Problem Of Motion Research Articles

Integrated Mathematics and Science Instruction on Motion Problems in Grade 9 Classes

The integration of mathematics and science in teaching facilitates student learning, engagement, motivation, problem-solving, critical thinking, and real-life application. Although curriculum integration is theoretically desirable for many educators, what to integrate and how to integrate are often the big questions facing teachers working within education systems premised on a culture of segregated subject delivery. This quasi-experimental study reports on a 2-week inquiry of the implementation of an integrated unit of learning on motion problems, within upper secondary education in Turkey. In order to reveal the effect of the instruction on students with different mathematics achievements, the study was conducted with 131 students in two different schools. In the design of the integrated unit, continuum model of learning and four-stages of learning model were employed. The study employed a quantitative approach and examined the key aspects of the practice of the integration of mathematics and science teaching. In light of the data obtained, it was concluded that teaching the subject Motion Problems through an integrated design had a positive effect on students’ learning for the experimental groups in each school.

A new physically realisable internal 1:1 resonance in the coupled pendulum–slosh system

The problem of dynamic coupling between a rectangular container undergoing planar pendular oscillations and its interior potential fluid sloshing is studied. The Neumann boundary-value problem for the fluid motion inside the container is deduced from the Bateman–Luke variational principle. The governing integro-differential equation for the motion of the suspended container, from a single rigid pivoting rod, is the Euler–Lagrange equation for a forced pendulum. The fluid and rigid-body partial differential equations are linearised, and the characteristic equation for the natural and resonant frequencies of the coupled dynamical system are presented. It is found that internal 1:1 resonances exist for an experimentally realistic setup, which has important physical implications. In addition, a new instability is found in the linearised coupled problem whereby instability occurs when the rod length is shorter than a critical length, and an explicit formula is given.

Characteristics of frailty phenotype in Chinese nursing home population and significance of motor function indicators in frailty assessment.

The objectives of this study were to analyze the distribution characteristics of frailty phenotypes in older adults of Chinese nursing homes, and to compare some motor function characteristics of older adults in nursing homes between frailty and non-frailty, to determine which motor function and frailty are related. This cross-sectional study included 177 older adults living in nursing homes. Frailty was diagnosed by Fried's phenotype, and motor function assessment characteristics (including muscle tone, ROM, and balance) were also evaluated. Chi-square and logistic regression analyses were performed. Frailty prevalence was 53% in nursing homes in big Chinese cities (average age 82.0 ± 6.1). Low levels of physical activity (90.4% in frail elder), decreased handgrip strength (98.9% in frail elder) and slowed walking speed (100% in frail elder) were the 3 main components of the frailty phenotype of frail adults in nursing homes in China. It is worth noting that 74.7% of the non-frail elders also had reduced handgrip strength. Further analysis showed that balance (P < .001), muscle tone (upper, P = .028, lower, P = .001) and the range of motion (P < .001) were associated with frailty in older adults. The frailty of the elders in Chinese nursing homes was characterized by the decline of motor function. And surprisingly, both frail and non-frail elders were found to have poor strength. Frail nursing home seniors also have body muscle tone, range of motion and balance problems. The elderly of China should focus on strength, stretch and balance training to improve motor function, especially strength training, which is important for prevention frailty.

Deposition, diffusion, and nucleation on an interval

Motivated by nanoscale growth of ultra-thin films, we study a model of deposition, on an interval substrate, of particles that perform Brownian motions until any two meet, when they nucleate to form a static island, which acts as an absorbing barrier to subsequent particles. This is a continuum version of a lattice model studied in the applied literature. We show that the associated interval-splitting process converges in the sparse deposition limit to a Markovian process (in the vein of Brennan and Durrett) governed by a splitting density with a compact Fourier series expansion but, apparently, no simple closed form. We show that the same splitting density governs the fixed deposition rate, large time asymptotics of the normalized gap distribution, so these asymptotics are independent of deposition rate. The splitting density is derived by solving an exit problem for planar Brownian motion from a right-angled triangle, extending work of Smith and Watson.

The Cross Diagram for Kinematics Problems

The cross diagram is a way to illustrate and plan the solutions for all kinds of constant-acceleration kinematics problems—including projectile motion, multistage, and multiple-object problems. The cross diagram arranges the kinematic variables in a logical way, making the kinematic relationships between them easy to identify. Combined with a method to visually mark known information and equations, it provides a framework to plan out which equations will be used in the solution of a problem. This paper introduces the cross diagram through its use in a series of example problems.

