males 8 female) performed repetitive bilateral hopping on a force platform while sagittal plane kinematics of the lower leg were recorded. Additionally, maximal isometric plantarflexion was measured. To obtain structural parameters of the lower leg, the right lower leg of each participant was scanned with magnetic resonance imaging. The cross-sectional areas of the Achilles tendon, soleus, lateral and medial gastrocnemius were measured, while muscle volumes, muscle mass, and Achilles tendon moment arm length were calculated. Contrary to our initial assumption, longer Achilles tendon moment arm did not result in superior hopping performance. Interestingly, neither maximal isometric plantarflexion force nor muscle size correlated with repetitive bilateral hopping performance. We can assume that the mechanical characteristics of the tendon and the effective utilization of the stored strain energy in the tendon may play a more important role in repetitive hopping than the structural parameters of the lower leg.

Nonlinear dynamics of novel flight-style autonomous underwater vehicle with bow wings, Part I: ASE and CFD based estimations of hydrodynamic coefficients, Part II: Nonlinear dynamic modeling and experimental validations

Accurate dynamic modeling is essential for precise prediction of six degrees-of-freedom (6-DOF) motion and model-based controller design of an autonomous underwater vehicle (AUV). The accuracy of dynamic model of an AUV largely depends upon the precise estimation of hydrodynamic coefficients. Accordingly, to establish the dynamic model based on ASE-estimated hydrodynamic coefficients of the novel flight-style AUV and experimental validations, the study is presented in two parts (Part I: ASE and CFD based estimations of hydrodynamic coefficients and Part II: Nonlinear dynamic modeling and experimental validations).Part I: In this part complete set of nonlinear hydrodynamic coefficients including, added mass, drag, and lift forces and moment coefficients are estimated using ASE technique, which is specifically developed to accurately comprehend the novel AUV design including, AUV hull, fixed wings, control fins, and appendages. Additionally, an improved ASE approach is also proposed to estimate cross flow drag force coefficients. In proposed improved ASE technique, (Cdc) in mathematical formulation is taken from the experimental results of 3D flow past over circular cylinder instead of 2D, as followed previously to estimate the nonlinear cross-flow drag force and moment coefficients (Yvv,Zww,Mww,Nvv,Yrr,Zqq,Mqq&Nrr). The proposed ASE technique is verified and validated in two stages: first, by comparing the ASE-estimated results with CFD-based estimations, and second, by investigating the 6-DOF motion response of the AUV. When compared ASE-estimations with the CFD results for the cross-flow drag force and moment coefficients, the proposed ASE technique has shown a significant improvement (approximately 20%) over the previously employed ASE method. The ASE-estimated results are validated through 6-DOF motion response of AUV during free-running underwater experiments, provided in ‘Part II’. Overall, the proposed ASE technique is considered more effective, direct, and less costly in terms of time and computational efforts, compared to CFD-based or experimental-based estimations of hydrodynamic coefficients of AUVs, particularly torpedo-shaped AUVs.Part II: This part presents a nonlinear dynamic model for a newly designed torpedo-shaped flight-style AUV having complex bow and stern fixed wings and control fins configuration. The model includes precise mathematical formulations to accurately represent the physics of the AUV and underwater environment in terms of hydrodynamic derivatives such as added mass, drag, and lift forces and moment coefficients. These coefficients have been estimated using an ASE method provided in ‘Part I’. The 6-DOF motion response of the AUV has been simulated in both horizontal and vertical planes which includes, zigzag yaw, circle, zigzag pitch, and spiral maneuvers. The lift generated by the bow and stern control fins has been investigated both separately and collectively, especially during complex spiral ascending maneuvers. Moreover, improved ASE technique for cross flow drag coefficients has also been validated through 6-DOF free-running underwater experiments of AUV and insights on impact of cross flow drag coefficients on 6-DOF motion response of AUV has also been provided. Overall, the comparison between the simulated AUV motion and free-running underwater experiments demonstrated consistency, thereby validating the accuracy of the nonlinear dynamic modeling, ASE-based hydrodynamic coefficient predictions, and effectiveness of the newly designed flight-style AUV for underwater operations.

Cascaded 2D Micromirror with Application to LiDAR.

