Problem Of Motion Research Articles

Analyze the moment of inertia of an object in uniformly accelerated linear motion and angular motion

Abstract. In studying particle kinematics, calculus plays an important role in analyzing and solving motion problems as a key mathematical tool. This paper mainly discusses the application of calculus in uniformly accelerated linear motion (LM) and angular motion (AM), focusing on the relationship between position, velocity, and acceleration and the analysis of the rate of change of motion. Through the study of uniformly accelerated LM, this paper guides researchers to use calculus to establish the mathematical relationship between position, velocity, and acceleration and verifies the accuracy of these formulas through practical cases. Similarly, in AM, this paper provides an in-depth understanding of the dynamic behavior of an object rotating around a fixed axis through calculus and calculates and applies important parameters in AM to solve practical problems by analyzing angular velocity and acceleration. In addition, this paper demonstrates the potential of calculus for a wide range of applications in dealing with variable speed motion and rate of change analysis. By integrating the rate of change of displacement and acceleration, it provides a precise tool for the optimization and resolution of engineering problems. In conclusion, calculus not only enriches the theory of kinematics but also demonstrates its important value in practical applications.

Uncovering the Secrets of Motion: A Literature Review of Lagrange and Newtonian Mechanics

Physics is a branch of natural science. Since ancient times, humans have been interested in the movement of objects around them and motion is an area studied in mechanics. This research aims to understand the principles of mechanics in Lagrange and Newtonian mechanics for solving motion problems and their applications. The method used is the literature review method. Literature is a comprehensive overview of previous research on a particular topic. Literature review is a systematic process for identifying, evaluating, and synthesizing previously published scientific works on a particular topic. There are 20 sources used, consisting of books and scientific journals. The research results show that motion is an object that experiences movement from one place to another. Problems of motion of objects can be solved using the laws and principles of Newtonian and Lagrange mechanics. Lagrange mechanics is used to solve complex problems that cannot be solved with Newtonian mechanics. Lagrange mechanics focuses on the forces that cause objects to move, while Newtonian mechanics focuses on the energy that causes objects to move.

On the Motion of a Point Particle on a Homogeneous Gravitating Ball with a Spherical Inclusion

A problem of motion of a point particle on a surface of a homogeneous gravitating ball with a spherical inclusion of a differing density is considered. It is assumed that the body rotates uniformly around its symmetry axis. It is supposed that "besides the gravitation force, the particle is subjected to dry friction. The gravitational properties outside the ball are described. The dependence of existence, bifurcations, and stability of relative equilibria of the point particle on the body surface on the parameters of the problem is studied. The results are represented both analytically and as numerically obtained bifurcation diagrams.

A singularly perturbed ruin problem for a two-dimensional Brownian motion in the positive quadrant

Abstract We consider the following problem: the drift of the wealth process of two companies, modelled by a two-dimensional Brownian motion, is controllable such that the total drift adds up to a constant. The aim is to maximize the probability that both companies survive. We assume that the volatility of one company is small with respect to the other, and use methods from singular perturbation theory to construct a formal approximation of the value function. Moreover, we validate this formal result by explicitly constructing a strategy that provides a target functional, approximating the value function uniformly on the whole state space.

On bifurcation of non-isolated singular points arising in a problem of two-phase fluid motion in a pipe

The dynamics of gas suspension in a pipe is studied. It is described by a system of three autonomous differential equations, whose equilibrium (singular) points are not isolated, but form several continuous curves. One of these curves belongs to the transonic plane. The dynamics in a neighborhood of this plane is interesting from the physical viewpoint. In this work, the dynamics in a neighborhood of the curves of singular points is investigated. The main tools of this work are the center manifold theorem and the reduction principle. A peculiarity of the system is that the curves of singular points intersect each other. Moreover, at the intersection point a bifurcation occurs. Results of the work are the description of the dynamics in a neighborhood of singular points, the proof that a curve of singular points belongs to a center manifold and the description of the bifurcation, which occurs at the intersection point of the curves of singular points.