Exploring the Argumentation Level in Inquiry Learning of Force and Motion

One of the learning methods that is proven to be able to develop and improve students' critical thinking skills is to apply an argumentation strategy with ADI (Argumentation-Driven-Inquiry). This study aims to investigate the level of student argumentation on the subject of motion and force. This study focused on identifying the level of student argumentation after the ADI model was applied. The research population was students of Physics Education, Surabaya State University, whose year class is 2020. The sample selection used a random sampling cluster technique. The used instrument consisted of a multiple-choice test with 10 questions and 2 essays to determine the level of student argumentation. The results showed that the students' arguments were at level 3, namely the ability to analyse problems related to motion and force. Based on the results of the study, it can be concluded that the argumentation abilities of students who do not contribute to give argumentation or who are at level 1, are not able to answer analytical questions about motion and force phenomena properly. Meanwhile, students who are at level 2 are still fixated on one concept or method, and still have difficulty when trying to apply other methods to solve problems. Students whose argumentation are at level 3, 4, and 5 have been able to fulfil all the characteristics of critical thinking, but some still have weaknesses, namely the ability to analyse motion and force problems.

Free surface in two-dimensional potential flow: singularities, invariants and virtual fluid

We study a two-dimensional (2-D) potential flow of an ideal fluid with a free surface with decaying conditions at infinity. By using the conformal variables approach, we study a particular solution of the Euler equations having a pair of square-root branch points in the conformal plane, and find that the analytic continuation of the fluid complex potential and conformal map define a flow in the entire complex plane, excluding a vertical cut between the branch points. The expanded domain is called the ‘virtual’ fluid, and it contains a vortex sheet whose dynamics is equivalent to the equations of motion posed at the free surface. The equations of fluid motion are analytically continued to both sides of the vertical branch cut (the vortex sheet), and additional time invariants associated with the topology of the conformal plane and Kelvin's theorem for a virtual fluid are explored. We called them ‘winding’ and virtual circulation. This result can be generalized to a system of many cuts connecting many branch points, resulting in a pair of invariants for each pair of branch points. We develop an asymptotic theory that shows how a solution originating from a single vertical cut forms a singularity at the free surface in infinite time, the rate of singularity approach is double exponential and supersedes the previous result of the short branch cut theory with finite time singularity formation. The present work offers a new look at fluid dynamics with a free surface by unifying the problem of motion of vortex sheets, and the problem of 2-D water waves. A particularly interesting question that arises in this context is whether instabilities of the virtual vortex sheet are related to breaking of steep ocean waves when gravity effects are included.

Approximating the first passage time density from data using generalized Laguerre polynomials

This paper analyzes a method to approximate the first passage time probability density function which turns to be particularly useful if only sample data are available. The method relies on a Laguerre-Gamma polynomial approximation and iteratively looks for the best degree of the polynomial such that a normalization condition is preserved. The proposed iterative algorithm relies on simple and new recursion formulae involving first passage time moments. These moments can be computed recursively from cumulants, if they are known. In such a case, the approximated density can be used also for the maximum likelihood estimates of the parameters of the underlying stochastic process. If cumulants are not known, suitable unbiased estimators relying on κ-statistics might be employed. To check the feasibility of the method both in fitting the density and in estimating the parameters, the first passage time problem of a geometric Brownian motion is considered.

Research on the Behavioral Dynamics Motion Planning Method of the Human-Vehicle Social Force Model.

The interactive motion planning between unmanned vehicles and pedestrians in urban road environments is the key to realizing the autonomous motion of unmanned vehicles in hybrid traffic scenarios. The problem of human-vehicle interaction motion planning modeling at complex intersections is studied for an unmanned vehicle in this article. First, the motion planning of pedestrians and the unmanned vehicles is established according to the social force model and the behavioral dynamics model. Then, the autonomous vehicle is added to the crowd, and the human-vehicle interaction force is established. The virtual force is added to the social force model and the behavioral dynamics model, respectively, and the improved social force model and the behavioral dynamics model are used for the motion planning of pedestrians and unmanned vehicles. In this way, the established model solves the problems of simple pedestrian interaction motion planning in the social force model and single-body motion planning in the behavioral dynamics and thus provides a strong support for multibody motion planning. Finally, through the interactive motion planning trajectory of pedestrians and unmanned vehicles in different scenes, the vehicle and pedestrian motion planning trajectory can effectively avoid overlapping or crossing, so as to avoid the collision, which verifies the effectiveness and feasibility of the proposed model.

An exact DtN artificial boundary condition for motion analysis of water wave with undulated seabed

This paper is concerned with three-dimensional water wave motion over undulated seabed. For the wave motion problem in seawater of finite depth, the fluid domain is usually unbounded horizontally but bounded vertically by free water surface and seabed which have their own boundary conditions. To study local wave motion over undulated region only, a novel Dirichlet-to-Neumann (DtN) boundary condition is suggested on an artificial circular cylindrical surface by which the fluid domain is divided into an interior region with finite volume and an exterior region. A unique solution of wave motion in the interior region is guaranteed by the novel boundary condition on the artificial cylindrical surface and the other boundary conditions on mean free water surface and undulated seabed. The solution is obtained by using Boundary Integral Equation (BIE) with all boundary conditions including the novel artificial boundary condition. Upon verification for a submerged square cylinder, the present model is extended to the case of an array of rounded-rectangular cylinders or circular paraboloidal shoals.

