Laws Of Motion Research Articles

Income and Price Effects in Intertemporal Consumer Problems

Abstract We study income and price effects for intertemporal consumer problems with monetary and non-monetary dynamic constraints. We focus on short and long-run responses to a permanent change in income or price, and we characterize how such responses depend on the law of motion of non-monetary dynamic constraints and on time discounting. We provide a dynamic analog to the Slutsky equation, and we show the conditions under which the elasticity of demand to income or price is smaller in the long than in the short run, or even has opposite sign.

The Interaction of Shock Waves With Biological Tissue - Momentum Transfer, the Key for Tissue Stimulation and Fragmentation.

Shock waves in medicine have gained enormous importance and have spread since 1980, and the first kidney stone was successfully fragmented in a patient in Munich. Meanwhile, the spectrum of medical applications of shock waves ranges from powerful fragmentation of kidney stones to diverse indications such as wound healing, chronic pelvic pain, spasticity, erectile dysfunction, and others, to neuro-stimulation in the context of Alzheimer's disease. A comprehensive working mechanism for this diverse field of medical indications are still missing. Investigation of the physical basis of the working mechanism of shock waves in medical applications. We developed a model based on the mechanical forces generated by the momentum transfer at the acoustic interfaces of different layers of biological tissue. The generated forces are strong enough to crash brittle material and provide an adequate mechanical stimulus to activate mechano-transduction and mechano-sensory-transduction with nerve stimulation, thereby affecting the neural memory function of the central nervous system. The key to generating appropriate forces in the millisecond range is the mechanism of momentum transfer at the interfaces between tissue layers with different acoustic impedances. According to Newton´s laws of motion, a change in momentum (momentum transfer) generates force F=dP/dt. The inherent shear forces can stretch biological membranes to release biomolecules such as VEGF and NO. A most favourable feature of this mechanism is the selective effect on soft tissue interfaces and small tissue inhomogeneities to generate small forces in the range of few (≤ 10) Newton to stimulate tissue and nerve cells, while the same shock wave can generate forces ≥ 200 Newton and more on hard tissue interfaces such as bones or stones. The mechanism of momentum transfer is the basis for mechano-transduction and mechano-sensory transduction. It offers the opportunity to stimulate peripheral nerves and modify the motor reflex patterns of "pathologic" reflexes by hyper stimulation. The new technique of transcranial pulse stimulation (TPS) may be based on direct stimulation and reactivation of neurons in the brain. Momentum transfer is the basic physical mechanism and the initiator for successive biological processes in medical shock wave therapy.

Performance evaluation of Osprey optimization algorithm-based proportional integral derivative controller for speed control of a brushless direct current motor

Owing to diversity of application, speed regulation of Brushless Direct Current (BLDC) motor is essential in order to achieve best performance of the motor. In this paper, an appropriately tuned controller such as Proportional Integral Derivative (PID) is employed to achieve effective speed control of the motor. In tuning the parameters of PID controller, conventional techniques often pose great difficulties due to non-linearity often exhibited by DC motors. As a solution, metaheuristic optimization techniques are adopted to optimally tune the PID controller parameters for optimal performance of the BLDC motor in terms of speed. Thus, Osprey Optimization Algorithm (OOA) tuned PID controller (OOA-PID) was used to achieve better performance of BLDC motor speed. Kirchoff’s Voltage Law and Newton’s second law of motion were employed to derive the BLDC motor mathematical model. The PID mathematical equation was also described and an optimization model was formulated using the Integral of Time Multiplied Absolute Error (ITAE) and optimized using OOA. The performance of the OOA-PID controller with BLDC motor was evaluated using performance metrics such as rise time, settling time, overshoot and steady state error. Simulations were done using MATLAB (R2021b). Simulation result shows that an OOA-PID controller gave better response when compared with existing ziegler Nichols PID (ZN-PID) used for the same purpose.

