Analytical Mechanics Research Articles

Об одной задаче управления квадрокоптером с заданными промежуточными значениями разных частей координат

The work is devoted to the issues of mathematical modeling of the spatial motion of a quadcopter and the construction of program control laws that ensure flight with the values of part of the coordinates of the phase vector specified at intermediate times. A structural diagram of a quadcopter with four propeller engines is used, which allows for movement in space, vertical takeoff and landing. Based on the laws of theoretical mechanics, a system of differential equations is obtained that describes the spatial motion of such a quadcopter. For a linearized mathematical model of quadcopter motion, the problem of constructing program control laws with given initial and final values of the phase vector, as well as the values of part of the coordinates of the phase vector at two intermediate moments of time, has been solved. A necessary and sufficient condition for the existence of program control is obtained and the corresponding movement of the quadcopter is described. Control functions and corresponding phase trajectories of motion are constructed. To illustrate the results obtained, for specific initial, final and intermediate values, explicit expressions of the program control function, program motion are obtained and the corresponding graphs are constructed.

Exploring and Evaluating a Blended Learning Model of Theoretical Mechanics under the Ideological and Political Education

Exploring and Evaluating a Blended Learning Model of Theoretical Mechanics under the Ideological and Political Education

Construction and Practice of the Case Base of Theoretical Mechanics Course in Military Colleges Based on Sports Events

Construction and Practice of the Case Base of Theoretical Mechanics Course in Military Colleges Based on Sports Events

К моделированию задачи осаждения твердой частицы в вязкой несжимаемой жидкости методом гидродинамики сглаженных частиц (SPH)

In this paper was formulates the settling velocity determining problem for a single particle. To solve it, an original version of the smoothed particle method (SPH) is proposed where settling particle affects on surrounding fluid particles movement. Herewith the calculation of forces acting on particle (except for inertial forces which takes attached mass effect) is performed according by analytical mechanics formulas for a material point. This mathematical formulation and calculation algorithm was verificated by using open source code «SPH_Lab2d». Dependences for the particle settling velocity on its diameter are obtained for various cases of fluid volume discretization. The results demonstrate a good conformance this property to values, that determined by the experimental data and known phenomenological dependences for quartz sand.

Восприятие естественной асимметричности знакомых и незнакомых лиц

Background. Despite the abundance of human face recognition models and research carried out in this area over the past half-century, there are still open questions about the uniqueness of the facial perception processes and about the oneness or difference of the mechanisms of perception of familiar and unfamiliar faces. Objective. Research into the mechanisms of perception of (a)symmetry of familiar and unfamiliar faces. Study Participants. 34 people participated in the study: 25 classmates (11 female and 14 male, Мage = 16, SD = 0,49) and 9 teachers (6 female and 3 male, Мage = 33, SD = 8,71). Methods. Methods of inversion and horizontal mirroring of face images were used to compare the mechanisms of perception of facial symmetry in familiar and unfamiliar faces. Mirroring allowed to change the face itself without violating its recognition and maintaining the overall degree of its (a)symmetry. The inversion impaired the perception of the facial configuration. Study participants assessed the degree of asymmetry in the images of familiar (photographs of classmates) and unfamiliar faces in four presentation conditions: original / mirrored faces presented upright / inverted. Results. The study results demonstrated that when presented upright, familiar mirrored faces are perceived as more asymmetrical than the original ones; no difference was revealed for unfamiliar faces. When inverting images, the ratings of the original and mirrored versions of the faces do not differ significantly for both familiar and unfamiliar faces. A small inversion effect was found in the ratings of original familiar faces: inverted familiar faces were rated as more asymmetrical than upright ones. Conclusions. The study results generally support the hypothesis that the mechanisms of perception of (a)symmetry in familiar and unfamiliar faces differ. Furthermore, there is reason to consider the assessment of a face (a)symmetry as involving not only configural, but also analytical mechanisms of its perception.