Anterolateral Thigh Flap Coverage for Large Posterior Defects of the Elbow.

This study highlights the advantages and disadvantages of Anterolateral Thigh (ALT) free flap using the brachial artery as the recipient vessel in large posterior defects of the elbow with early mobilization. Eight patients with a soft tissue defect on the posterior elbow underwent reconstruction with an ALT free flap. Average age and follow-up were 29.5years (range, 18-43years) and 54months (range, 35-76months), respectively. All defects were on the posterior side, and brachial arteries on the anterior side were used as the recipient artery in all cases. Four defects were created by tumor excision, four were exposed with hardware after fixation of distal humeral and/or proximal ulna fractures. The dimensions of defects were between 80 and 352cm2. Cases were evaluated according to function (ROM), complications, tissue quality anticipated from reconstruction and immobilization time after the reconstruction. All flaps except one survived and met the tissue quality anticipated from this reconstruction. In the bigger flaps, an apparent ugly scar at the donor site was the main problem. The flap on the posterior, and recipient artery on the anterior had no adverse effects on early motion of the elbow. Two cases with fractures had minimal restriction of elbow movement due to post-traumatic stiff elbow. There was one case of partial flap loss after myocardial infarction. After the patient was medically stable, the remaining distal defect was closed with a pedicled radial forearm flap. ALT free flap has numerous advantages in covering defects at the posterior elbow such as being pliable, thin and durable skin, with a long and reliable pedicle reaching the brachial artery without causing any problem in early motion and surgical reconstruction can be easily completed in the supine position.

To the Problem of Motion Cueing Simulation on a Robotic Stand for Aircraft Flight

Various simulators with motion cueing simulation stands, which make it possible to create an acceleration environment for the pilot that is close to a real flight, are used for training aircraft pilots. The article considers the formulation of the motion cueing simulation on a stand based on an industrial manipulator. Motion cueing simulation algorithms include two phases: motion cueing simulation phase and phase of return to the working area center. During simulation phase the stand must implement such a movement that the angular accelerations acting on the person and the overload vector acting on the center of mass of the operator completely coincide with the real ones. If it is not possible then just the directions of these vectors should coincide. During the second phase the stand end point must return to the working area center with acceleration values below the threshold, but in the fastest way. This task can be presented as a generalization of the brachistochrone problem. The article considers the problem of the material point motion in a uniform gravity field along a curve located in a vertical plane, in the presence of restrictions on the trajectory curvature. It is necessary to choose the curve shape in such a way that the descent time is minimal. The problem solution is obtained by optimal control methods, the cases of regular and singular control realization are considered, the question of its conjugation. Also, the switching number between sections of regular and singular control is studied.

Clinical implications of compromised 82Rb PET data acquisition

BackgroundWe wished to document the prevalence and quantitative effects of compromised 82Rb PET data acquisitions on myocardial flow reserve (MFR). Methods and ResultsData were analyzed retrospectively for 246 rest and regadenoson-stress studies of 123 patients evaluated for known or suspected CAD. An automated injector delivered pre-determined activities of 82Rb. Automated quality assurance algorithms identified technical problems for 7% (9/123) of patients. Stress data exhibited 2 instances of scanner saturation, 1 blood peak detection, 1 blood peak width, 1 gradual patient motion, and 2 abrupt patient motion problems. Rest data showed 1 instance of blood peak width and 2 abrupt patient motion problems. MFR was lower for patients with technical problems flagged by the quality assurance algorithms than those without technical problems (1.5 ± 0.5 versus 2.1 ± 0.7, P = 0.01), even though rest and stress ejection fraction, asynchrony and relative myocardial perfusion measures were similar for these two groups (P > 0.05), suggesting that MFR accuracy was adversely affected by technical errors. ConclusionIt is important to verify integrity of 82Rb data to ensure MFR computation quality.

Modeling and Control of Satellite Formations: A Survey

This survey deals with the problem of the group motion of spacecraft, which is rapidly developing and relevant for many applications, in terms of developing the onboard control algorithms to ensure the fulfillment of a given mission. The paper provides a comprehensive overview of spacecraft formation flight control. The bibliography is divided into three main sections: the multiple-input–multiple-output approach, in which the formation is treated as a single entity with multiple inputs and multiple outputs; the leader–follower formation, in which individual spacecraft controllers are linked hierarchically; and a virtual structure formation, in which spacecraft are treated as rigid bodies embedded in a common virtual rigid body. This survey expands a 2004 survey and updates it with recent results.