Evaluating large language models in high school physics education: addressing misconceptions and fostering conceptual understanding

Abstract Large language models (LLMs), which are a specific subset of artificial intelligence (AI), may have the potential to revolutionize education by addressing common student misconceptions in physics. This study investigates the effectiveness of popular LLMs, such as OpenAI ChatGPT, Google Gemini, and Microsoft Copilot, in identifying and addressing misconceptions related to Newtonian mechanics in high school physics. The focus solely is on the misconception that for an elevator to move upward, the force exerted by the cable must be greater than the gravitational force acting downward on the elevator, which contradicts Newton’s first law of motion. To explore this, thirty-two experienced instructors engaged in dialogues with the LLMs, simulating learners with this misconception. Instructors evaluated the LLMs’ accuracy, personalization, and pedagogical effectiveness. The findings indicate that most instructors recognized the substantial potential of LLMs to improve student learning, particularly in addressing misconceptions through interactive dialogue, targeted questioning, and clear explanations tailored to each learner’s needs. ChatGPT ranked highest, demonstrating capabilities in delivering clear explanations, adapting to individual learners, and implementing effective teaching strategies. Google Gemini followed closely, while Microsoft Copilot was the least effective. This capability holds promise for enhancing conceptual understanding and student engagement in physics education. However, limitations were noted in the LLMs’ ability to facilitate personalized scientific discussions and utilize visual aids, such as physics diagrams, simulations, to enhance understanding. This research demonstrates the significant potential of LLMs as valuable tools for identifying and addressing misconceptions in physics education.

Integrating flight mechanics, energetics and migration ecology in vertebrates.

Animal locomotion is constrained by Newtonian laws of motion and therefore biomechanics is a useful approach for quantitative analysis of force and power requirements. Aerial locomotion in vertebrates is no exception, and arguably the most significant developments are to be found in this journal. Evolutionary birds and bats are very successful groups, doubtless largely because of their ability to shift location in a short time. This has enabled birds and to a lesser extent bats to perform seasonal long-distance migrations between habitats suitable for reproduction and survival. Power required to fly and potential flight range in relation to fuel load are two fundamental relationships derived from flight mechanics, which both serve as a foundation for the development of optimal migration theory. From this framework where biomechanics, energetics and ecology combine, we can analyse which of the alternative strategies migrants adopt. Such adaptive behaviours include the selection of optimal flight speed and the migratory travel itinerary. However, despite decades of research efforts, there are still many unsolved problems concerning flight mechanics and energetics of vertebrate flight. One such is how the power-speed relationship maps onto metabolic rate during flight, the so-called energy conversion efficiency. There is conflicting empirical evidence concerning how energy conversion possibly varies with flight speed, body mass and body size. As ultimately it is the metabolic energy consumption that is under selection pressure, this is an urgent question for the utility of flight mechanical principles in ecology. In this Review, I discuss this and other knowledge gaps in vertebrate flight and migration.

CFD-DEM simulation of the motion law of magnetic flocs during waste slurry disposal in shield tunnel

The sustainable treatment and reuse of waste slurry in slurry shield construction have gained significant attention. This paper explores the application of magnetic flocculation technology for treating slurry. The CFD-DEM coupling method simulates the migration of magnetic flocs during centrifugation. Two evaluation indexes of magnetic content of floc residue (MCFR) and magnetic seed recovery rate (MSRR) are introduced. The study examines how magnetic seed concentration, feed rate, and differential speed affect floc movement, magnetic seed separation, and recovery, proposing directions for optimizing separation technology. Due to computational limitations, the simulation focuses exclusively on the process from floc entry into the decanter centrifuge to its exit at the drum’s end. Results indicate that changes in centrifugal parameters significantly affect floc movement, with feed rate showing the strongest positive correlation with MSRR, followed by differential speed. As magnetic seed concentration increases, both MCFR and MSRR rise. However, when concentration becomes too high, MSRR begins to decrease. Feed rate strongly influences magnetic floc behavior, with MCFR and MSRR showing complementary trends. Through the transformation of the separation equipment, the MSRR can be increased to 93.4%.

Mixed mathematics and metaphysical physics: Descartes and the mechanics of the flow of water.

Mixed mathematics and metaphysical physics: Descartes and the mechanics of the flow of water.