Seismic performance of confined prestressed hollow core wall panels part II: Numerical simulation and analysis

In Part I of this research, confined prestressed hollow core wall structures were proposed and experimental tests of 19 specimens were conducted to study its mechanical behaviors. In this part, a detailed finite element model was developed in ANSYS to provide a tool for further investigating the seismic behaviors of confined prestressed hollow core wall structures. Contact elements were applied to simulate the interaction between material interfaces. Techniques in ANSYS including coupling of degrees of freedom (CP) of overlapped nodes and deactivation of concrete elements (EKILL) were adopted, along with restart analysis (REST) to simulate nonlinear mechanical behaviors of the structural system. The developed modeling method was verified by the experimental test results and was shown to accurately predict the global and local behaviors such as failure modes and load bearing capacities of precast hollow core walls. Parametric analysis on shear span ratio, axial load ratio, rigidity of floor systems as well as strength of vertical wall-wall joints was conducted, and relevant design recommendations were provided for prestressed hollow core wall structures. Results show that for a ductile prestressed hollow core wall structure, the axial load ratio is recommended to be smaller than 0.06 and the story number less than 5. Influence of rigidity of floor systems requires further study with dynamic tests, but low-strength vertical wall-wall joint is highly recommended for this system. Two analytical mechanisms that are shear-flexural mechanism and truss mechanism were proposed for calculation of load bearing capacities. These two mechanisms provide good predictions for an upper bound and a lower bound for load bearing capacities of prestressed hollow core walls, respectively. From Part I and II of this research, the mechanical behaviors of prestressed hollow core wall structures are verified experimentally, numerically, and theoretically, and it is concluded that they can be used as a potential choice for low-rise buildings in rural areas.

Regarding the issue of aquaplaning and the interaction of a car tire with the road surface through a layer of water

Problem. The process of interaction of a pneumatic tire of a car wheel with the surface of the road surface, which is covered with a layer of water, affects the safety of the vehicle movement, therefore, the assessment of the effect of aquaplaning when writing the conclusions of the auto technical examination is an actual direction of research. The study of the effect of aquaplaning will allow forensic experts and specialists in the automotive industry to make an objective analysis and form non-subjective conclusions. Goal. The purpose of the work is to determine the design parameters and operational features of the pneumatic tire, as well as the speed of the vehicle on the process of interaction of the car wheel tire with the surface of the road coating, which is covered with a layer of water. Methodology. The approaches adopted in the work to solve the set goals are based on the theory of aquaplaning, the theory of the interaction of the pneumatic tire with the road surface, the theory of the vehicle and the laws of theoretical mechanics. Results. The obtained results of the research in the form of an analysis make it possible to assess the impact of the aquaplaning effect of a pneumatic tire on road safety. It was established that the thickness of the water layer affects the conditions for meeting the requirements established by the traffic rules, since the decrease in the height of the tire tread pattern leads to unstable contact of the tire with the road surface. Originality. The results of the study provided an opportunity to get an idea of the influence of the design parameters of tires on road safety in terms of forming the conclusions of the motor-technical examination. Practical value. The obtained results can be recommended to forensic experts when writing expert opinions and for expert research

Didactic Film in Computer-Aided Education of People with Visual and Hearing Impairments

Artificial intelligence mechanisms enable fast speech transcription and printed text recognition (Optical Character Recognition). Speech synthesizers for reading any digital documents have also become popular. In most cases, these are free solutions that can significantly support the education and functioning of people with visual and hearing impairments. Unfortunately, the knowledge of parents and caregivers on this subject is insufficient. Bearing this in mind, a suitable series of educational videos was prepared and published on YouTube. Subsequently, research was conducted to determine whether and to what extent there is a demand for video materials on this topic. For this purpose, the method of implicit observation was used, carried out using YouTube Analytics mechanisms. Its results are available in the form of numerous reports and summaries. Based on the collected materials, a considerable interest in the study was found. It was possible to determine which issues are of particular interest to the recipients. The obtained results will allow for further development of the educational offer.

High-temperature superconductivity mechanism and an alternative theoretical model of Maxwell’s classical electromagnetism theory

In the 21st century, understanding the mechanism of high-temperature superconductivity has emerged as a pinnacle achievement in condensed matter physics, capturing the lifelong interest of numerous physicists. This paper endeavors to offer a theoretical elucidation for this mechanism, advancing the broader field of physics. Recognizing that high-temperature superconductivity is an aspect of condensed matter physics — underpinned by Maxwell’s classical electromagnetic theory — we turn to theoretical mechanics and field theory, which are foundational perspectives in the contemporary scientific era. By framing Maxwell’s classical electromagnetic theory within the context of theoretical mechanics and field theory, this paper not only sheds light on the mechanism of high-temperature superconductivity but also recasts Maxwell’s theory within a purer theoretical mechanics and field theory domain. This represents a paradigmatic shift and cognitive transformation in physics. Furthermore, leveraging this theoretical mechanics and field theory interpretation of electromagnetic phenomena, we discern that electromagnetic phenomena can be more aptly explained without resorting to the concepts of charges and electric fields, leading to a reinterpretation of Coulomb’s law. We propose that protons and electrons might exist as entities devoid of charge-specific attributes and negate the possibility of a strongly correlated particle system within them.