Application of the Kovacic algorithm for the investigation of motion of a heavy rigid body with a fixed point in the Hess case

AbstractIn 1890, Hess found new special case of integrability of Euler–Poisson equations of motion of a heavy rigid body with a fixed point. In 1892, Nekrasov proved that the solution of the problem of motion of a heavy rigid body with a fixed point under Hess conditions reduces to integrating the second‐order linear differential equation. In this paper, the corresponding linear differential equation is derived and its coefficients are presented in the rational form. Using the Kovacic algorithm, we proved that the Liouvillian solutions of the corresponding second‐order linear differential equation exist only in the case, when the moving rigid body is the Lagrange top, or in the case, when the constant of the area integral is zero.

Moving Object Detection Based on Weighted Kernel Norm and Saliency Constrained RPCA

Focusing on the issue that the accuracy of object detection is reduced when the foreground target moves slowly and there is interference in the background, a moving object detection method based on weighted kernel norm and saliency constraint RPCA is proposed. In the new method, the weighted kernel norm is used to restore a relatively clean background, which is helpful to separate the slow moving target from the background. The l 1 norm is used to constrain the sparsity of moving objects, and the Frobenius norm is used to detect noise, and a saliency constraint is introduced to detect slow-moving objects. Experiments show that this method can effectively deal with the problems of slow foreground motion and background interference. Compared with the suboptimal algorithm, the average measured value F of the proposed algorithm is improved by 15%.

Problem of Motion of a Rigid Body with a Fixed Point in a Particle Flow

Problem of Motion of a Rigid Body with a Fixed Point in a Particle Flow

Spacecraft Relative Motion Dynamics and Control Using Fundamental Modal Solution Constants

This paper explores expressing the relative state in the close-proximity satellite relative motion problem in terms of fundamental modal solution constants. The nominal uncontrolled relative state can be expressed in terms of a weighted sum of fundamental and geometrically insightful modal motions. These fundamental motions are obtained using the Lyapunov–Floquet theory. In the case that the dynamics are perturbed by the action of a controller or by unmodeled dynamics, the weights on each fundamental solution are allowed to vary as in a variation-of-parameters approach, and in this manner function as state variables. This methodology reveals interesting insights about satellite relative motion and enables elegant control approaches. This approach can be applied in any dynamical environment as long as the chief orbit is periodic, and this is demonstrated with results for relative motion analysis and control in the eccentric Keplerian problem and in the circular restricted three-body problem. Some commentary on the extension of the methodology beyond the periodic chief orbit case is also provided. This is a promising and widely applicable new approach to the close-proximity satellite relative motion problem.

A numerical technique to solve a problem of the fluid motion in a straight plane rigid duct with two axisymmetric rectangular constrictions. An alternative approach

A numerical technique is devised to solve a problem of the steady laminar fluid motion in a straight plane hard-walled duct with two local axisymmetric rectangular constrictions. It uses the stream function, the vorticity and the pressure as the basic variables, has the second order of accuracy in the spatial and the first order of accuracy in the temporal coordinates, provides high stability of a solution, and needs significantly less computational time to obtain a result compared to appropriate techniques available in a scientific literature. The technique consists in: a) introducing the stream function and the vorticity, and subsequent transiting from the non-dimensional governing relations for the fluid velocity and the pressure to the corresponding non-dimensional relations for the stream function, the vorticity and the pressure; b) deriving their discrete counterparts in the nodes of the chosen space-time computational grid; c) integrating the systems of linear algebraic equations obtained after making the discretization. The discretization is based on applying appropriate differencing schemes to the terms of the equations for the basic variables. These are the two-point temporal onward difference for the unsteady term of the vorticity equation, as well as the two-point backward differences (for its convective term) and the five-point approximations (for its diffusive term and for the Poisson’s equations for the stream function and the pressure) in the axial and cross-flow coordinates. As for the velocity components, the appropriate central differences are applied to discretize their expressions. The above-mentioned systems of linear algebraic equations for the stream function and the pressure are integrated by the iterative successive over-relaxation method. The algebraic relation for the vorticity does not need application of any method to be solved, because it is a computational scheme to find this quantity based on the known magnitudes computed at the previous instant of time.

Obstacle avoidance flocking motion in multi-agent systems with limited sensing radius and heterogeneous input constraints

This paper addresses the leaderless and leader-followers flocking motion problems of multi-agent systems in a workspace with obstacles. We consider inertial agents with equally limited communication radius and heterogeneous input constraints. Using the notion of proximity graphs, we provide distributed controllers to induce the desired flocking behaviour. Unlike previous results, our controller designs do not require predicted states or a target determination scheme and allow edge deletions. Also, by taking advantage of the group's heterogeneity, our controllers allow agents with less restrictive input constraints to compensate for the control effort that their less capable neighbours cannot provide. We illustrate the effectiveness of our proposals through numerical simulations.