Arcsine laws for Brownian motion with Poissonian resetting.

We analyze the equivalents of the celebrated arcsine laws for Brownian motion undergoing Poissonian resetting. We obtain closed-form formulas for the probability density functions of the corresponding random variables in the cases of the first and second arcsine law. Furthermore, we obtain numerical results for the third law.

Nonlinear forced response of non-uniform beams carrying point masses using the harmonic balance method with an arc-length continuation scheme

This work examines the forced vibrations of a non-uniform Euler-Bernoulli beam carrying point masses and subjected to a concentrated transverse harmonic force. By the means of Newton’s second law of motion, the integro-partial differential equation of motion is derived. The Galerkin approach is applied, and the normalized mode shapes of the non-uniform base beam are used to derive the nonlinear governing equation of motion that contains cubic and quintic nonlinearities. The method of harmonic balance method (HB) in conjunction with the pseudo arc-length continuation scheme are employed to obtain the amplitude-frequency curves. Non-uniform beams with two different boundary conditions are considered in this study; cantilever and simply supported beams. To examine the accuracy and validity of the proposed method and solution, some results obtained by the suggested approach have been compared with those found through numerical integration, where a good agreement was achieved. The influences of several factors such as the non-uniformity parameter, the magnitude of the point masses, and the boundary conditions on the steady state amplitude have been examined. It is observed that these parameters have significant effects on the dynamic behavior of the non-uniform beams. For generality and convenience, the results are displayed in dimensionless forms.

N-body plasma simulation of classical and Bohm diffusion employing Kepler's analytical solutions

A numerical approach to the simulation of two- and three-dimensional self-consistent N-body charged-particle dynamics is developed employing analytical solutions, with Kepler's laws of planetary motion being applied to close encounters of two particles. In the presence of a uniform magnetic field, in a quiet homogeneous plasma without microscopic instabilities, the diffusion process of electrons induced by Coulomb collisions is investigated. With an accurate treatment of binary collisions, it is found that the numerically computed electron diffusion rates match quantitatively with the results of an analytical approach that incorporates individual scattering angles into the random step size. In two dimensions, it is found that the diffusion coefficient Dei,class is inversely proportional to the square of the magnetic field strength B0: Dei,class∝1/B02. When the collision frequency becomes comparable to the electron cyclotron frequency, Bohm diffusion Dei,Bohm∝1/B0 is obtained. The diffusion rate according to the N-body simulation is consistently higher than that expected when only electron–ion collisions are considered, which suggests that electron–electron collisions play roles in enhancing electron transport. Relaxation of electron distribution function is demonstrated by preliminary three-dimensional N-body simulations.

Analysis of Short-range Contact Forces in Peridynamics Endowed with an Improved Nonlocal Contact Model

Analysis of Short-range Contact Forces in Peridynamics Endowed with an Improved Nonlocal Contact Model

Re-examining the law of energy conservation-A Euclidean geometric proof

The law of energy conservation is a cornerstone of physics, limiting energy use and dictating the efficiency of thermodynamic processes. The primary objective of this paper is to challenge the traditional acceptance of the law of energy conservation as an unprovable axiom by presenting a novel, provable, and purely geometric approach within the framework of Euclidean geometry, thereby re-evaluating its theoretical and empirical foundations. Driven by the ongoing pursuit of solutions to energy crises, the paper critically examines attempts to disprove the law and the search for alternative energy sources. Contrary to prevailing beliefs, it posits two key viewpoints: the lack of rigorous proof establishing the law’s validity and the obscured motivations driving the invention of new energy sources. Highlighting the gap between theoretical acceptance and empirical evidence, the paper introduces a geometric framework to elucidate the empirical limitations and precision of energy conservation. Through this lens, it challenges the law’s universal applicability, particularly debunking the notion of perpetual motion machines as proof of its validity. The findings include a geometric and practical redefinition of isolated systems, a proof of Newton’s laws of motion, a geometric derivation of the Newtonian kinetic energy equation, and the demonstration of these geometric concepts’ practicality independent of experiments. These insights call for a re-evaluation of the traditional understanding of energy conservation and offer transformative implications for future energy exploration and innovation.

