Principles Of Classical Mechanics Research Articles

An online teaching learning sequence with home experiments and simulations on relativity of motion and the equivalence principle in classical mechanics

We designed a teaching-learning sequence on relative motion in classical mechanics, based on the fundamental design principle of highlighting those conceptual elements which could be valuable in the future learning of special and general relativity In order to highlight selected key concepts and motivate students in their exploration, we used a series of experiments based on video analysis and interactive simulations, which can be modified on the fly by the students. In this study, we introduce a pilot investigation focused on testing the instructional sequence, and we provide initial outcomes regarding students’ understanding. The sequence of activities was tested with a group of 24 undergraduate students in an online laboratory course during the COVID-19 pandemic.

The tendency of the schematic structure to maintain stability can be interpreted as mental inertia.

This paper incorporates schematic concepts related to mental inertia and provides an avenue for interpreting psychology using the principles of classical mechanics. Schemas find wide application in diverse fields, ranging from ergonomics to psychotherapy. Nonetheless, it is crucial to incorporate schemas themselves into a more unified and comprehensive theoretical framework. Drawing upon the free energy principle (FEP) and the second law of thermodynamics, it is evident that humans possess a natural inclination to construct and maintain consistent cognitive structures. This characteristic contributes to the stability of schemas within a defined range. The particular scope of the model is closely intertwined with its structure, leading to variations among individuals in diverse environments. The coherence of the schema within a defined range can be perceived as the magnitude of mental inertia. This psychological analogy emphasizes the importance of considering the influences exerted by the external environment and their effects on mental inertia when predicting the human mind and behavior.

Applying the Action Principle of Classical Mechanics to the Thermodynamics of the Troposphere

Advances in applied mechanics have facilitated a better understanding of the recycling of heat and work in the troposphere. This goal is important to meet practical needs for better management of climate science. Achieving this objective may require the application of quantum principles in action mechanics, recently employed to analyze the reversible thermodynamics of Carnot’s heat engine cycle. The testable proposals suggested here seek to solve several problems including (i) the phenomena of decreasing temperature and molecular entropy but increasing Gibbs energy with altitude in the troposphere; (ii) a reversible system storing thermal energy to drive vortical wind flow in anticyclones while frictionally warming the Earth’s surface by heat release from turbulence; (iii) vortical generation of electrical power from translational momentum in airflow in wind farms; and (iv) vortical energy in the destructive power of tropical cyclones. The scalar property of molecular action (@t ≡ ∫mvds, J-sec) is used to show how equilibrium temperatures are achieved from statistical equality of mechanical torques (mv2 or mr2ω2); these are exerted by Gibbs field quanta for each kind of gas phase molecule as rates of translational action (d@t/dt ≡ ∫mr2ωdϕ/dt ≡ mv2). These torques result from the impulsive density of resonant quantum or Gibbs fields with molecules, configuring the trajectories of gas molecules while balancing molecular pressure against the density of field energy (J/m3). Gibbs energy fields contain no resonant quanta at zero Kelvin, with this chemical potential diminishing in magnitude as the translational action of vapor molecules and quantum field energy content increases with temperature. These cases distinguish symmetrically between causal fields of impulsive quanta (Σhν) that energize the action of matter and the resultant kinetic torques of molecular mechanics (mv2). The quanta of these different fields display mean wavelengths from 10−4 m to 1012 m, with radial mechanical advantages many orders of magnitude greater than the corresponding translational actions, though with mean quantum frequencies (v) similar to those of radial Brownian movement for independent particles (ω). Widespread neglect of the Gibbs field energy component of natural systems may be preventing advances in tropospheric mechanics. A better understanding of these vortical Gibbs energy fields as thermodynamically reversible reservoirs for heat can help optimize work processes on Earth, delaying the achievement of maximum entropy production from short-wave solar radiation being converted to outgoing long-wave radiation to space. This understanding may improve strategies for management of global changes in climate.

Basic Mechanics of Lagrange and Hamilton as Reference for STEM Students

This paper discusses the use of Lagrangian and Hamiltonian dynamics as alternative approaches for understanding the motion of objects in classical mechanics. These approaches, which are based on different mathematical techniques, can provide a deeper understanding of the principles of classical mechanics and the motion of objects, but may not be covered in high school physics curricula or undergraduate STEM courses. The review paper approach is used to combine information from a variety of sources, and the material is conceptualized to aid reader understanding. These advanced topics may be of interest to advanced high school students who are interested in exploring topics beyond the high school physics curriculum, and can be studied independently by those with a strong foundation in classical mechanics and familiarity with advanced mathematical concepts.

