Uniform Rectilinear Motion Research Articles

Application of Difference Schemes to Decision the Pursuit Problem

The problem of the pursuit curve construction in the case when the tangent to pursuer’s motion trajectory passes at any time through the point representing the pursued is considered. A new approach to construct the pursuit curves using difference schemes is proposed. The proposed technique eliminates the need to derive the differential equations for the description of the pursuit curves, which is quite difficult task in the general case. In addition, the application of difference methods is justified in a situation where it is complicated to find the analytical solution of an existing differential equation and it is possible to obtain the pursuit curve only numerically. Various modifications of difference schemes respectively equivalent to the Euler, to the Adams – Bashforth and to the Milne methods are constructed. Their software implementation is realized by using the mathematical package Mathcad. We consider the case of a uniform rectilinear motion of the pursued whose differential equation describing the path of the pursuer and its analytical solution are known. We compare the numerical solutions obtained by the different methods with the well-known analytical solution. The error of the obtained numerical solutions is examined. Moreover, an application is considered illustrating the construction of the difference schemes for the case of an arbitrary trajectory of the pursued. Also, we extend the proposed method to the case of cyclic pursuit with several participants in the three-dimensional space. In particular, we construct a difference scheme equivalent to the Euler method for a three-dimensional analogue of the "bugs problem". The results obtained are demonstrated by means of animated examples for either two-dimensional or three-dimensional cases.

Algorithm for Reconstructing EAS-Type Events of the TUS Orbital Detector

On April 28, 2016, the TUS (Tracking Ultraviolet Setup), an orbital detector of extreme energy cosmic rays (EECRs) was launched into near-Earth orbit as a part of the Lomonosov satellite’s scientific equipment. The detector measures the fluorescent radiation of extensive air showers (EASes) appearing in the atmosphere after cosmic rays with energies of 100 EeV and higher penetrate into it. An algorithm is presented for reconstructing directions of the arrival of an EECR particle, based on an approximation of the track (EAS image) on the photodetector matrix in the form of a uniform rectilinear motion of a point (the image’s centroid). The technique is validated and its accuracy in the case of a Gaussian point spread function (PSF) is estimated using model examples. It can be used when reconstructing events of the TUS and similar missions in the future (e.g., K-EUSO).

OF IMITATION OF THE OPTICAL LOCATION DEVICE UNIFORM MOTION

The aim of the work is to develop a method of physico-mathematical modeling of opticalelectronic systems functioning conditions that solve the problem of reducing the time and cost of experimental studies.The main idea of the simulation method was to replace the uniform rectilinear motion of an optical-location device (OLD) with respect to the object under investigation by scanning its field of view along a fixed MS.Physical modeling of the OLD uniform motion was carried out by scanning the radiation along a reflecting surface bent according to the Archimedes’ helix shape.The mechanical and mirror scanning methods schemes of radiation by a spiral MD are presented. The criteria for the suitability of scanning methods for various types of OLD depending on the radiation pattern of the receiving-transmitting unit, the scanner’s mirror size and the angle of its installation, as well as the range of simulated driving speeds are indicated.A mathematical model of the simulation method, which determines the dependence of the OLD amplitude of the reflected radiation on the distance (the law of squares of distances) and the angle of incidence of the radiation on the MD (Lambert’s law), was developed.A functional analysis is carried out and the calculation results of the dependence on the MD radiation angle incidence on the polar radius rotation angle, which determines the simulated range value, are presented. The variation limits of the distance measuring relative error from 20 to 9%, introduced by the variable angle of radiation reflection in the range of the radiation incidence angle of 0 ... π, respectively, are established. The analytical expression for the angular correction of the reflected radiation amplitude, which compensates for the angular error of the simulation method, is given.The field and simulation measurements results of the OLD base model distance characteristics based on an optocoupler LED AL107 - FD155K photodiode are presented.Comparison of the results showed ascent at small distances with a tendency to decrease with increasing distance. In this case, the absolute measurement error is significantly reduced as a result of the calculated angular correction. The average value of the simulation measurements relative error was ~ 20%, and taking into account the angular correction - ~ 15%.The work results showed the applicability of the method of OLD uniform rectilinear motion imitation using a spiral MS.