A Class of Anti-Windup Controllers for Precise Positioning of an X-Y Platform with Input Saturations

The windup phenomenon occurs and results in performance degradation while the designed positioning controller output makes actuators saturated. This study presents significant and effective anti-windup controllers for performance improvement and comparison of the position tracking. To address real-world industrial scenarios, the trajectory with a T-curve velocity profile is planned to regulate hardware limitations and maintain efficiency throughout the control process. At first, the dynamic model of an inertia load for a servo control system is established using Newton’s law of motion. Then, anti-windup controllers are designed and implemented based on basic PID controllers. The conducted simulations validate its effectiveness and feasibility. Finally, experimental results demonstrate that the proposed algorithms achieve smaller overshoot and faster settling time under input saturations when executing specific paths on the X-Y platform, even though the given control commands change. It is verified that the proposed approaches can, indeed, effectively mitigate the windup phenomenon, leading to improved positioning accuracy in industrial applications.

A New Hybrid Improved Kepler Optimization Algorithm Based on Multi-Strategy Fusion and Its Applications

The Kepler optimization algorithm (KOA) is a metaheuristic algorithm based on Kepler’s laws of planetary motion and has demonstrated outstanding performance in multiple test sets and for various optimization issues. However, the KOA is hampered by the limitations of insufficient convergence accuracy, weak global search ability, and slow convergence speed. To address these deficiencies, this paper presents a multi-strategy fusion Kepler optimization algorithm (MKOA). Firstly, the algorithm initializes the population using Good Point Set, enhancing population diversity. Secondly, Dynamic Opposition-Based Learning is applied for population individuals to further improve its global exploration effectiveness. Furthermore, we introduce the Normal Cloud Model to perturb the best solution, improving its convergence rate and accuracy. Finally, a new position-update strategy is introduced to balance local and global search, helping KOA escape local optima. To test the performance of the MKOA, we uses the CEC2017 and CEC2019 test suites for testing. The data indicate that the MKOA has more advantages than other algorithms in terms of practicality and effectiveness. Aiming at the engineering issue, this study selected three classic engineering cases. The results reveal that the MKOA demonstrates strong applicability in engineering practice.

Enhancing supply chain resilience: The role of security practices and performance in mitigating disruptions in ghana’s manufacturing sector

At the current stage, the retail industry is undergoing unprecedented changes. From traditional physical stores to online shopping platforms, and then to the new retail model that integrates online and offline, customers’ demand for shopping experience is constantly changing. To meet these demands, retailers need to constantly explore and apply new technologies to optimize the retail environment and enhance customer experience. Biomechanics is the study of the internal and external mechanical behavior of living organisms, which is concerned with the structure, function and motion laws of living organisms. Applying the knowledge of biomechanics to retail environment design can effectively improve customers’ shopping experience. Based on this, this paper takes intelligent container as an example, gives a visual solution of detecting goods in intelligent container based on deep neural network, and proposes a twin-based pairwise image difference detection algorithm named DiffNet as the core algorithm of intelligent container solution, which aims to help enterprises deploy intelligent container flexibly, safely and at low cost. Enhance the customer’s offline self-service shopping experience.

The Size Distribution Characteristics and Spatial Motion Law of Granular Top-Coal in Longwall Top-Coal Caving (LTCC)

The Size Distribution Characteristics and Spatial Motion Law of Granular Top-Coal in Longwall Top-Coal Caving (LTCC)

Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order

Abstract We compute the gravitational radiation-reaction force on a compact binary source at the fourth-and-a-half post-Newtonian (4.5PN) order of general relativity, i.e., 2PN order beyond the leading 2.5PN radiation reaction. The calculation is valid for general orbits in a general frame, but in a particular coordinate system which is an extension of the Burke-Thorne coordinate system at the lowest order. With the radiation-reaction acceleration, we derive (from first principles) the flux-balance laws associated with the energy, the angular and linear momenta, and the center-of-mass position, in a general frame and up to 4.5PN order. Restricting our attention to the frame of the center of mass, we point out that the equations of motion acquire a non-local-in-time contribution at the 4.5PN order, made of the integrated flux of linear momentum (responsible for the recoil of the source) together with the instantaneous flux of center-of-mass position. The non-local contribution was overlooked in the past literature, which assumed locality of the radiation-reaction force in the center of mass frame at 4.5PN order. We discuss the consequences of this non-local effect and obtain consistent non-local equations of motion and flux balance laws at 4.5PN order in the center-of-mass frame.

