Motion Of Point Research Articles

Realization of Self-Adaptive Higher Teaching Management Based Upon Expression and Speech Multimodal Emotion Recognition.

In the process of communication between people, everyone will have emotions, and different emotions will have different effects on communication. With the help of external performance information accompanied by emotional expression, such as emotional speech signals or facial expressions, people can easily communicate with each other and understand each other. Emotion recognition is an important network of affective computers and research centers for signal processing, pattern detection, artificial intelligence, and human-computer interaction. Emotions convey important information in human communication and communication. Since the end of the last century, people have started the research on emotion recognition, especially how to correctly judge the emotion type has invested a lot of time and energy. In this paper, multi-modal emotion recognition is introduced to recognize facial expressions and speech, and conduct research on adaptive higher education management. Language and expression are the most direct ways for people to express their emotions. After obtaining the framework of the dual-modal emotion recognition system, the BOW model is used to identify the characteristic movement of local areas or key points. The recognition rates of emotion recognition for 1,000 audios of anger, disgust, fear, happiness, sadness and surprise are: 97.3, 83.75, 64.87, 89.87, 84.12, and 86.68%, respectively.

Biomechanical and psychophysiological features of qualified veteran boxers of various fighting styles

Purpose: to give a comparative description of the peculiarities of motor activity of boxers-veterans of different styles of fighting based on the analysis of psychophysiological and biomechanical parameters.
 Material and Methods: The study involved 42 qualified veteran boxers (age 45-50 years, body length - 178.67±8.26 cm, body weight - 70.96±9.38 kg). The biomechanical indicators of a direct blow in boxing were recorded using the Kinovea program, version 0.8.15, and psychophysiological indicators using the Psychodiagnostics program. As biomechanical indicators, the speed of movement of various points of the limbs and the angles in the joints were determined. As psychophysiological indicators, the speed of a simple visual-motor reaction, a reaction of choice in various testing modes was recorded. Based on these indicators, the mobility and endurance of the nervous system were determined. The reliability of differences between groups of different fighting styles was determined.
 Results. Tempo-style boxers differ from representatives of other fighting styles in their lower mobility of the nervous system and greater endurance for speedy and precise actions. Tempo-style boxers have the lowest values ​​of the angle in the knee joint throughout the movement (p<0.05, p<0.01) and the highest speed of movement. Play style boxers are characterized by the greatest angle in the shoulder joint at the very beginning of the movement (p<0.05, p<0.001), the highest speed of fist and shoulder movement at the very beginning of the movement (p<0.001). Power style boxers develop maximum movement speed at the end of a straight punch compared to the beginning. Power style boxers are distinguished by the smallest values ​​of the angle in the elbow joint, which is especially noticeable at the end of the movement (p<0.001).
 Conclusions. Psychophysiological features of boxers of different styles of fighting are reflected in the features of the technique of a direct blow. The lack of speed when tempo-style boxers are engaged in movement is supplemented and compensated by the high speed of movement. Play style boxers are characterized by high speed of movement at the very beginning of punching. Power style boxers are distinguished by the gradual development of movement speed.

Methods on Visual Positioning Based on Basketball Shooting Direction Standardisation

The existing basketball training shooting direction correction method has the problems of low correction accuracy and poor self-adaptability, and proposes a basketball training shooting direction correction method based on visual perception. A visual localisation algorithm for tracking feature points of object targets is used as the basis for the process of visual robot localisation and its effects, from camera calibration, template matching, background modelling and foreground target separation to feature point extraction, motion estimation, and Kalman filtering. An in-depth understanding and analysis of the traditional corner point detection algorithm is presented, on the basis of which improvements are proposed. An accurate tracking method based on improved Harris corner point extraction is introduced, which builds on the traditional Harris feature point detection by using the changing relationship between the gradient of the grey value of the pixels near the corner point, using simple operations and analysis to exclude some pseudocorner points and noncorner points, and further processing the retained points to derive the correct feature points. The code of this algorithm is written to finally achieve its detection effect, and compared with the traditional algorithm, it is concluded that this algorithm can then extract more accurate corner points in a shorter time, which lays the foundation for the next step of accurate basketball tracking, reflecting the practicality of this algorithm.