Study of the kinematic characteristics of the motion of the car from the top to the design point

Objective: to describe the speed of the car at each section of the descent part of the hump using the principles of classical mechanics; to get a generalized model of the speed of movement of the car at the estimated point of the hump, which allows speeding up the process of building graphs and changing the kinematic characteristics of the car’s movement; to present the change in the instantaneous speed of movement of the car along the entire length of the descent part of the hump in the form of a graph of the step function. The resulting model allows quickly analyzing the mode of shunting cars from the humps, the combination of power of brake positions and improve the accuracy of determining the permissible velocity of impact of cars in the sorting yards. This paper is the most important step for solving a promising task of designing an automated system for calculating the dynamic characteristics of a car in a hump yard.

Studies on the Performance of Equal Strength Cantilever Beam-Based FBG Acceleration Sensors

Based on the principle of FBG sensing and classical mechanics model of acceleration,the fundamental frequency and acceleration sensitivity coefficient of the fiber Bragg grating (FBG) acceleration sensor are theoretically analyzed in this study. An equal strength cantilever beam-based FBG acceleration sensor was designed based on the vibration frequency of conventional bridges and carried out experimental research. The results show that the fundamental frequency of the sensor increases when the cantilever beam thickness increases, while the sensitivity coefficient decreases. However, when the block mass increased, the fundamental frequency decreased in contrast to an elevated sensitivity coefficient. The experimental findings were found to be in line with the theoretical hypothesis. The sensors had good signal response performance and anti-transverse interference performance. In order to solve the problem of low sensitivity coefficient of sensor, the sensor was optimized and tested following the plane section assumption principle of classical mechanics. The result shows that the fundamental frequency of the optimized sensor remains unchanged, the sensitivity coefficient is increased by 2.6 times. The research provided an FBG acceleration sensor with suitable fundamental frequency, high sensitivity and other excellent performance for bridge monitoring.

A dedicated mental resource for intuitive physics

In daily life, we continually evaluate the physical structure of our environments to plan our decisions and actions – e.g., packing a grocery bag in a way that will not crush the items at the bottom or building a sandcastle that does not topple. The physical scenarios that we regularly encounter can vary dramatically in their contents, yet we can intuitively understand their underlying physical structure and predict their future behavior. How? We might draw on domain-general mental resources to reason about physical behavior in an ad-hoc fashion, but an intriguing alternative is that we possess a dedicated set of mental resources for physical inference, allowing us to flexibly apply the principles of classical mechanics to any scene we encounter. Here, we tested for a dedicated mental resource for intuitive physics by evaluating individual differences in performance on a battery of intuitive physics tasks. We presented participants with five tasks, spanning a broad range of physical scenarios: 1) stability judgments of block towers; 2) trajectory predictions for bouncing pucks; 3) mass inferences from observed collisions; 4) predictions of collision outcomes based on objects’ masses, velocities, and geometry; and 5) mass inferences from observation of people’s interactions with the objects of interest. A factor analysis revealed that this collection of tasks draws on a common underlying mental resource that is distinct from other facets of cognition such as spatial reasoning and working memory. Further, we found that a reduced task battery (lasting ~15 minutes) captured ~90% of the reliable variance of the full battery, providing a measure that can be efficiently applied in a variety of contexts to evaluate intuitive physics abilities (e.g., in clinical populations, in longitudinal studies, or in training studies). Our findings point to a specialized mental resource for intuitive physics that is distinct from other cognitive domains.

FOUNDATIONS OF CLASSICAL PHYSICS AND CHRISTIAN THEOLOGY

The article discusses the twists and turns of the history of formulation of the inertia principle of classical mechanics and their dependence on the theological concepts of their time. The points of view on the movement and inertia of Aristotle, the authors of late scholasticism, Galileo, Descartes and Newton are subject to discussion. The fundamental concepts of classical mechanics are also compared with the tradition of Protestant theology.