Circular and rectilinear Sagnac effects are dynamically equivalent and contradictory to special relativity theory

The Sagnac effect, named after its discoverer, is the phase shift occurring between two beams of light, traveling in opposite directions along a closed path around a moving object. A special case is the circular Sagnac effect, known for its crucial role in GPS and fiber-optic gyroscopes. It is often claimed that the circular Sagnac effect does not contradict special relativity theory (SRT) because it is considered an accelerated motion, while SRT applies only to uniform, non-accelerated motion. It is further claimed that the Sagnac effect, manifest in circular motion, should be treated in the framework of general relativity theory (GRT). We counter these arguments by underscoring the fact that the dynamics of rectilinear and circular types of motion are completely equivalent, and that this equivalence holds true for both non-accelerated and accelerated motion. With respect to the Sagnac effect, this equivalence means that a uniform circular motion (with constant w) is completely equivalent to a uniform rectilinear motion (with constant v). We support this conclusion by convincing experimental findings, indicating that an identical Sagnac effect to the one found in circular motion, exists in rectilinear uniform motion. We conclude that the circular Sagnac effect is fully explainable in the framework of inertial systems, and that the circular Sagnac effect contradicts special relativity theory and calls for its refutation.

The one-dimensional asymmetric persistent random walk

Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic and symmetric 1D persistent random walk is governed by the telegrapher’s equation, also called the hyperbolic heat conduction equation. These equations have been designed to resolve the paradox of the infinite speed in the heat and diffusion equations. The finiteness of both the speed and the correlation length leads to several classes of random walks: Persistent random walk in one dimension can display anomalies that cannot arise for Brownian motion such as anisotropy and asymmetries. In this work we focus on the case where the mean free path is anisotropic, the only anomaly leading to a physics that is different from the telegrapher’s case. We derive exact expression of its Green’s function, for its scattering statistics and distribution of first-passage time at the origin. The phenomenology of the latter shows a transition for quantities like the escape probability and the residence time.

Study of Kynematics and Dynamics in the Traffic of Rembangan Tourism in the Jember Regency as Learning Resources for Physics Learning in the Senior High School

One branch of physics is mechanics. Based on interviews to Senior High School teacher in Jember, mechanics is difficult to learn. The eksternals factor this chapter is dificult to learn is learning Resources. The learning Resources are often less contextuall with around the phenomenon of students. The contextuall learning Resources in the Jember Regency is study of kynematics and dynamics in the traffic of Rembangan Tourism. From this experiment, we get data can be used as a learning resources chapter uniform rectilinear motion, decelerated uniform rectilinear motion, accelerated uniform rectilinear motion, Newton’s Law, and circular motion.

Optimization of Rectilinear Motion Experiments using Tracker Application

Physics is one part of Natural Sciences which underlies the development of technology, so that the process of learning Physics should not only emphasize the mastery of the concept but also on aspects of the discovery as the scientist did. Therefore, experimental activities are considered very important in Physics learning. In the experimental activities, it is important to have appropriate tools and methods of measurement to obtain accurate findings. One of the experimental activities of physics which conducted in school is a uniformly acceleration rectilinear motion using a set of dynamics train experiment and Atwood experiment. The measurement methods of both experiments generally use conventional tools, i.e. ruler, stopwatch and ticker timer that are susceptible to interruptions and errors in the data acquisition process. One method of measuring and processing data that considered has more precision is to use the application tracker. In this research, a uniform rectilinear motion kinematics experiments have been done with two methods of measurement using conventional tools and compared with using the tracker by recording the movement of objects using high definition camera (HD) with 24 fps shooting speed. The results showed that the result using tracker to produce some acceleration data is more constant than the result using conventional methods. In addition, time-positions graphs (s = f (t)) are formed in the form of quadratic and time-velocity graphs (v = f (t)) are straight lines with a constant gradient corresponding to the rectilinear motion theory. Based on the results of the research, the use of tracker application in the experimental kinematics of rectilinear motion produces more accurate data so it can be used as an alternative to optimize the experiments of rectilinear motion.

Process of establishing a plane-wave system on ice cover over a dipole moving uniformly in an ideal fluid column

We consider a planar evolution problem for perturbations of the ice cover by a dipole starting its uniform rectilinear horizontal motion in a column of an initially stationary fluid. Using asymptotic Fourier analysis, we show that at supercritical velocities, waves of two types form on the water–ice interface. We describe the process of establishing these waves during the dipole motion. We assume that the fluid is ideal and incompressible and its motion is potential. The ice cover is modeled by the Kirchhoff–Love plate.

