Theory Of Motion Research Articles

Application of simple harmonic motion theory to the prediction of floating wind turbine first order motions

An alternative solution for achieving a high stability floating foundation for supporting large horizontal axis wind turbines is compared against current floating offshore wind solutions. The testing of a 1:36th scale model of the solution, called Starfloat, in the wind/wave basin of the Cantabria Coastal and Ocean Basin, Santander and the design of this physical model, including scaling issues, is discussed. A method for calculating the added mass of entrained water in heave and surge and the added mass moment of inertia in pitch for semi-submerged cylindrical columns is presented and the computed natural periods of motion are compared against physical trial measurements obtained from motion decay tests. The wave forces exciting the simple harmonic motion are calculated and the resultant approximate solution for the uncoupled floating platform motions in heave, pitch and surge are compared against response amplitude operator curves obtained from the physical model trials, showing reasonable correlation. The importance of depth correction for wave particle velocities and accelerations is very evident and emphasises the need for physical models to be exposed to the correct orbital particle motions over the water column if measured pitch and surge motions are to be a realistic representation of full scale performance.

Formal Verification of Robot Rotary Kinematics

With the widespread application of robots in aerospace, medicine, automation, and other fields, their motion safety is essential for the well-being of humans and the accomplishment of vital socially beneficial programs. Conventional robot hardware and software designs mainly rely on experiential knowledge and manual testing to ensure safety, but this fails to cover all possible testing paths and adds risks. Alternatively, formal, mathematically rigorous verifications can provide predictable and reliable guarantees of robot motion safety. To demonstrate the feasibility of this approach, we formalize the mathematical coordinate transformation of a robot’s rigid-body kinematics using the Coq Proof Assistant to verify the correctness of its theoretical design. First, based on record-type matrix formalization, we define and verify a robot’s spatial geometry by constructing formal expressions of the matrix’ Frobenius norm, trace, and inner product. Second, we divide rotary motion into revolution and rotation construct and provide their formal definitions. Next, we formally verify the rotational matrices of angle conventions (e.g., roll–pitch–yaw and Euler), and we complete the formal verification of the Rodriguez formula to formally verify the correctness of the motion theory in specific rotating kinematics problems. The formal work of this paper has a variety of essential applications and provides a generalizable kinematics analysis framework for robot control system verification. Moreover, it paves the way for automatic programming capabilities.

THEORETICAL SUBSTANTIATION OF THE RESULTS OF MEASURING ANOMALIES OF SPACECRAFT TRAJECTORIES

It is about the solar acceleration of spacecraft. The prevailing opinion that classical properties of the fundamen¬tal laws of statics can be successfully used in the celestial mechanics of low speeds (v << c) has been refuted because the involvement of relativistic methods does not improve the situation due to the smallness of the gravity mag¬netic acceleration. The essence of the problem is that the known classic methods of the theory of motion operate solely on the transverse component of the velocity vector concerning the orientation of the radius vector of the gravitational interaction. In the article, an insufficient longitudinal component was introduced into the electrogravity theory of motion, the effect of which turned out to be an order of magnitude higher than the effect of the transverse one.

Research on the Mechanism of Treating Insomnia with Wendan Decoction from the Theory of Circular Motion

Research on the Mechanism of Treating Insomnia with Wendan Decoction from the Theory of Circular Motion

Internal lipid bilayer friction coefficient from equilibrium canonical simulations

A fundamental result in the theory of Brownian motion is the Einstein-Sutherland relation between mobility and diffusion constant. Any classical linear response transport coefficient obeys a similar Einstein-Helfand relation. We show in this work how to derive the interleaflet friction coefficient of lipid bilayer by means of an adequate generalisation of the Einstein relation. Special attention must be paid in practical cases to the constraints on the system center of mass position that must be enforced when coupling the system to thermostat.

Center manifold theory for the 1-dimensional collective motions of camphor disks with delta functions in the <inline-formula><tex-math id="M1">$ L^2 $</tex-math></inline-formula>-framework

Camphor boat and disk are types of interfacial self-propellers that rely on the modification of forces present at the air-liquid interface. In a one-dimensional circuit, self-organized congestion and clustering phenomena are observed experimentally and numerically [11,43]. Although the center manifold theories proposed in [5,7] are useful in the analysis of collective motions, the requirement in the reduction process is not fulfilled because the linearized operator involves Dirac delta functions. To overcome such mathematical difficulties, a theory in the $ (H^1)^* $-framework was developed in [17]. However, the reduced equation does not include any nonlinearity. Thus, information on the collective motions could not be obtained. The objectives of the present study are to propose a new approach to establish the existence and uniqueness of a center manifold in a system with delta functions in the $ L^2 $-framework and to derive a reduced system with suitable nonlinearity from the original model in [33].