Methodology for Designing Vibration Devices with Asymmetric Oscillations and a Given Value of the Asymmetry of the Driving Force

In mechanical engineering, the building industry, and many other branches of industry, vibration machines are widely used, in which circular and directed oscillations predominate in the form of movement of the working equipment. This article examines methods for generating asymmetric oscillations, which are estimated by a numerical parameter, namely by the coefficient of asymmetry of the magnitude of the driving force when changing the direction of action in a directed motion within each period of oscillations. It is shown that for generating asymmetric mechanical vibrations, vibration devices are used, consisting of vibrators of directed vibrations, called stages. These stages form the total asymmetric driving force. The behavior of the total driving force of asymmetric vibrations and the working equipment of the vibration machine are described by analytical equations, which represent certain laws of motion of the mechanical system. This article presents a numerical analysis of methods for obtaining laws of motion for a two-stage, three-stage, and four-stage vibration device with asymmetric oscillations. An analysis of the methodology for obtaining a generalized law of motion for a vibration device with asymmetric oscillations is performed based on the application of polyharmonic oscillation synthesis methods. It is shown that the method of forming the total driving force of a vibration device based on the coefficients of the terms of the Fourier series has limited capabilities. This article develops, substantiates, and presents a generalized method for calculating and designing a vibration device with asymmetric oscillations by the value of the total driving force and a given value of the asymmetry coefficient in a wide range of rational designs of vibration machines. The proposed method is accompanied by a numerical example for a vibration device with an asymmetry coefficient of the total driving force equal to 10.

Navigating the Cosmos: The Evolution and Impact of Newtonian Mechanics

Mechanics is one of the most fundamental subfields of physics. Founded primarily by Isaac Newton, mechanics has strong relations with astronomy, one of the oldest sciences. It has astronomical origins and exhibits significant applications in astronomical problems. A historical perspective is necessary to grasp the big picture of physics, so this paper traces back to the very beginning of classical mechanics to discover its development through the literature review method. Starting from Keplers planetary motion laws and Newtons theories, then moving to two-body and three-body problems, this essay demonstrates the delicacy of classical mechanics and how it effectively solves different issues. Also, after centuries of development, the implications of Newtonian mechanics have been greatly expanded upon, serving as the foundation for numerous subsequent theories. In the end, this essay provides an outlook for other theories that either derive from or relate to Newtonian mechanics, like chaos theory and analytical mechanics. The paper finds that Newtonian mechanics is essential because it not only provided solutions to many of the modern astronomical difficulties but also encouraged the emergence of other important ideas

Analytic Determination of the Roller Length of a Hydraulic Jump in an Open Channel Flow Using a Bouncing Ball

A hydraulic jump is a natural occurrence that occurs in spillways, rivers, and other open channel flows when water or other liquid flowing with a high velocity discharges into a region of lower velocity with an attendant abrupt rise in the liquid surface. Such a phenomenon, known as hydraulic jump, is normally accompanied by substantial dissipation of energy. Many researchers, in the past, focus attention in the numerical study of the hydraulic jump, under varied working situations. Few attempts are made to study the occurrence analytically. In this paper, the author studied the incident analytically using a bouncing ball to develop a model to examine the lengths of hydraulic jumps in a horizontal open channel flow. The model development is based on the laws of motion, the principles of impulse and momentum, and the classical hydraulic jump formula. The model was later verified with the roller length obtained from the series of experiments conducted in a large-size facility. The roller length that the new model estimated compared well with the experimental results conducted within the Froude number ranges of 2.00 and 16.00. The model is ease to use and its accuracy as determined by the Pearson correlation coefficient is between 0.93 and 1.00.