Reverse scaling of a bonded-sphere DEM model: Formulation and application to lignocellulosic biomass microstructures

We explore scaling laws for adapting a bonded-sphere discrete element method (BS-DEM) model developed for woody structural mechanics at the millimeter scale to model the mechanics of realistic lignocellulosic biomass microstructures. Two scaling approaches, i.e., the reverse coarse graining (RCG) and equivalent bulk behavior (EBB), are proposed based on the classical mechanics principles and assessed in the single-particle compression and rectangular cuboid block tension tests. The EBB approach is recommended for BS-DEM models with general 3D geometries and is applied to simulate the microindentation test on a realistic microscale pinewood specimen. Simulations are performed to elucidate the impact of specimen thickness and loading position on the specimen’s force–deformation behavior. The range of Young’s modulus obtained from the calibrated BS-DEM simulations can match the experimental measurements. This is the first-of-its-kind study that has explored scale-bridging modeling approaches in biomass micromechanics and has proposed solutions based on BS-DEM models in the microscale. • First-of-its-kind reverse scaling laws for bonded-sphere discrete element model. • Reverse coarse graining applicable for maintaining equivalent single-bond behavior. • Equivalent bulk behavior recommended for BS-DEM model with general 3D geometries. • Impact of specimen thickness and loading position on material response analyzed. • Young’s moduli from simulations using EBB can match the experimental measurements.

On the effect of the central body small deformations on its satellite trajectory in the problem of the two‐body gravitational interaction

AbstractThe problem of the two‐body gravitational interaction has been solved numerically based on the classical mechanics principles. One of the bodies is a deformable three‐axis ellipsoid (central body) and the other is a material point (satellite). The relationship of the angular discrepancy between the calculated and actual positions of the satellite pericenter with central body's gravity anomaly has been established.

On Hierarchical Applications of Finite Element Methods and Classical Applied Mechanics Approaches for Complex Structures

In this paper, hierarchical studies based on both analytical and computational approaches have been employed to validate and improve current structural designs of mud holding tanks for hydraulic fracturing in petroleum industries. Through detailed comparisons at different levels of approximations for both real world complex structural design problem and a simplified stiffened plate with extreme geometrical aspect ratios, proper design procedures have been reiterated and validated. It is highly recommended that low-dimensional structures with emphasis on classical mechanics principles should be considered before full-fledged three-dimensional computational analyses. Both Castigliano’s Theorems and Galerkin methods are utilized along with simulation packages such as ADINA and Solidworks. The hierarchical approximation procedures reemphasize important subjects such as planes and shells, strength of materials, structural mechanics, asymptotic and perturbation analysis no longer required in some engineering programs, yet often necessary for the study of complex three-dimensional structural systems.

A Mathematical Model for Determining the Specific Structural Weight of a Tillage Implement

The authors have shown that the tillage specific constructive weight affects the working width and penetration ability. In order to increase the working width of the tillage implement, and therefore its performance and economic efficiency as well as its penetration ability, it is preferable to minimize the value of this indicator. It is taken into account that the implement specific structural weight will depend on the actual number of working tools and frame elements per unit of the working width. (Research purpose) The aim of the work is to develop a mathematical model to determine the minimum allowable and actual specific structural weight depending on the tillage implement operating conditions and its structural design and technological scheme. (Materials and methods) The research methodology is based on mathematical modeling, abstraction, analysis, synthesis, and principles of classical mechanics. (Results and discussion) The proposed mathematical model for determining the minimum allowable and actual specific structural weight was developed. The model takes into account the physical and mechanical characteristics of the cultivated soil, the number of working bodies and frame elements per unit of the tillage implement working width. It was found out that an increase in the working width makes it possible to reduce the implement actual specific structural weight, all other things being equal. It was proposed to use the mathematical model for designing tillage tools, carrying out force calculations and comparative assessment of metal consumption, depending on the installation and location of working bodies with different working widths. (Conclusions) It was found out that with the soil ultimate compressive strength of 100,000 pascal, the implement minimum allowable structural weight should be 334 kilograms per meter to ensure the tillage tool penetration to a given depth. Under the considered conditions, the implement actual specific structural weight will have a minimum value at the working width of 0.7 and 0.8 meters – 375 kilograms per meter and 335 kilograms per meter, respectively.