PERTURBED MOTIONS OF A NEARLY DYNAMICALLY SPHERICAL RIGID BODY WITH A MOVABLE MASS SUBJECT TO CONSTANT BODY-FIXED TORQUE

The problem of motion of a rigid body about a fixed point is one of the classical problems of mechanics. The interest to the problems of the rigid body dynamics has increased in the second half of the XX century in connection with the development of rocket and space technologies. A spacecraft or satellite, while orbiting about its center of mass, experiences torques from forces of diverse physical nature. This includes torques generated by the motion of internal masses, which can arise from factors such as presence of rotating components (like rotors or gyroscopes), and the activities of crew members aboard the crew vehicle. The dynamics of rigid body incorporated moving masses is a significant focal point in classical mechanics. Extensive research is dedicated to investigating the rotation of a rigid body featuring motion of internal masses. It is assumed that the body contains a viscoelastic element that is modeled by a moving mass connected to the body by a strong damper. The moving mass model loosely attached elements in a space vehicles, which can significantly affect the vehicle’s motion about its center of mass during a long period of time. Some cases are considered of the motion of a rigid body containing internal masses connected to the body by means of elastic and dissipative elements. A number of works are devoted to the analysis of various problems of the dynamics of space vehicles containing internal movable masses. The paper develops an approximate solution by means of averaging method to the system of Euler’s equation terms for a nearly dynamically spherical rigid body containing a viscoelastic element under the action of constant body-fixed torque. We obtained the system of motion equations in the standard form which refined in square-approximation by small parameter. Asymptotic approach permits to obtain some qualitative results and to describe evolution of angular motion using simplified averaged equations and numerical solution. The main objective of this paper is to extend the previous results for the problem of motion about a center of mass of a rigid body under the influence of small internal torque (cavity filled with a fluid of high viscosity) or external torque (resistive medium). The importance of the results is in progress of moving mass control motion of spinning projectiles.

Role of inhibition in overcoming interferences of misconception under similar feature saliency: An eye-tracking study of the projectile motion problem

Misconceptions coexisting with scientific understanding pose significant challenges in physics education. Inhibitory control may enable individuals to overcome interference from misconceptions. However, discerning the role of inhibitory control becomes intricate when the saliency of scientific- and misconception-related features varies in a problem. This study investigates the role of inhibitory control in overcoming such misconceptions when scientific and misconception-related features are similarly salient, particularly focusing on the range-time (range determines flight time) misconception. We adopted a negative priming (NP) paradigm with the eye-tracking technique in the study. Thirty-six college physics majors participated in the experiment. In the NP paradigm, the participants first compared the flight times in a neutral (same range) or incongruent (longer range, less flight time) primes and then completed the same task in a congruent (longer range, more flight time) probe. Results revealed longer reaction times for incongruent primes compared to neutral primes and longer reaction times to respond to congruent probes following incongruent primes than when neutral primes were present beforehand, suggesting that the inhibitory control may be involved in overcoming the interference from the range-time misconception. Moreover, the eye-tracking analysis highlighted an early overt attention to the salient misconception-related feature (longer range) during primes, along with additional attentional investment necessary to inhibit the range-time misconception. During probes, an early shift of attention away from the salient misconception-related feature and a greater investment of attention on processing the congruent probes after the incongruent primes than that after the neutral primes were observed, indicating a possible effect of the previous inhibitory control in the primes on the subsequent cognitive process on the probes. These findings contribute to a deeper understanding of the cognitive process underlying physics conceptual change and provide insights into physics education. Published by the American Physical Society 2024

Impact of repetitive ELM transients on ITER divertor tungsten monoblock top surfaces

Abstract Owing to the high stored energy of ITER plasmas, the heat pulses due to uncontrolled Type I edge localized modes (ELMs) can be sufficient to melt the top surface of several poloidal rows of tungsten monoblocks in the divertor strike point regions. Coupled with the melt motion associated with tungsten in the strong tokamak magnetic fields, the resulting surface damage after even a comparatively small number of such repetitive transients may have a significant impact on long-term stationary power handling capability. The permissible numbers set important boundaries on operation and on the performance required from the plasma control system. Modelling is carried out with the recently updated MEMENTO melt dynamics code, which is tailored to tackle melt motion problems characterized by a vast spatio-temporal scale separation. The crucial role of coupling between surface deformation and shallow angle heat loading in aggravating melt damage is highlighted. As a consequence, the allowable operational space in terms of ELM-induced transient heat loads is history-dependent and once deformation has occurred, weaker heat loads, incapable of melting a pristine surface, can further extend the damage.

A study into the correlation between single array-hull configurations and wave spectrum for floating solar photovoltaic systems

Floating photovoltaic (FPV) systems offer a viable renewable energy solution due to easy installation and cost-effectiveness compared to other renewable energy generation methods. On the other hand, land-based solar photovoltaics face challenges such as space scarcity and environmental impacts. Shifting to nearshore locations unlocks vast ocean space potential, though waves expose significant challenges to FPV systems. Several novel FPV system designs are proposed, inspired by high-speed vessel multihulls, including catamaran, trimaran, quadrimaran, and pentamaran configurations, as floating supports for solar panels. Simulations were conducted to determine Response Amplitude Operators (RAOs) under various irregular wave spectrum conditions in a free-floating initial state. The FPV motion problem was solved using linear potential-flow theory with the Boundary Element Method (BEM) with Green-Function approach. Superposition of wave spectral energy and motion RAOs was used to obtain spectral structural responses. Motion in heave, roll, and pitch modes was evaluated across wave spectrum types. Results show that adding hulls reduces the significant amplitude response in all motion modes. In summary, valuable insights into floater designs and the hydrodynamic evaluation of FPV systems are presented.