O projeto “Lançamento de Projéteis”: uma perspectiva para o ensino e aprendizagem da matemática no ensino médio

http://dx.doi.org/10.5007/1981-1322.2016v11n2p300Este artigo apresenta resultados do projeto Lançamento de Projéteis, desenvolvido por um grupo de estudantes do terceiro ano do Ensino Médio, no âmbito de uma pesquisa cujo objetivo foi investigar o desenvolvimento de Projetos de Trabalho, considerando diferentes estratégias, procedimentos e recursos, visando à construção de conhecimentos matemáticos. O trabalho possibilitou a retomada e desenvolvimento de conhecimentos relacionados às áreas de Matemática e Física, sendo que, particularmente, foram desenvolvidos aspectos referentes às Funções Afim e Quadrática, Movimento Retilíneo Uniforme e Uniformemente Variado e do Lançamento Oblíquo. Para tal, foram utilizados elementos advindos da Modelagem Matemática, bem como utilizado o software Excel para construir, modelar e analisar as situações que se apresentaram. O trabalho constituiu-se, também, em possibilidade de modificação do papel do professor e dos estudantes, permitindo a esses tornarem-se atuantes e participativos, a partir de ações que envolveram trabalho em grupo, organização, planejamento, pesquisa e o enfrentamento e solução de situações tanto práticas quanto teóricas.

The Algorithm for Compensating Distortion of Images of Type “Blur”

The paper considers the model of linear blurring with a uniform rectilinear motion of an object when its speed is constant, and its direction is parallel to the lines of the formed image. An algorithm for linear blurring compensation based on the account of the physical processes of its formation when obtaining the images is proposed. A system of equations for the restoration of the original video signal samples undistorted image of the object is obtained. Processed the frame of a real video sequence with a horizontal blur and presented its results. Considered the comparison of the results of the restoration of distorted images by the proposed algorithm with known methods.

An acoustic space-time and the Lorentz transformation in aeroacoustics

In this paper we introduce concepts from relativity and geometric algebra to aeroacoustics. We do this using an acoustic space-time transformation within the framework of sound propagation in uniform flows. By using Geometric Algebra we are able to provide a simple geometric interpretation to the space-time transformation, and are able to give neat and lucid derivations of the free-field Green's function for the convected wave equation and the Doppler shift for a stationary observer and a source in uniform rectilinear motion in a uniform flow.

An Acoustic Space-Time and the Lorentz Transformation in Aeroacoustics

In this paper we introduce concepts from relativity and geometric algebra to aeroacoustics. We do this using an acoustic space-time transformation within the framework of sound propagation in uniform flows. By using Geometric Algebra we are able to provide a simple geometric interpretation of the space-time transformation, and are able to give neat and lucid derivations of the free-field Green's function for the convected wave equation and the Doppler shift for a stationary observer and a source in uniform rectilinear motion in a uniform flow.

Rigorous treatment of barycentric stellar motion

High-precision astrometric and radial-velocity observations require accurate modelling of stellar motions in order to extrapolate measurements over long time intervals, and to detect deviations from uniform motion caused for example by unseen companions. We aim to explore the simplest possible kinematic model of stellar motions, namely that of uniform rectilinear motion relative to the Solar System Barycentre, in terms of observable quantities including error propagation. The apparent path equation for uniform rectilinear motion is solved analytically in a classical (special-relativistic) framework, leading to rigorous expressions which relate the (apparent) astrometric parameters and radial velocity to the (true) kinematic parameters of the star in the barycentric reference system. We present rigorous and explicit formulae for the transformation of stellar positions, parallaxes, proper motions, and radial velocities from one epoch to another, assuming uniform rectilinear motion and taking into account light-time effects. The Jacobian matrix of the transformation is also given, allowing accurate and reversible propagation of errors over arbitrary time intervals. The light-time effects are generally very small but exceeds 0.1 mas or 0.1 m/s over 100 yr for at least 33 stars in the Hipparcos Catalogue. For high-velocity stars within a few tens of pc from the Sun light-time effects are generally more important than the effects of the curvature of their orbits in the Galactic potential.