An analysis on Quantum mechanical Stability of Regular Polygons on a Point Base Using Heisenberg Uncertainty Principle

Abstract: It is a well-known fact in physics that classical mechanics describes the macro-world, and quantum mechanics describes the atomic and sub-atomic world. However, principles of quantum mechanics, such as Heisenberg’s Uncertainty Principle, can create visible real-life effects. One of the most commonly known of those effects is the stability problem, whereby a one-dimensional point base object in a gravity environment cannot remain stable beyond a time frame. This paper expands the stability question from 1- dimensional rod to 2-dimensional highly symmetrical structures, such as an even-sided polygon. Using principles of classical mechanics, and Heisenberg’s uncertainty principle, a stability equation is derived. The stability problem is discussed both quantitatively as well as qualitatively. Using the graphical analysis of the result, the relation between stability time and the number of sides of polygon is determined. In an environment with gravity forces only existing, it is determined that stability increases with the number of sides of a polygon. Using the equation to find results for circles, it was found that a circle has the highest degree of stability. These results and the numerical calculation can be utilized for architectural purposes and high-precision experiments. The result is also helpful for minimizing the perception that quantum mechanical effects have no visible effects other than in the atomic, and subatomic world. Keywords: Quantum mechanics, Heisenberg Uncertainty principle, degree of stability, polygon, the highest degree of stability

English

This new study on effects of gyroscope demonstrates the action on the spinning disc that the eight interrelated inertial torques system generated by its rotating masses. The physics behind this inertial torques manifest the action of the resistance and precession torques, which physics are described and explained. The latest research on the gyroscopic properties revealed the deactivation of the inertial torques that contradicts the principles of classical mechanics. Practical tests of the blocking of the gyroscope motion around one axis displays the deactivation of inertial torques acting around the axis of the load torque. In this condition, the gyroscope with one side support turns down under the action of its weight and frictional forces produced by the action of the precession torque and weight of the movable components. The precession torque is presented by the change in the angular momentum, while other inertial torques is deactivated. These phenomena present the new unknown gyroscopic effect that needs a deep study and explanation. This work considers the attempt to describe the physics of the deactivation of the gyroscopic inertial torques around two axes and the action of the precession torque in a case of the gyroscope motion around one axis. Key words: Gyroscope theory, inertial torque, deactivation of inertial torques

ДОСЛІДЖЕННЯ ЕНЕРГОВИТРАТ ТАРІЛЧАСТИХ ЖИВИЛЬНИКІВ ДЛЯ СИПКИХ МАТЕРІАЛІВ

Creation of mathematical models that allow determining the relationship between the design and technological parameters of the plate feeders and the energy consumption arising during their operation. Methodology. The work uses the classical mechanics principles, the contact interaction of solids theory and the mathematical modeling method. Findings. The paper considers the design and operation principle of a continuous plate feeder, defines its main design and technological parameters. The factors that create mechanical loads on the drive of the feeder plate are investigated. Mathematical models have been developed that make it possible to determine the moments of resistance and the power consumed by an electric motor during the equipment operation. The proposed models make it possible to determine the load on the drive in static and dynamic operation modes and take into account the design, technological parameters of the equipment and the bulk material physical and mechanical properties. The study results of the friction coefficients influence, the knife position and the force of its pressing on the plate surface, the plate rotation speed on the loads acting on the electric drive are presented. It has been found that the drive calculation is expedient for the mode in which the distance between the knife edge and the rotation axis of the plate is maximum, which corresponds to the operation at maximum load. It has been determined that a change in the feeder technological parameters (plate rotation speed, knife position) can lead to a change in the load on the electric drive by 86%, which must be taken into account when choosing a drive. Originality. Mathematical models of the continuous plate feeder operation have been developed, which make it possible to determine the relationship between the design and technological parameters of the plate feeders and energy consumption. Practical value. The results obtained make it possible to determine the load on the plate drive by the known design, technological parameters and bulk material physical and mechanical properties.

A variational perspective on the thermodynamics of non-isothermal reacting open systems

We make a review of the variational formulation of nonequilibrium thermodynamics as an extension of the Hamilton principle and the Lagrange-d’Alembert principle of classical mechanics. We then focus on the case of open systems that include the power exchange due to heat and matter transfer, with special emphasis on reacting systems which are very important in biological science.