Design and Optimization Analysis of an Adaptive Knee Exoskeleton

To solve the problem of undesired relative motion of human-machine interaction positions caused by misalignment of the human-machine joints rotation axis of the knee exoskeleton, this study designed an adaptive knee exoskeleton based on a gear-link mechanism (GLM) by considering the human body as a component of the exoskeleton mechanism. Simultaneously, the concept of the wearable area (WA) was proposed, which transformed the operation of aligning the exoskeleton rotation axis with the human knee joint rotation axis into a "face alignment point" in the sagittal plane, reducing the difficulty of aligning the human-machine joint rotation axis. In the kinematic analysis of GLM, the phenomenon of instantaneous movement of the central axis of the human knee joint was considered. Based on the kinematic model, the WA, velocity transfer ratio, and initial position static stiffness of GLM were analyzed. The NSGA-II optimization algorithm was used to optimize the size parameters of GLM, which increased the WA by 18.4%, the average velocity transfer ratio by 4.98%, and the average initial position static stiffness by 6.01%. Finally, the ability of the exoskeleton to absorb movement displacement (MD) was verified through simulation, and the good human-machine kinematic compatibility of the exoskeleton was verified through wearable tests conducted on the initial mechanism principle prototype.

On the Stability of Planetary Motions During Stellar Approaches

The problem of the spatial motion of a passively gravitating body during an to the central body of a perturbing body – a test star – is considered. Using the exact expression of the force function, an integral invariant relationship – a quasi-integral – was found. Due to the quasi-integral, the regions of possible motion of the passively gravitating body, the surfaces of minimal energy (a generalization of the zero velocity surfaces), and the singular points of these surfaces were determined. The stability of planetary motion according to Hill during the approach of a test star to the Solar System was investigated. Criteria for the possibility, as well as the impossibility of capturing the passively gravitating body by the test star, were established. According to the Hill stability criteria, critical values of the orbital parameters of the test star were established, at which the planets of the Solar System either become satellites of the test star or leave the bounds of the Solar System.

PPLICATION OF KINEMATIC APPROACHES IN GEOMETRIC PROBLEMS

This work is devoted to the use of kinematic methods in the process of solving geometric problems. The first part of the work is devoted to solving geometric problems by considering the movements of some image points. The minimum knowledge required to apply the kinematic method in elementary geometry is briefly outlined. Then a solution to a generalized version of a well-known geometric problem is presented. The importance of studying elements of operator calculus from an interdisciplinary perspective is also presented. The next part of the article examines problems selected according to the principle of gradual complication, from high school to bachelor’s degree. In these problems, the radius of curvature at various points is determined by kinematic way. Using the result of solving a kinematic problem about a body thrown in a horizontal direction, the expression for the radius of curvature of a parabola is determined. One physical method for determining the radius of curvature of a cycloid is presented. The problem of motion, which generates the equations of an ellipse and a hyperbola, is considered, and a kinematic version of determining the radii of curvature at the points of intersection of these curves and axes of symmetry is presented. The main methodological novelty of the work lies in the development, generalization and systematic presentation of kinematic problems that bring geometric results. Some methodological guidelines and arguments are also given to substantiate the importance of the discussed kinematic approaches to solving geometric problems.

Landau levels for charged particles with anisotropic mass

The problem of the two-dimensional motion of a charged particle with constant mass in the presence of a uniform constant perpendicular magnetic field features in several undergraduate and graduate quantum physics textbooks. This problem is very important to studies of two-dimensional materials that manifest quantum Hall behavior, as evidenced by several major discoveries over the last few years. Many real experimental samples are more complicated due to the anisotropic mass of the electrons. In this work, we provide the exact solution to this problem by means of a clever scaling of coordinates. Calculations are done for a symmetric gauge of the magnetic field. This study allows a broad audience of students and teachers to understand the mathematical techniques that lead to the solution of this quantum problem.