The landslide velocity

Abstract. Proper knowledge of velocity is required in accurately determining the enormous destructive energy carried by a landslide. We present the first, simple and physics-based general analytical landslide velocity model that simultaneously incorporates the internal deformation (nonlinear advection) and externally applied forces, consisting of the net driving force and the viscous resistant. From the physical point of view, the model represents a novel class of nonlinear advective–dissipative system, where classical Voellmy and inviscid Burgers' equations are specifications of this general model. We show that the nonlinear advection and external forcing fundamentally regulate the state of motion and deformation, which substantially enhances our understanding of the velocity of a coherently deforming landslide. Since analytical solutions provide the fastest, most cost-effective, and best rigorous answer to the problem, we construct several new and general exact analytical solutions. These solutions cover the wider spectrum of landslide velocity and directly reduce to the mass point motion. New solutions bridge the existing gap between negligibly deforming and geometrically massively deforming landslides through their internal deformations. This provides a novel, rapid, and consistent method for efficient coupling of different types of mass transports. The mechanism of landslide advection, stretching, and approaching the steady state has been explained. We reveal the fact that shifting, uplifting, and stretching of the velocity field stem from the forcing and nonlinear advection. The intrinsic mechanism of our solution describes the fascinating breaking wave and emergence of landslide folding. This happens collectively as the solution system simultaneously introduces downslope propagation of the domain, velocity uplift, and nonlinear advection. We disclose the fact that the domain translation and stretching solely depend on the net driving force, and along with advection, the viscous drag fully controls the shock wave generation, wave breaking, folding, and also the velocity magnitude. This demonstrates that landslide dynamics are architectured by advection and reigned by the system forcing. The analytically obtained velocities are close to observed values in natural events. These solutions constitute a new foundation of landslide velocity in solving technical problems. This provides practitioners with key information for instantly and accurately estimating the impact force that is very important in delineating hazard zones and for the mitigation of landslide hazards.

Five-Axis Trajectory Generation Considering Synchronization and Nonlinear Interpolation Errors

Abstract This paper presents a novel real-time interpolation technique for five-axis machine tools to attain higher speed and accuracy. To realize computationally efficient real-time interpolation of 6-DOF tool motion, a joint workpiece–machine coordinate system interpolation scheme is proposed. Cartesian motion of the tool center point (TCP) is interpolated in the workpiece coordinate system (WCS), whereas tool orientation is interpolated in the machine coordinate system (MCS) based on the finite impulse response filtering. Such an approach provides several advantages: (i) it eliminates the need for complex real-time spherical interpolation techniques, (ii) facilitates efficient use of slower rotary drive kinematics to compensate for the dynamic mismatch between Cartesian and rotary axes and achieve higher tool acceleration, and (iii) mitigates feed fluctuations while interpolating near kinematic singularities. To take advantage of such benefits and realize accurate joint WCS–MCS interpolation scheme, tool orientation interpolation errors are analyzed. A novel approach is developed to adaptively discretize long linear tool moves and confine interpolation errors within user set tolerances. Synchronization errors between TCP and tool orientation are also characterized, and peak synchronization error level is determined to guide the interpolation parameter selection. Finally, blending errors during non-stop continuous interpolation of linear toolpaths are modeled and confined. Advantages of the proposed interpolation scheme are demonstrated through simulation studies and validated experimentally. Overall, proposed technique can improve cycle times up to 10% while providing smooth and accurate non-stop real-time interpolation of tool motion in five-axis machining.

Simulation of heat and fluid flow in porous medium and fractures by material point method

PurposeThe material point method (MPM)is a particle-based numerical method suitable for solid–liquid simulation and large deformation problems. However, MPM is generally used in solid deformation at present, to develop a multi-physics coupling MPM; the purpose of this study is to extend the MPM to simulate the heat and fluid flow and address the thermal-hydrological (TH) coupling problems.Design/methodology/approachThe porous medium was discretized into two sets of Lagrangian points, and the motion of fluid points follows the Darcy’s law. Two sets of heat transport equations were established for the heat conduction and heat exchange in the pore fluid and solid skeleton. Fractures were considered by adding the porosity gradient term in the governing equations; also a transition function was introduced to smoothen the fracture boundary.FindingsFour cases of heat and fluid flow in porous medium and fractures were presented to verify the feasibility of the proposed method. And the effects of fractures on heat and fluid flow were investigated. Additionally, a case of geothermal extraction was solved and the importance of the interstitial convective heat transfer coefficient was analyzed.Originality/valueThe proposed method extends the conventional MPM, using two sets of material points and two sets of heat transport equations to simulate the heat and fluid flow and address the TH coupling problems, which can be applied in both porous medium and fractures.