This paper introduced a novel approach to enhance the vertical scanning angle of a large aperture 2D electromagnetic micromirror through the utilization of a cascaded torsional beam design. The primary objective was to increase the vertical scanning angle without compromising the robustness, which was achieved by optimizing the trade-off between the rotation angle and the first mode of resonant frequency. The cascaded design provides flexibility to either increase the outer frame's rotation angle without sacrificing torsional stiffness or enhance the torsion beam's stiffness while maintaining the same rotation angle, thus elevating the first-mode resonant frequency and overall robustness. The effectiveness of the cascaded design was demonstrated through a comparative study with a non-cascaded 2D micromirror possessing the same aperture size, torque, and mass moment of inertia. Theoretical analysis and finite-element simulation are employed to determine critical parameters such as the stiffness ratio between the cascaded torsion beams, and to predict improvements in the scanning angle and primary resonant frequency brought by the cascaded design. Prototypes of both cascaded and non-cascaded designs are fabricated using a flexible printed circuit board combined with Computer numerical control (CNC) machining of a Ti-alloy thin film, confirming the superior performance of the cascaded 2D micromirror. The cascaded design achieved vertical scanning angles up to 26% higher than the traditional design when both were actuated at close resonance frequencies. Additionally, the micromirror was successfully integrated into a 3D LiDAR system. The light detection and ranging (LiDAR) system was modelled in Zemax OpticStudio to find the optimized design and assembly positions.

In‐flight force estimation by flight mill calibration

AbstractThe study of insect flight is important for conservation and sustainability efforts, as predicting insect dispersal can aid management programmes in tackling economic and ecological harm from, for example, invasive species. Flight mills are invaluable tools for measuring the factors of insect flight under laboratory conditions, as they lower several technical and financial barriers to conduct experiments. It is especially difficult, however, to make assumptions about the energetic cost of tethered flights conducted using different tethers, or even on different flight mills, due to the mechanical variability of the bearing friction and air resistance of the rotating assembly. This additional uncertainty necessitates a larger number of replicates for any given standard of statistical confidence. By characterising flight mill friction, this uncertainty can both be reduced in magnitude and assigned a specific, well‐defined numerical value. We present a simple methodology to characterise this friction through dynamic calibration of the flight mill, at a high statistical confidence. This study uses videography of a flight mill undergoing free velocity decay due to friction, using an in‐house developed software to extract angular velocity from video data. However, the technique is readily adaptable to other measurement techniques. Using the velocity, alongside the mass moment of inertia of the flight mill, allows us to determine the rotational friction coefficient. This friction coefficient provides precise measurements of thrust production, and therefore the energy expenditure of flight, by the tethered insect.

Quantifying hinge torque in self-folding, shape memory polymer origami under varying thermal loads

Self-folding origami actuated by thermally responsive shape memory polymers (SMPs) presents a promising mechanism for the deployment of space structures. Pre-strained SMP sheets shrink when heated. The SMP sheets are patterned with black ink hinges that heat locally via a surface heat flux when exposed to infrared (IR) light. The localized heating induces gradients in shrinking, or shape recovery, which in turn produces folding. However, the thermal and mechanical loads applied to the structure during deployment pose unique challenges to the application of SMP as actuators. Herein, we investigate the effects of thermal loads (variable IR flux and convection) and folding resistance (mass moment of inertia) on self-folding behavior of polystyrene (PS) SMP sheets. We analyze digital video recordings to determine the transient bending angle (the angle traversed by the folding face of the SMP sheet) and hinge torque. It is observed that higher heat fluxes and reduced convection lead to higher maximum bending angles, lower fold start times, and higher hinge torques. We found that the measured hinge torque increases with increasing folding resistance. In addition, we highlight the significance of convective heat transfer by demonstrating self-folding under vacuum at IR flux intensities as low as 2,622 W/m2 at a wavelength of 980 nm and identify a minimum surface heat flux required to induce self-folding in the presence of convection. Comparisons to dynamic mechanical analysis (DMA) and a thermal finite element analysis (FEA) offer insight to the initiation of folding under varying thermal loads. These results provide a necessary understanding of the effects of varying thermal loads on the behavior of self-folding origami for deployable space structures.

Relativistic binary-disc dynamics and the timing of OJ-287’s flares

ABSTRACT We revisit the precessing black hole binary model, a candidate to explain the bizarre quasi-periodic optical flares in OJ-287’s light curve, from first principles. We deviate from existing work in three significant ways: (1) Including crucial aspects of relativistic dynamics related to the accretion disc’s gravitational moments. (2) Adopting a model-agnostic prescription for the disc’s density and scale height. (3) Using Markov chain Monte Carlo methods to recover reliable system parameters and uncertainties. We showcase our model’s predictive power by timing the 2019 Eddington flare within 40 h of the observed epoch, exclusively using data available prior to it. Additionally, we obtain a novel direct measurement of OJ-287’s disc mass and quadrupole moment exclusively from the optical flare timings. Our improved methodology can uncover previously unstated correlations in the parameter posteriors and patterns in the flare timing uncertainties. According to the model, the 26th optical flare is expected to occur on the 21st of August 2023 ± 32 d, shifted by approximately a year with respect to previous expectations.