ОЦІНКА СТІЙКОСТІ ПОКРІВЛІ У ВУГЛЕПОРОДНОМУ МАСИВІ, ЩО ВМІЩАЄ ВИРОБКИ ПРИ РОЗРОБЦІ КРУТИХ ВУГІЛЬНИХ ПЛАСТІВ

Purpose. Estimation of stability of a roof of a steep coal seam in the coal massif for maintenance of an operational condition of mine workings. Methods. To achieve this goal, analytical studies were performed using the basic principles of classical mechanics, the theory of elasticity and resistance of materials, when the roof of the coal seam was studied in the form of a model of a beam with a support. Results. As a result of the performed researches it is established that for an inclined single-girder beam with supports, at any regularity of distribution of loading on a surface the maximum deflection around the middle of span within (0,48 – 0,579) length of a beam is fixed. The value of the maximum deflection of the deformed load-bearing element depends on the angle of inclination and the ratio of the linear dimensions of the simulated beam. The curved axis is not perfectly symmetrical about the middle of the beam. The deviation from the symmetry depends on the linear dimensions of the model, the angle of inclination and is determined by the direction of the vector of total displacement of the beam. The deviation from the symmetry depends on the linear dimensions of the model, the angle of inclination and is determined by the direction of the vector of total displacement of the beam. The area in which the loss of stability of the load-bearing element is possible, occupies about 10% of the length of the inclined beam. In the presence of an asymmetrical deflection, to avoid loss of stability of the model, the placement of the system of supporting supports is advisable in this area of the beam. Scientific novelty. For the roof of a steep coal seam in its modeling in the form of an inclined single-girder beam with supports, when the external load is distributed on the surface naturally, the direction of the vector of complete displacement of the loaded model determines the contour of the curved axis of the deformed load-bearing element. Practical significance. The stability of the lateral rocks of the steep coal seam, which determines the operational condition of the mine workings in the coal massif, is provided by a system of supporting supports, the deformation characteristics of which are determined by the predicted deflection of the roof in the produced space. Keywords: stability, lateral rocks, coal massif, mining, deflection, supporting support.

First Principles of the Classical Mechanics and the Foundations of Statistical Mechanics on the Example of a Disordered Spin System

We study the classical multicomponent disordered 3D spin system taking into account the temperature of the medium in the framework of the model of nearest neighbors. The latter allows the 3D problem with a cubic lattice to reduce to the 1D Heisenberg spin glass problem with a random environment. Using the Hamilton equations of motion, a recurrent equation is obtained that connects three spins in successive nodes of 1D lattice, taking into account the influence of a random environment. This equation, together with the corresponding conditions of a local minimum energy in nodes, allows to construct node-by-node a stable spin chains and, accordingly, to calculate all parameters of statistical ensemble from the first principles of classical mechanics, without using any additional assumptions, in particular, the main axiom of statistical mechanics – the equiprobability of statistical states. Using the example of 1D Heisenberg spin glass model, the features of the new approach are studied in detail and the statistical mechanics of the system are constructed without using the standard representation of the partition function (PF).

Development of a stand for maintenance and repair of railway equipment units

The development of a stand for maintenance and repair of railway equipment units includes theoretical and practical research. Theoretical research is the basis for obtaining practical results. Special attention is paid to the calculations of critical components and parts. By means of the stand, cars, locomotives, electric locomotives and other rolling stock can be brought into working condition. The purpose of the work is to develop a stand for maintenance and repair of railway equipment units. The object of the study is the technological process of the stand for the maintenance and repair of railway equipment units. The scientific novelty of the work is: theoretical justification of the stand design parameters; design and technological scheme of the stand; optimal design and operating parameters of the stand; estimated performance indicators of the stand. The practical significance lies in the use of the stand on the repair sections of the railway, reducing the labor intensity of the work performed, ease of maintenance, and the lowest cost of manufacturing. Theoretical methods were based on the principles of classical mechanics, mathematical analysis, synthesis, modeling, etc. Experimental data processing was performed using the application programs “Compass-3D”, Statistica 6.0, MathCAD. Calculations of the metal structure for bending strength, welded joints, and bed clamps were performed. The calculation of the bending strength of the metal structure was performed and the maximum stresses were found to be within the permissible limits. The condition for the strength of the welded joint is met. The calculation of the bed clips showed that the condition of wear resistance is met.

From variational to bracket formulations in nonequilibrium thermodynamics of simple systems

A variational formulation for nonequilibrium thermodynamics was recently proposed in Gay-Balmaz and Yoshimura (2017a, 2017b) for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include irreversible processes. In this paper, we show that this variational formulation yields a constructive and systematic way to derive, from a unified perspective, several bracket formulations for nonequilibrium thermodynamics proposed earlier in the literature, such as the single generator bracket and the double generator bracket. In the case of a linear relation between the thermodynamic fluxes and the thermodynamic forces, the metriplectic or GENERIC bracket is recovered. We also show how the processes of reduction by symmetry can be applied to these brackets. In the reduced setting, we also consider the case in which the coadjoint orbits are preserved and explain the link with double bracket dissipation. A similar development has been presented for continuum systems in Eldred and Gay-Balmaz (2020) and applied to multicomponent fluids.