On the Construction of Conservative Semi-Lagrangian IMEX Advection Schemes for Multiscale Time Dependent PDEs

This article is devoted to the construction of a new class of semi-Lagrangian (SL) schemes with implicit-explicit (IMEX) Runge-Kutta (RK) time stepping for PDEs involving multiple space-time scales. The semi-Lagrangian (SL) approach fully couples the space and time discretization, thus making the use of RK strategies particularly difficult to be combined with. First, a simple scalar advection-diffusion equation is considered as a prototype PDE for the development of a high order formulation of the semi-Lagrangian IMEX algorithms. The advection part of the PDE is discretized explicitly at the aid of a SL technique, while an implicit discretization is employed for the diffusion terms. In this way, an unconditionally stable numerical scheme is obtained, that does not suffer any CFL-type stability restriction on the maximum admissible time step. Second, the SL-IMEX approach is extended to deal with hyperbolic systems with multiple scales, including balance laws, that involve shock waves and other discontinuities. A conservative scheme is then crucial to properly capture the wave propagation speed and thus to locate the discontinuity and the plateau exhibited by the solution. A novel SL technique is proposed, which is based on the integration of the governing equations over the space-time control volume which arises from the motion of each grid point. High order of accuracy is ensured by the usage of IMEX RK schemes combined with a Cauchy–Kowalevskaya procedure that provides a predictor solution within each space-time element. The one-dimensional shallow water equations (SWE) are chosen to validate the new conservative SL-IMEX schemes, where convection and pressure fluxes are treated explicitly and implicitly, respectively. The asymptotic-preserving (AP) property of the novel schemes is also studied considering a relaxation PDE system for the SWE. A large suite of convergence studies for both the non-conservative and the conservative version of the novel class of methods demonstrates that the formal order of accuracy is achieved and numerical evidences about the conservation property are shown. The AP property for the corresponding relaxation system is also investigated.

An Analysis for Variable Physical Properties Involved in the Nano-Biofilm Transportation of Sutterby Fluid across Shrinking/Stretching Surface.

In this article, we explore how activation energy and varied transit parameters influence the two-dimensional stagnation point motion of nano-biofilm of Sutterby fluids incorporating gyrotactic microbes across a porous straining/shrinking sheet. Prior investigations implied that fluid viscosity as well as thermal conductance are temperature based. This research proposes that fluid viscosity, heat capacity and nanofluid attributes are all modified by solute concentration. According to some empirical research, the viscosity as well as heat conductivity of nanoparticles are highly based on the concentration of nanoparticles instead of only the temperature. The shooting approach with the RK-4 technique is applied to acquire analytical results. We contrast our outcomes with those in the existing research and examine their consistency and reliability. The graphic performance of relevant factors on heat, velocity, density and motile concentration domains are depicted and discussed. The skin friction factor, Nusselt number, Sherwood number and the motile density are determined. As the concentration-dependent properties are updated, the speed, temperature, concentration and motile density profiles are enhanced, but for all concentration-varying factors, other physical quantities deteriorate.

Experimental studies on wake structures of a circular cylinder with different surface roughness heights

In the present study, the effects of surface roughness height (k/D) on wake characteristics of a circular cylinder were examined experimentally in a water flume at a Reynolds number of 2520 using particle image velocimetry (PIV). The surface roughness was simulated by using 3D printed hemispheres uniformly distributed over the cylinder surface. Four relatively large roughness heights with k/D = 5%, 10%, 15% and 20%, and a coverage ratio of 79%, which were not explored systematically in the literature, were considered, and the results were compared with that of a smooth cylinder (k/D = 0%). It is found that the surface roughness disturbs the shear layers of the cylinder, affecting the vortex shedding frequency and the wake formation region. The Strouhal number decreases with the increase of k/D. This can be attributed to the forward movement of the shear layer separation points. This phenomenon is also confirmed by smoke-wire flow visualisation. Besides, the regularity of the vortex shedding and the magnitudes of the Reynolds stresses are enhanced with the existence of roughness. The proper orthogonal decomposition (POD) analysis shows that with the existence of surface roughness, the large-scale Kármán vortex structures is intensified. This study extends the understanding of the influence of k/D on flow characteristics of a circular cylinder.