Correction to: Analytical Determination of Mass and Magnetic Moment of Baryons in Diquark Model

Correction to: Analytical Determination of Mass and Magnetic Moment of Baryons in Diquark Model

Numerical investigation of the power performance of a wave energy converter comprising a multi-body power take-off

This article presents a wave energy converter exploiting the pitch of a floating body moored to the seabed. When the floating body tilts under the action of an incoming wave, a movable mass, placed inside the hull, moves relative to the floating body and actuates an electrical generator. Most devices of this type have the drawback that the moving mass sequentially accelerates, slows down, stops and then repeats this sequence in the opposite direction. This generates an irregular instantaneous power output. The proposed concept consists of (at least) two eccentric bodies having the same mass and revolving atopposite speeds around a vertical axis. In this « counterrotating » solution, the oscillations of the float result in the continuous circular motion of the direct-drive PTO, though the global centre of gravity of the eccentric bodies moves back-and-forth along the symmetry axis of the device. If the eccentric bodies move at constant speed, their global centre of gravity moves in a sinusoidal manner along its pathway. The present study aims to investigate, through modelling and numerical simulations, the influence of the main parameters, such as the phase and the PTO mass moment, on the performance of a counter-rotating device exposed to waves of various heights and various wavelengths. Optimal phase and mass moment are determined numerically. The resulting output power is close to the theoretical maximum power that can be harvested by the floating body.

Tuning Wave Energy Converters to local wave conditions

A Wave Energy Converter (WEC) cannot operate efficiently if left alone floating to the mercy of the random sea surface. Moreover, high waves may impose destructive forces while contributing nil energy production in return. For a WEC to be efficient, its natural frequency should be close to the peak frequency of a wave spectrum. At the resonance or another lower natural frequency, dynamic responses are more regular, and thus, the power take-off system (PTO) can operate in a more efficient manner. This paper introduces a general systematic methodology for tuning the natural frequency of a resonant WEC for the desired degree of freedom and converting dynamic responses into power. A barge is used as a case study to tune its roll and heave natural period, which in general are much lower than the peak period of swells. The roll natural period is increased by hanging subsea structures to the sides of the vessel by means of mooring lines, see Fig. 1. The size of the structures and their entrapped water increase the roll mass moment of inertia to achieve the desired period. For the heave response, the natural period raises by adding skirts to the sides of the vessel, increasing the entrapped water. The resonant motions are significantly suppressed by means of the drag force acting on the subsea structures. Thus, the extreme drag forces acting on the structures act as a damper to the vessel response. These forces are transferred to the mooring lines, which can be converted into a rotary motion of a shaft of the PTO. Our application focuses on the Galapagos Islands, where narrow, low-frequency southerly swells with a typical 13 s peak period dominate the wave climate. This study allows for a systematic design of resonant-type WECs, which is necessary for the development of technical and economic feasibility studies of various novel and existing concepts.
 
 Figure 1: Schematic representation of resonant WEC with tuned roll natural period

Is It Possible to Measure the Lense–Thirring Orbital Shifts of the Short-period S Star S4716 Orbiting Sgr A*?

The maximal values of the general relativistic Lense–Thirring (LT) orbital shifts ΔI LT, ΔΩLT, and Δω LT of the inclination I, the longitude of the ascending node Ω, and the perinigricon ω, respectively, of the recently discovered star S4716, which has the shortest orbital period of all the S stars that orbit the supermassive black hole (SMBH) in Sgr A*, are of the order of ≃5–16 arcseconds per revolution . Given the current error σ ω = 0.°02 in determining ω, which is the most accurate orbital parameter of S4716 among all those affected by the SMBH's gravitomagnetic field through its angular momentum J •, about 48 yr would be needed to reduce σ ω to ≃10% of the cumulative LT perinigricon shift over the same time span. Measuring ΔI LT and ΔΩLT to the same level of accuracy would take much longer. Instead, after just 16 yr, a percent measurement of the larger gravitoelectric (GE) Schwarzschild-like perinigricon shift Δω GE, which depends only on the SMBH's mass M •, would be possible. On the other hand, the uncertainties in the physical and orbital parameters entering Δω GE would cause a huge systematic bias of Δω LT itself. The SMBH's quadrupole mass moment induces orbital shifts as little as ≃0.01–0.05″ rev−1.