Universal Practical Tracking Control of a Planar Underactuated Vehicle

AbstractIn this article, a universal controller is proposed for a planar underactuated vehicle to track arbitrary trajectories including feasible/non‐feasible ones and fixed points. The controller design relies on several coordinate/input transformations, auxiliary trajectory design and the back‐stepping technique. The stability analysis shows that the position and orientation tracking errors are uniformly globally practically asymptotically convergent (UGPAC), and the velocity tracking errors are uniformly globally asymptotically convergent (UGAC) to a ball of origin. Moreover, if the tracked target is in uniform rectilinear motion or motionless, the whole closed‐loop tracking error system is uniformly globally practically asymptotically stable (UGPAS). The effectiveness of proposed control law is verified by simulation examples.

The Blurring and Restoring Process of the Moving Object Images

For the relative motion between an imaging system and its objects, it results in motion-blurred images in acquiring images. The physical theory of motion-blurred images for moving objects are analyzed in this paper, then the motion-blurred process is researched to establish blurring-model and the essential elements of the process are extracted to form the expressions. The every grey scale value of images pixels is computed and processed to form the motion-blurred images, then based on the contradictorily computing analysis, the restoring model of blurring imaging is established and the restoring expressions are gained. The processing courses of motion-blurred and restoring images are achieved by computing program VC++. The simulation experiments show that the method of images process can be used to make motion-blurred images and restoring images when the objects motion is two dimensions uniform velocity rectilinear motion effectively.

Determination of line scan camera parameters via the direct linear transformation

A direct linear transformation (DLT) model is derived to describe the scan imagery of a line scan camera undergoing a uniform rectilinear motion. When more than five points on scan image and their corresponding three-dimensional space points are substituted in the DLT model, 11 coefficients are settled directly and linearly without any approximations. After that, the 11 physically meaningful line scan camera parameters are worked out from the 11 DLT coefficients through a group of analytical operations. The performance is tested and verified by both simulated experiment and demonstration of a real line scan camera.

Kinematic Characteristics and Optimization Analysis of Oval Geared Hoeken Mechanism

Kinematic characteristics of Hoeken mechanism is analyzed. Variable ratio transmission characteristics of oval gear is obtained. Oval geared Hoeken mechanism is presented. Kinematic characteristics of oval geared Hoeken mechanism is clarified. Eccentricity is optimized. The oval geared Hoeken mechanism with approximate uniform rectilinear motion is designed. The methods in this paper facilitate the innovation design of the mechanism with approximate uniform rectilinear motion.

Frequency Characteristics Analysis of Simulated Horizontal and Vertical Motion Blurred Image

This paper based on the degradation model of the blurred image by uniform rectilinear motion, simulated horizontal and vertical motion blurred images. The Fourier transform method was employed to analyze the frequency characteristics of blurred images. The simulation test result shows that ideally via the frequency characteristics of the blurred images, we can obtain the motion parameter, including distance and direction. These can be of great useful for image restoration of many blurring circumstances such as camera and printing images.

Kinematic Analysis and Optimization Design of Elliptical Geared Double-Rocker Mechanism

Kinematic characteristics of double-rocker mechanism is analyzed. Based on variable ratio transmission characteristics of elliptical gear, elliptical geared double-rocker mechanism is presented. Kinematic characteristics of elliptical geared double-rocker mechanism is clarified. Eccentricity is optimized. The elliptical geared double-rocker mechanism with approximate uniform rectilinear motion is designed. The methods in this paper facilitate the innovation design of the mechanism with approximate uniform rectilinear motion.

Line-scan camera calibration in close-range photogrammetry

A novel line-scan camera calibration method in close-range photogrammetry is proposed. Since the line-scan camera is only sensing in one dimension, it's hard to recognize the space points from the linear data captured in static state. To address this problem, the camera is fixed to a programmable linear stage. With the help of the linear stage, a scan image of the pattern is grabbed by the line-scan camera in uniform rectilinear motion state. Therefore, the image points are definitely matched with the space points on the pattern. A pair of projective equations is established to describe this dynamic imaging model, which is determined by six extrinsic camera parameters, five intrinsic camera parameters and three other motion parameters. All the fourteen parameters are estimated approximately by using the direct linear transformation of a reasonably simplified camera model firstly, and then the results are further refined by non-linear least square mean (LSM). Both computer simulated data and real data are used to test our calibration method. The robustness and accuracy are verified by lots of simulated experiments, and for the real data, the root mean square error of re-projected points is less than 0.3 pixels.