Substantiation of cultivator points form of the lowest draught for stratifier tillage machine

Soil cultivating loosening and separating stratifier machine performs soil detachment by separating lumps according to the working depth. When lifting and separating soil, the rotor rippers carry weeds onto the treated field surface. The machine can be used in systems of “No till” technologies, however, in order to reduce the energy intensity of operations on soil cultivation by a mechanical method, when developing soil-cultivating loosening-separating machines, it is important to substantiate the form of the cultivator points of the lowest draught. The cultivator points of the tillage machine are designed for cutting the soil layer, directing the soil to the loosening-separating device. The indicator of the energy intensity of the process is the resistance force of the movement of the cultivator points in the soil. To find the extremum of the functional, the direct method of the Ritz calculus of variations was used. As a result, a graph is obtained that depicts the shape of the line of the lowest draught. In order to determine the reliability of the results of theoretical studies, the energy indicators of the operation of the cultivator points device for cutting and lifting soil were calculated. The cultivator points with a theoretically substantiated profile, compared to the sidewall of the straight profile, have draught of 38.5%.

Analysis of the Operation of Kinematic Seismically Isolated Foundations Taking into Account the Vertical Component of the Seismic Impact

The analysis of the work of kinematic foundations under seismic impact is carried out. In this case, the seismic action is set by two harmonic functions, one of which describes the vertical component of the movement of points on the day surface during an earthquake. The equation of motion of the considered seismically isolated supports is reduced to the form of the well-known Mathieu-Hill equation, the solutions of which can be both bounded and infinitely increasing functions. Thus, the possibility of occurrence in the considered system of seismic isolation of the phenomenon of parametric resonance has been proved and the parameters of the system and the parameters of seismic impact, on which the occurrence of this phenomenon depends, have been identified. The values of the damping parameters in the system and the amplitude of the vertical component of the seismic action, at which the movement of the kinematic supports is unstable, have been established. The construction of the zones of instability of oscillations of supports on the plane of change of the coefficients of the Mathieu-Hill equation is carried out. Also, the value of damping in the seismic isolation system is obtained, which is necessary to ensure the stability of motion under the combined action of the vertical and horizontal components of the seismic action.

Quantum induced broadening: A challenge for cosmic neutrino background discovery

A recent preprint by Cheipesh et al. pointed out that the zero-point motion of tritium atoms bound to graphene may blur the measured energies of $\ensuremath{\beta}$ electrons. Smearing due to zero point motion is well known. Such an effect features in studies of the $\ensuremath{\beta}$ spectrum expected in experiments like KATRIN using diatomic tritium. The recent preprint may, however, challenge new planned experiments seeking to discover the cosmic neutrino background (CNB) neutrinos (and/or other neutrinos of masses smaller than 0.1 eV), which plan to use tritium adsorbed onto graphene or other materials. Our paper clarifies these issues and examines the more general problem of smearing induced by quantum uncertainty. We find that the effect of Cheipesh et al. is reduced considerably. The importance of the chemical evolution of the $^{3}\mathrm{H}$ atom hosting the tritium nucleus into a tightly bound neutral $^{3}\mathrm{He}$ atom is emphasized. We estimate the excess blurring caused by the dense spectrum near the lowest state of the graphene or other hosts of the tritium atom, generated by the electronic response to the ``sudden'' escape of the $\ensuremath{\beta}$ electron. Our analysis suggests yet larger effects and difficulties facing many experiments searching for small mass neutrinos. We speculate on a possible experimental setup, which could minimize quantum broadening.

Component migration, bone mineral density changes, and bone turnover markers in cementless and cemented total knee arthroplasty: a prospective randomized RSA study in 53 patients with 2-year follow-up.