Research on virtual electronic experimental teaching of theoretical mechanics in engineering departments

This study aims to investigate the application and effectiveness of virtual electronic experiments in engineering theoretical mechanics education. By reviewing the current research status both domestically and internationally, the concept and advantages of virtual experiment teaching are analyzed. In addition, the interface and operational process of the virtual electronic experiment are designed and applied to engineering theoretical mechanics classrooms. Through analyzing students' experimental results and learning feedback, the teaching effect is evaluated and improvement strategies are proposed. The aim is to promote the development of virtual electronic experiment teaching in engineering theoretical mechanics, improve teaching effectiveness, and enhance students' learning experience.

On the Content of the Notion «Customs Payments» and the Customs System

The financial stability of budget revenues is the key to the successful functioning of the state. Therefore, each country seeks to offset the influence of various factors on the financial stability of its income. For the most effective management of public financial resources, it is important to know the theoretical mechanics of the actions of the main sources of income (tax and non-tax). Customs payments relate to both tax and non-tax revenues of the federal budget. The article analyzes the definitions of the concept of «customs payments» presented in scientific studies, summarizes the available approaches to its definition. The main signs of customs payments have been identified. Since customs payments are received in the revenues of the federal budget due to the operation of the customs taxation system, the customs system is considered. The main elements of the customs system are proposed. The functions of the customs system are defined. The tools of the customs authorities performance are described, with the help of which the functions of the customs system are implemented.

Integrated optimization design and motion control of multi-configuration unmanned metamorphic vehicle

An unmanned metamorphic vehicle is a new deformable robot that can transform its configuration according to different road conditions in order to realize wheeled driving or legged walking. This paper proposes a method of multi-objective integrated optimization design based on the motion control of unmanned metamorphic vehicle. The aim of this method is to improve the stability and reduce energy consumption of multi-configuration motion. The vehicle state configuration and the humanoid state walking performance were designed. The kinematic model of reconfiguration and humanoid walking was established from screw theory, while the Lagrangian dynamics model for reconfiguration and humanoid walking using analytical mechanics. Reconfiguration and gait planning were carried out for an unmanned metamorphic vehicle, and a sliding mode controller was designed for position feedback control of the zero moment point in order to improve the stability of reconfiguration and walking. In order to improve the kinematic performance of an unmanned metamorphic vehicle under multiconfiguration, the NSGA-II intelligent optimization algorithm was used to optimize the multi-objective integrated design of the structural parameters, posture parameters, and control parameters of the sliding mode controller of the system. The simulation and test results showed that the integrated design performs higher reconfiguration stability, lower energy consumption, and higher control quality than the sequential design and pre-optimization under the reconfiguration condition; in the vehicle state, the transient steering stability and the steady-state steering stability of the system during driving are significantly improved; in the humanoid state, the energy consumption of the striding process and the movement of the center of mass to the single-legged support region in the walking process is reduced and the walking stability is improved, thus is more conducive to walking.

Experimental study on failure characteristics and rheological properties of pillar-like rock samples with different shapes

The stability of coal pillar is extremely important to the control of rock strata movement and surface subsidence. It is of great significance for mining design to analyze the stability and failure characteristics of coal and rock pillars left after mining and to study the failure characteristics and rheological properties of coal and rock with different shapes. In this paper, based on uniaxial compression and rheological tests on rock samples, the rheological properties of rock samples with different shapes were discussed by using the nonlinear theoretical mechanics and damage theory, and the rheological mechanical characteristics of coarse yellow sandstone samples under the action of different free surface areas and the same loading contact area were investigated by means of experimental research, theoretical analysis and numerical simulation. The following conclusions were drawn: the failure characteristics and dynamic change process of rock samples with different shapes under the same loading contact area are obtained by uniaxial compression test and multi-stage rheological loading. The uniaxial compressive strengths of rock samples with the same loading contact surface area and different free surface areas are inversely proportional to their free surface areas. For the round sample, the stress level in the rheological test is obviously lower than the instantaneous peak uniaxial compression strength, while for the other samples, the stress level in the rheological test is close to the instantaneous peak uniaxial compression strength. For rock all these samples, both the ratio of steady-state rheological time to final failure time and the deformation degree decrease with the increase of free surface area.