Analytical Solution to the Steady Navier-Stokes Equation for a Supersonic Cone in the Area of Boundary Layer Behind the Shock Wave by Means Tunnel Mathematics

The means of tunnel mathematics (the theory of functions of a spatial complex variable) allow for an analytical solution to the problem of supersonic flow around a cone in the area of the boundary layer and beyond. The peculiar feature of the Navier-Stokes equations is that they allow for the determination of analytical velocity fields of fluids only for a small number of simple problems. Of course, the problem of the supersonic motion of fluid around a cone is not included in this number. Tunnel mathematics is a method for finding analytical vector velocity fields for steady flows of fluids with axial symmetry. The Navier-Stokes equations are then used to determine pressure and temperature distributions. The main theorem of tunnel mathematics allows for the determination of these distributions for planes z = const (similar to constructing slices of a brain in an MRI procedure). By collecting these “slices,” we can obtain full space distributions of pressure and temperature around a supersonic cone. At this stage of investigation, the conclusions obtained through tunnel mathematics make it possible to qualitatively assess the thickness of the boundary layer on the cone's surface, the shape of the shock wave, and whether the shock wave intersects the boundary layer. First of all, we focused on ensuring that the resulting solutions corresponded to the physical pattern of phenomena. No doubt, solutions obtained through tunnel mathematics must be confirmed experimentally.

Intelligent ankle–foot prosthesis based on human structure and motion bionics

The ankle–foot prosthesis aims to compensate for the missing motor functions by fitting the motion characteristics of the human ankle, which contributes to enabling the lower-limb amputees to take care of themselves and improve mobility in daily life. To address the problems of poor bionic motion of the ankle–foot prosthesis and the lack of natural interaction among the patient, prosthesis, and the environment, we developed a complex reverse-rolling conjugate joint based on the human ankle–foot structure and motion characteristics, the rolling joint was used to simulate the rolling-sliding characteristics of the knee joint. Meanwhile, we established a segmental dynamics model of the prosthesis in the stance phase, and the prosthetic structure parameters were obtained with the optimal prosthetic structure dimensions and driving force. In addition, a carbon fiber energy-storage foot was designed based on the human foot profile, and the dynamic response of its elastic strain energy at different thicknesses was simulated and analyzed. Finally, we integrated a bionic ankle–foot prosthesis and experiments were conducted to verify the bionic nature of the prosthetic joint motion and the energy-storage characteristics of the carbon fiber prosthetic foot. The proposed ankle–foot prosthesis provides ambulation support to assist amputees in returning to social life normally and has the potential to help improve clinical viability to reduce medical rehabilitation costs.

МАТЕМАТИКА КУРСУН ОКУТУУДА КЫЙМЫЛ МАСЕЛЕЛЕРИН ЧЫГАРУУНУН МЕТОДИКАЛЫК КӨРСӨТМӨЛӨРҮ

At present, in accordance with the program of basic general education, a special place in mathematics teaching is occupied by the development of students' independence in solving motion problems. There is no doubt that the mathematical problem of motion enables the student to formulate mathematical concepts correctly, to clarify various aspects of his environment, and to apply theoretical concepts. Solving full-scale problems defined by the program contributes to knowledge building for students. In setting motion problems, students are exposed to facts of cognitive, educational significance. Motion problems-one of the most common types of algebra problems. Simple motion problems are taught in elementary school. In grades 6-7, the solution of motion problems is reduced to a linear equation or a system of linear equations. Here we will consider motion problems related to the rational fraction equation.

Results of neck-specific exercise for altered postural sway in individuals with chronic whiplash-associated disorders: a longitudinal case–control study

Postural sway has not been investigated before or after a neck exercise intervention in individuals with chronic whiplash-associated disorders (WAD). The aim of the study was to investigate postural sway in individuals with chronic WAD grades 2 and 3: (a) compared with healthy matched controls at baseline; (b) after three months of neck-specific exercise and (c) to investigate the correlation between postural sway with self-reported dizziness during motion and balance problems/unsteadiness. This is a longitudinal prospective experimental case–control intervention study. Individuals with WAD (n = 30) and age- and gender-matched healthy volunteers (n = 30) participated. Postural sway was assessed using an iPhone application. Measurements were carried out at baseline, and for those with WAD a second measurement was performed at the three-month follow-up when neck-specific exercise intervention ended. The WAD group performed significantly worse than the healthy group in both pathway and ellipse area double stance eyes closed at baseline (main outcome), but not at the three-month follow-up. The WAD group significantly improved after rehabilitation in both pathway double stance eyes closed and pathway single stance eyes open. The correlation between postural sway and self-rated dizziness during motion and balance problems was low to moderate. One may conclude that postural sway was improved after a neck-specific exercise programme. The study results strengthen earlier findings that individuals with WAD have worse balance outcome when they have to rely on neck proprioception (eyes closed). The study results may be important for the development of improved rehabilitation methods for WAD.