Cementless tibial components migrate initially until osseointegration and preserve periprosthetic bone. Cemented tibial components are fixed from surgery but loose periprosthetic bone. Little is known about bone formation and resorption biomarkers in relation to component fixation and bone mineral density (BMD) changes of cementless and cemented total knee arthroplasty. We hypothesize a similar migration of cemented and cementless tibial components between 1- and 2-year follow-up indicating a stable long-term fixation. In a prospective patient-blinded randomized study, we compared cementless (n = 27) and cemented (n = 26) tibial components with radiostereometry measured migration (MTPM = Maximum Total Point Motion: point of component that migrates the most) and changes in BMD and biochemical bone turnover markers (BTMs) until 24months after surgery. The mean MTPM between 12 and 24months were similar between groups with -0.06mm (95% CI -0.23; 0.11) in the cementless group compared to 0.02mm (95% CI -0.07; 0.11) in the cemented group. However, there was a higher proportion of cementless components (16/25) than cemented components (7/24) with continuous migration (MTPM > 0.2mm) (p = 0.02). In the medial and anterior region below the tibial components, the BMD increased by mean 1.8% and 7.4% for cementless components and decreased by mean 8.6% and 4.2% for cemented components until 24-month follow-up. In both groups, BTMs initially showed increased bone resorption (CTx) and bone formation (P1NP) followed by normalization to pre-operative levels at 6months post-surgery. More cementless components than cemented components showed continues migration which suggest a higher risk of early revision. Bone turnover increased post-surgery in both groups, but did not explain the difference in change in periprosthetic BMD. I.

Observer design for a flexible structure with distributed and point sensors

The paper is devoted to the observability study of a dynamic system, which describes the vibrations of an elastic beam with an attached rigid body and distributed control actions. The mathematical model is derived using Hamilton's principle in the form of the Euler-Bernoulli beam equation with hinged boundary conditions and interface condition at the point of attachment of the rigid body. It is assumed that the sensors distributed along the beam provide output information about the deformation in neighborhoods of the specified points of the beam. Based on the variational form of the equations of motion, the spectral problem for defining the eigenfrequencies and eigenfunctions of the beam oscillations is obtained. Some properties of the eigenvalues and eigenfunctions of the spectral problem are investigated. Finite-dimensional approximations of the dynamic equations are constructed in the linear manifold spanned by the system of eigenfunctions. For these Galerkin approximations, observability conditions for the control system with incomplete information about the state are derived. An algorithm for observer design with an arbitrary number of modal coordinates is proposed for the differential equation on a finite-dimensional manifold. Based on a quadratic Lyapunov function with respect to the coordinates of the finite-dimensional state vector, the exponential convergence of the observer dynamics is proved. The proposed method of constructing a dynamic observer makes it possible to estimate the full system state by the output signals characterizing the motion of particular point only. Numerical simulations illustrate the exponential decay of the norm of solutions of the system of ordinary differential equations that describes the observation error.

Comparison of soft tissue changes between incisor tipping and translation after premolar extraction.

ObjectiveThis study compared soft tissue changes after extraction of the four premolars followed by maximum retraction of the anterior teeth according to the type of anterior teeth movement tipping and translation.MethodsPatients who had undergone orthodontic treatment involving the extraction of four premolars were retrospectively selected and divided into either the tipping (n = 27) or translation (n = 26) groups based on the retraction of the incisor root apex and the axis changes of the incisors during the treatment period. Lateral pre- and post-treatment cephalograms were analyzed.ResultsThere were no significant differences between the tipping and translation groups before treatment. The retraction amounts of the root apex of the upper and lower incisors in the tipping group were 0.33 and 0.26 mm, respectively, and 5.02 and 5.31 mm, respectively, in the translation group (p < 0.001). The posterior movements of soft tissue points A and B in the tipping group were 0.61 and 1.25 mm, respectively, and 1.10 and 3.25 mm, respectively, in the translation group (p < 0.01). The mentolabial sulcus angle increased by 5.89° in the tipping group, whereas it decreased by 8.13° in the translation group (p < 0.001).ConclusionsAn increased amount of retraction of the incisor root apex led to the increased posterior movement of soft tissue points A and B, and this appeared more distinct in cases involving the lower incisor and lower lip.

Impact response of a thin shallow doubly curved linear viscoelastic shell rectangular in plan

In this paper, we consider the problem on a transverse impact of a viscoelastic sphere upon a viscoelastic shallow doubly curved shell with rectangular platform, the viscoelastic features of which are defined via the fractional derivative standard linear solid models; in so doing, only Young’s time-dependent operators are preassigned, while the bulk moduli are considered to be constant values, since the bulk relaxation for the majority of materials is far less than the shear relaxation. Shallow panel’s displacement subjected to the concentrated contact force is found by the method of expansion in terms of eigen functions, and the sphere’s displacement under the action of the contact force, which is the sum of the shell’s displacement at the place of contact and local bearing of impactor and target’s materials, is defined from the equation of motion of the material point with the mass equal to sphere’s mass. Within the contact domain, the contact force is defined by the modified Hertzian contact law with the time-dependent rigidity function. For decoding the viscoelastic operators involving the problem under consideration, the algebra of Rabotnov’s fractional operators is employed. A nonlinear integro-differential equation is obtained either in terms of the contact force or in the local bearing of the target and impactor materials. Using the duration of contact as a small parameter, approximate analytical solutions have been found, which allow one to define the key characteristics of impact process.