Modeling cable-pulley deployment systems of transformable rod structures

The aim of this article is to develop a simplified method for modeling cable-pulley deployment systems of rod structures based on the calculation of cable tensions and nodal driving forces with account for friction and other features of the system. Methods of theoretical mechanics, multibody dynamics, numerical integration of differential equations, and computer modeling were used during the research. The task of developing a simplified approach to modeling cable-pulley deployment systems for rod structures is considered. It is proposed to determine nodal driving forces by calculating cable tensions with account for friction and other features of the cable-pulley system, cables, and pulleys. To develop a model of cable-pulley deployment system, a rod system was chosen as the research object, which represents two sections of the transformable support truss of a reflector. Each section consists of diagonal and horizontal rods with tubular cross-sections. The sections are interconnected by hinge units. The structure is deployed using an upper and a lower cable, which pass through pulleys and are tensioned by an electric motor. The deploying forces are implemented by transferring the cable tension forces to the structure due to static friction and pressure between the cables and the pulleys. For further implementation of the model in an open-source software package, some simplifications were made due to the complexity of the design. A simplified method was developed for nodal driving force calculation in simulating rod structure deployment with the help of cables. The tensions, elongations, slacks, and neutral length of the cables and the forces transmitted from the cables to the pulleys were calculated as a function of time. Using them, the deployment of a rod structure was simulated for a constant cable speed. The results make it possible to control the rod system deployment time and rate depending on the characteristics and tension forces of the cables. The proposed approach is implemented using open-source software, and it provides modeling flexibility and reduces the model development and run time.

Comparison of different blade shapes of translatory moving soil tillage tools

BACKGROUND: The efficiency and energy capacity of translatory moving soil tillage tools are largely determined by the parameters of their blades. If the parameters do not match the specified operating conditions, clogging the working tools with plant residues becomes possible, and a less energy-consuming type of soil cutting — sliding — may be replaced with a more energy-consuming type — chopping cutting. In this regard, it is very important for scientists engaged in improving the designs of translatory moving soil tillage tools to have a method for assessing the shape of the blades.
 AIMS: Development of a method for comparative assessment of various blade shapes of translatory moving soil tillage tools.
 METHODS: For this study, the fundamentals of agricultural mechanics, higher mathematics, and theoretical mechanics were used. The objects of the study were the blades of various soil tillage tools, providing with sliding cutting of soil. The study was conducted at the Gorsky State Agrarian University in the period from 2022 to 2023. The calculations results were compared with the materials of the corresponding standards.
 RESULTS: The method that helps to determine the relative values and directions of the resultant force of soil cutting resistance with a translatory moving blade of a soil tillage tool having a diverse shape has been developed. An example of the application of the method for assessment the effectiveness of blades of a garden tool, the cutting part of which is described by the equation of a straight line, a circle, an Archimedes spiral, a logarithmic spiral, as well as an example of assessment of a curved blade for soil tillage tools of cultivators are given.
 CONCLUSIONS: The proposed method for assessing the influence of the shape of a translatory moving flat blade of the soil tillage tools on the value of soil cutting resistance forces is easy to use and can be the basis for further development in order to analyze the effectiveness of the knives’ blade shape performing a plane-parallel movement.

Pemetaan Pemahaman Konsep Analisis Pengukuran Fisika dan Mekanika Analitik Pada Mahasiswa Program Studi Pendidikan Fisika Tahun Pertama

Physics education study program students should have a high level of understanding of physics concepts. However, in reality the level of understanding of physics concepts for students in physics education study programs is still low. The aim of this research is to determine the distribution of students' level of conceptual understanding in the physics education study program in their first year. The research method used by the author is quantitative descriptive. This research was conducted on 43 Class C Physics Education study program students Class C of 2022 in their first year studying at Yogyakarta State University. The results of this research show that the level of conceptual understanding of Physics Education study program students in the Physics Measurement Analysis (APF) and Analytical Mechanics courses is very different in their first year of study with the average UAS score in the APF course being 2.89 and in the Analytical Mechanics course of 9.04. Therefore, alternatives are needed to improve and equalize student understanding of concepts in courses in the Physics Education study program, one of which is by improving the quality of teaching and organization in the learning process, increasing student involvement in learning physics, using effective learning methods to increase understanding. physics concepts, as well as increasing collaboration between students, lecturers and institutions in increasing understanding of physics concepts.