Analytical Determination of Mass and Magnetic Moment of Baryons in Diquark Model

Analytical Determination of Mass and Magnetic Moment of Baryons in Diquark Model

Inertia tensor estimation of tethered debris through tether tracking

Tethered systems, such as tethered harpoons or nets, are promising methods to capture uncooperative space debris, but suffer from complicated post-capture dynamics and control; control strategies could benefit from knowledge of the mass moments of inertia of the target debris, usually unknown without estimation. In this work, an Unscented Kalman Filter is proposed to estimate the moments of inertia, angular velocity, and attitude of tethered debris in the absence of end effectors and of sensors on the target. This is achieved by leveraging camera measurements of features on the target debris and a tension sensor. Estimation of the properties of (1) a symmetric target with a centered tether attachment point and of (2) a non-symmetric target with a non-centered tether attachment point is performed in simulation. The filter is found to be capable of accurately and precisely estimating both the attitude and angular rates of debris, although sustained loss of a tracked feature heavily impairs these estimates. The principal moments of inertia estimates are unaffected by the loss of a tracked feature and can be made both accurately and precisely when the tether is taut. Asymmetry of the target and of the tether attachment point can have a positive effect on the performance of the filter.

Quadrotor Trajectory Tracking Using Model Reference Adaptive Control, Neural Network-Based Parameter Uncertainty Compensator, and Different Plant Parameterizations

A quadrotor trajectory tracking problem is addressed via the design of a model reference adaptive control (MRAC) system. As for real-world applications, the entire quadrotor dynamics is typically unknown. To take that into account, we consider a plant model, which contains uncertain nonlinear terms resulting from aerodynamic friction, blade flapping, and the fact that the mass and inertia moments of the quadrotor may change from their nominal values. Unlike many known studies, the explicit equations of the parameter uncertainty for the position control loop are derived in two different ways using the differential flatness approach: the control signals are (i) used and (ii) not used in the parametric uncertainty parameterization. After analysis, the neural network (NN) is chosen for both cases as a compensator of such uncertainty, and the set of NN input signals is justified for each of them. Unlike many known MRAC systems with NN for quadrotors, in this study, we use the kxx+krr baseline controller, which follows from the control system derivation, with both time-invariant (parameterization (i)) and adjustable (parameterization (ii)) parameters instead of an arbitrarily chosen non-tunable PI/PD/PID-like one. Adaptive laws are derived to adjust the parameters of NN uncertainty compensator for both parameterizations. As a result, the position controller ensures the asymptotic stability of the tracking error for both cases under the assumption of perfect attitude loop tracking, which is ensured in the system previously developed by the authors. The results of the numerical experiments support the theoretical conclusions and provide a comparison of the effectiveness of the derived parameterizations. They also allow us to make conclusions on the necessity of the baseline controller adjustment.

Simple Mathematical Models for the Dynamics Of Spacecraft With Deployed Solar Panels

Most present day spacecrafts have large interconnected deployed solar panels having very low natural frequencies. The control torque applied to maneuver the spacecraft sets up transient oscillations in the spacecraft. The present work studies the nature of these interactions. The spacecraft in orbit can be modeled as a free rigid mass with flexible elements attached to it. It is shown that the oscillations of the spacecraft body are characterized by the dynamic characteristics of the flexible panel even if the mass and mass moment of inertia of the body is signifcantly higher than that of the flexible panels. A simple model consisting of an Euler-Bernoulli beam attached to a mass can represents such a system. The infuence of various parameters of the Euler-Bernoulli beam and the rigid element on the disturbances caused in the rigid element are investigated. The characteristics are determined for a step and also for a torque input. The responses are obtained in terms of nondimensionalised quantities. It is demonstrated that using the simple model developed the responses of spacecraft body can be easily obtained.

Charge gap in SU(3) Yang–Mills-plus-nonlinear-spinor-field theory

Particlelike solutions in SU(3) gauge Yang–Mills theory with color magnetic and electric fields sourced by a nonlinear spinor field are obtained. The asymptotic behavior of these fields is studied. It is shown that the electric field exhibits the Coulomb asymptotic behavior, and one of the color components of the magnetic field behaves asymptotically as the field of a magnetic dipole. This allows one to determine the corresponding charge and magnetic moment. It is shown that profiles of the color charge and magnetic moment have global minima, which may be called charge and magnetic moment gaps. The relationship between the total energy of the system and the color charge is obtained. The physical reason for the appearance of the mass, charge, and magnetic moment gaps in the theory under consideration is discussed.