Balanced task allocation and motion planning of a multi-robot system under fuzzy time windows

PurposeA fleet of mobile robots has been effectively used in various application domains such as industrial plant inspection. This paper proposes a solution to the combined problem of task allocation and motion planning problem for a fleet of mobile robots which are requested to operate in an intelligent industry. More specifically, the robots are requested to serve a set of inspection points within given service time windows. In comparison with the conventional time windows, our problem considers fuzzy time windows to express the decision maker’s satisfaction for visiting an inspection point.Design/methodology/approachThe paper develops a unified approach to the combined problem of task allocation and motion planning for a fleet of mobile robots with three objectives: (a) minimizing the total travel cost considering all robots and tasks, (b) balancing fairly the workloads among robots and (c) maximizing the satisfaction grade of the decision maker for receiving the services. The optimization problem is solved by using a novel combination of a Genetic Algorithm with pareto solutions and fuzzy set theory.FindingsThe computational results illustrate the efficiency and effectiveness of the proposed approach. The experimental analysis leverages the potential for using fuzzy time windows to reflect real situations and respond to demanding situations.Originality/valueThis paper provides trade-off solutions to a realistic combinatorial multi-objective optimization problem considering concurrently the motion and path planning problem for a fleet of mobile robots with fuzzy time windows.

RBF Neural Network for Chaotic Motion Control of Collision Vibration System

Aiming at the control problem of chaotic motion of a kind of collision vibration system with gap, a chaotic motion control of collision vibration system based on RBF neural network is proposed. Firstly, the system mechanical model and chaotic motion are introduced, and then a chaotic controller based on RBFNN is designed to control and simulate the chaotic attractor. The model information of the system is not used in the control method. In this paper, the model of the system is used only to generate the input / output data of the system, and it is not used for the design of the controller. The parameters of AHGSA algorithm are set as follows: the population size is 30, the maximum number of iterations is 100,G0, a = 18, and the proportional coefficient P = 0.96. Small disturbances are applied to the controllable parameter ωof the system to suppress the chaotic motion of the system and make the system tend to stable periodic motion. In order to more clearly show the control effect of chaotic motion, the chaotic motion is controlled when the system iterates 400 times. The results show that the chaotic motion can be quickly controlled to periodic 1-1 motion, the phase diagram is a closed curve, and there is a peak in the spectrum diagram. Chaotic motion can be quickly controlled as periodic 2-2 motion, the phase diagram is two closed curves, and two obvious peaks appear in the spectrum diagram. The proposed method can effectively control the chaotic motion of the system, and the expected target can be not only the fixed point of period 1, but also other periodic orbits.

Optimization of robot manipulator configuration calibration by using Zhang neural network for repetitive motion

High precision and low complexity control algorithm plays an important role in the developing of the end-effector instrumentation of different robot manipulators. In order to reduce the kinetic energy and the high-speed drift phenomenon of the repetitive motion tracking task, the robot manipulator needs to calibrate its configuration. In this paper, we formulate the configuration calibration of the robot manipulator for the repetitive motion task as a future quadratic programming optimization problem constrained with equality constraints, which is also regarded as a fundamental problem in artificial intelligence and modern control engineering. Zhang neural network, which is a canonical method, can be adopted to deal with the continuous form of the future optimization problem, named as temporally dependent quadratic programming problem with equality constraints. In order to overcome the issue of temporally dependent inverse computing, a novel Zhang neural network model and its uncertain disturbance tolerant model, which are termed as filtered reciprocal-kind Zhang neural network model and uncertain disturbance tolerant filtered reciprocal-kind Zhang neural network model, respectively, are proposed by integrating the energy-type cost function and Zhang neural network design formula for solving the temporally dependent quadratic programming problem with equality constraints in this paper. Based on the Euler discrete formula and the models, the discrete filtered reciprocal-kind Zhang neural network and the discrete uncertain disturbance tolerant filtered reciprocal-kind Zhang neural network algorithms are proposed for solving the future quadratic programming problem with equality constraints and the robot manipulator configuration calibration problem of repetitive motion. The convergence properties of the reciprocal-kind Zhang neural network model and its corresponding uncertain disturbance tolerant model are obtained by Lyapunov stability theory of nonlinear system and its corresponding perturbed system, while the convergence property of the filtered reciprocal-kind Zhang neural network model is analyzed by the limit thinking. For the repetitive motion task, three experiments for solving the configuration calibration problem of PUMA560, Kinova Jaco2, and Franka Emika Panda robot manipulators are performed to illustrate the effectiveness, robustness and superiority of our proposed discrete filtered reciprocal-kind Zhang neural network algorithms.