Formarea noțiunilor de momente de inerție ale sistemelor mecanice în cadrul mecanicii teoretice

Mechanics is the first branch of physics studied in university education. In this branch, a series of concepts and notions are formed, which are subsequently used in other branches. A good understanding of mechanics can enable students to better grasp other chapters of physics. Among the fundamental concepts of physics is the inertia of a body. The measure of the inertia of a body in its translational motion is the inertial mass. This physical quantity is encountered quite often. Much less frequently used are the notions of moments of inertia, which describe the inertia of a body in rotational motion. Determining these moments is necessary for describing rotational movements. The material presented in this article can serve as a support for students studying the course of Theoretical Mechanics.

Numerical simulation of an external ballistic problem using analytical approach and atmosphere flow visualization by finite element method

Purpose. Analysis of the dynamic characteristics of the cargo in the presence of the speed of its carrier, taking into account the influence of the external environment and the determination of factors that affect the operational characteristics and parameters for the dynamic system control. Methodology. An approximate analytical approach to solving the nonlinear problem of external ballistics of a system with time-dependent parameters, which is implemented using the asymptotic perturbation method, and a numerical algorithm for modeling a dynamic process using a 3D software complex and the finite element method, which allows to visualize the nature of the flow around the object under wind load conditions. Findings. An analytical approach to solving the nonlinear problem of external ballistics of a system with time-varying parameters is proposed, as well as a numerical model, solution and visualization of a dynamic process that can be applied in problems of mathematical physics and engineering calculations. Originality. The use of an approximate analytical approach to solving the nonlinear problem of external ballistics, which includes a system of time-varying parameters, is a significant innovative step. For the first time, a three-dimensional distribution of the free fall parameters under atmospheric conditions was obtained depending on the time of free fall under the condition of an initial velocity different from zero. Obtaining the characteristics of the distribution, taking into account the aerodynamic quality of the object, made it possible to adapt the methods of analytical mechanics and differential equations with variable coefficients to the solution of the applied problem. The obtained characteristic three-dimensional surface allows to perform a study of the aerodynamic quality of the object under study using numerical methods and to visualize dynamic processes in three-dimensional space in order to obtain a qualitative picture of the perturbation of the object by the air flow. This integrated approach to the study of ballistic characteristics of cargo forms the scientific principle to perform engineering calculations to solve the problem of controlling dynamic systems. Practical value. An approximate analytical approach and a calculation model of the dynamic process of a mechatronic unmanned system make it possible to increase its efficiency in the presence of an initial speed and ensure the accuracy of the application of ballistic cargo delivery systems in real operating conditions.

Quaternion and Biquaternion Methods and Regular Models of Analytical Mechanics (Review)

Quaternion and Biquaternion Methods and Regular Models of Analytical Mechanics (Review)

Contemporary philosophical works of the mind and the productivity of contemporary fine art

This research deals with the conceptual analysis of the mind in its contemporary philosophical form, as the philosophy of mind has increasingly grown through scientific practice that sought to analyze concepts and experimental issues related to the structure and function of the brain. This created a space for distinguishing between different types of mental phenomena from each other, and research About the characteristics that are necessary and sufficient to determine the mentality, which is seen to have the ability to determine mental specificity. Therefore, the research will focus on the most important of those concepts that have been philosophically worked on in defining the concept of the mind. Accordingly, the structure of the research was established within four chapters. The first chapter contained (the framework General) on the research problem, which the researcher summarized by asking (How do the philosophical works of the mind contribute to the production of contemporary art?), and the goal of the research is (to identify the concepts of contemporary philosophy of mind and activate them as analytical mechanisms for contemporary plastic work). As for the second chapter (theoretical framework), it included Two sections: The first section dealt with: (The mind in light of its contemporary problems), and the second section dealt with: (The mind and the works of contemporary philosophers). As for the third chapter (Research procedures), it included defining the research community. (3) artistic works were selected, and the researcher analyzed them as a sample. For the community, while the fourth chapter contained the results and conclusions.