Capture optimization for composite images

A composite image is an image created by combining portions of multiple separately-captured images. Stitching of captures of tiled portions of a larger scene can be used to produce a single composite image (a panorama) with a wider view angle and higher total resolution. Image stacking is a different type of compositing, in which the scene is not changing significantly across captures, but camera parameters might be systematically varied. Focus stacking can extend the depth of field, aperture stacking can implement apodization shaping the out-of-focus point spread function, and noise and motion reduction can be accomplished even using the same camera parameters for each capture to be stacked. These and other compositing methods are well known and commonly used, but the same fixed pattern is commonly used for ordering of captures and choice of capture parameters. This paper examines the problem of static, pseudo-static, or dynamic determination of the optimal capture parameters and ordering.

Математична модель руху сипкого матеріалу у вібраційному сепараторі

Aim. The aim is to construct the mathematical model of the movement of loose material in a vibrating separator. Method. The calculation scheme of the vibration separator with two eccentric vibrators with an independent drive was built. Based on the scheme, it is assumed that the vibration separator performs only vertical oscillations in the plane of rotation of the eccentric vibrators. A cylindrical vibrating separator was considered, due to the possibility of transmitting vibrations of greater force to the sieve and significantly more efficient use of the entire screening surface. A mathematical model of the motion of an arbitrary point of motion of the medium in the vibrating separator was also constructed. The methods of nonlinear mechanics and Lagrange equation of the second kind are used to build a mathematical model. The basis of the mathematical model of any movement of a point in the working capacity of the vibration separator is the law of movement of the centre of mass. Results. The obtained mathematical model makes it possible to investigate the influence of the parameters of the vibrating separator and the characteristics of the loose material on the efficiency and productivity of the separation process. The differential equations describing the movement of the geometric centre of the separator container and the equations describing the movement of an arbitrary point of the layer of loose material make it possible to construct the absolute trajectory of its movement and determine the effect of a change in the amplitude-frequency characteristics of the vibrating separator on the natural frequency of the loose material. Also, when substituting the necessary specified parameters of the separator into the mathematical model, we get equations for determining the amplitude and frequency of any point of the working container. Scientific novelty. Using the methods of nonlinear mechanics, a mathematical model of the movement of an arbitrary point in a vibrating separator was built, taking into account the parameters of the vibrating separator and the loose material. Practical significance. This mathematical model can be used in the future in the study of dynamic processes during vibration transportation and processing.

Theory of Harmonic Oscillations: A Gross Error in Physics

Theory of Harmonic Oscillations: A Gross Error in Physics

A Method of Investigating the Phenomenon of Bifurcation Memory in the Dynamics of River Vessels

The phenomenon of “bifurcation memory”, which can be detected during the steering of river vessels, is considered by researchers with the questions of equilibrium point’s bifurcations. It was noticed that in some dynamic systems during saddle-node bifurcation, areas are formed on the phase plane (so-called “phase spot”), passing through which the phase velocity of the representative point decreases. A decrease in phase velocity (e. g. during the steering of river vessel) can cause navigation accidents during shallow waters navigation. In order to improve sailing safety, it is necessary to investigate topological features of phase spots under any possible environmental conditions and steering angle values. In this paper, we propose a new method that makes it easy to get information about the localization of regions with decreased phase velocity. We gained the results related to the topology of areas of different types of motion (accelerated or decelerated) of representative point. In addition, the paper presents the process of evolution of these regions, according to the change of steering angles, as well as before and after the bifurcation. The new method, offered in the article, is more accurate for determining the boundaries of the areas compared to the methods of Feigin and Chirkova. This will allow us to make more correct predictions of changes in the dynamics of the object. The practical implication of the suggested method is that by using it, we can get information about the location of areas with different types of motion of the representative point on the phase plane for different values of steering angle and environmental conditions. This information can be used in the control algorithm of the driving object, for example, in order to predict the decreasing of phase velocities.