Velocity distribution and hydrodynamic drag in turbulent flow

This work aims to study the vertical velocity distribution in the near-wall layer of a pipe, channel, and boundary layer of a flat plate because these issues are of great practical and theoretical importance. Until now, engineering calculations of turbulent flows have been based on empirical formulas derived in the last century. The theory of turbulent fluid motion has not been completed, and the issues of velocity distribution and hydraulic resistance remain open for further study. It is known that velocity distribution in the flow is intricately linked to hydraulic resistance. Therefore, the study’s objectives also include determining the position of the point of maximum turbulent tangential stresses and comparing the change in tangential stresses with the logarithmic velocity profile. Based on calculation and analytical methods, we have researched the distribution of the turbulent component of the tangential stress along the depth of the flow. Derived an expression determining the position of the maximum point of the turbulent component of the tangential stress for smooth tubes. The contribution of the viscous component of the tangential stress at different points along the flow depth has been evaluated. The calculation results determining the position of the maximum point of the turbulent component of the tangential stress were compared with experimental data on velocity distribution in the flow. With the decrease of the hydraulic resistance coefficient, the point of maximum turbulent tangential stresses shifts towards the solid flow boundary. Based on the results of comparing the maximum turbulent tangential stresses with the total tangential stress, we can conclude that the contribution of the viscous component of the tangential stress to the total amount of friction and its influence on velocity distribution is significant. The angular coefficient of the velocity profile for the flow core is determined.

Kinetics study of ions in conductive filament growth process of electrochemical metallization resistive memory

<sec>In this work, a system of modified Mott-Gurney differential equations is based on Arrhenius’ law and the overpotential theory of ionic motion in bipolar electrochemical metallization (ECM) resistive devices. The average displacement of ions is solved by the modified Mott-Gurney equation. Then, the relation between the average displacement and the growth length of the conductive filament is obtained by a geometric model based on cells. The equation of applied voltage versus Forming/Set time and the equation of length of conductive filament growth versus time are deduced by using this relation.</sec><sec>In this work, an algorithm for extracting kinetic parameters of ions in a bipolar ECM device is also proposed. By using this algorithm, the characteristics of the applied voltage versus Forming/Set time for Ag/<i>γ</i>-AgI/Pt, Ag/TiO<sub>2</sub>/Pt, Ag/GeS<sub>2</sub>/W, and Cu/SiO<sub>2</sub>/Au devices are calculated and the calculation results are consistent with experimental data. It is found that in the Forming/Set process, the jump step of silver ion is the lattice constant along the <i>c</i> direction of a unit cell of the crystal for TiO<sub>2</sub> and the lattice constant of the cubic, <i>a</i>, for <i>γ</i>-AgI. These results are explained in the following. In a unit cell of the two crystals there are some tetrahedral and octahedral interstitial sites. The cationic motion path consists of alternating octahedral and tetrahedral sites or some octahedral sites. The cation jumps from tetrahedron to octahedron to tetrahedron, etc. in the <i>γ</i>-AgI with coplanar polyhedron and from octahedron to octahedron in the TiO<sub>2</sub> with edge shared octahedron. In GeS<sub>2</sub> crystal, it is found that the jump step of silver ions is the lattice constant in the <i>c</i> direction of a unit cell. Owing to the periodicity of the lattice, the pathways of the ion motion in the three materials can be expressed by a periodic potential barrier each. For the jump situation of the copper ion in amorphous SiO<sub>2</sub>, the jump step of copper ions is calculated to be 1.57 times the length of the O—O bond, and the jump pathway can also be explained by a periodic potential barrier.</sec><sec>By introducing the cosine potential barrier, the ionic activation frequency, potential barrier height, ionic mobility and diffusion coefficient, and characteristics of the conductive filament growth versus time in several devices are calculated. The criteria of selecting dielectric materials for bipolar ECM devices are discussed by using these data. It is found that the standards for selecting dielectric materials of bipolar ECM devices are the ion activation energy ≤0.5 eV, preferably between 0.1–0.2eV, and the DC conductivity as close to 10<sup> –4</sup> Ω<sup>–1</sup>·cm<sup>–1</sup> as possible.</sec>

Directional transport of two-dimensional coupled Brownian particles subjected to nonconserved forces

<sec>In recent years, biomolecular motors have received widespread attention. Biomolecular motors are biological macromolecules that convert chemical energy into mechanical energy. The biomolecular motor is only a few tens of nanometers in size. According to Brownian theory of motion, people have constructed different types of Brownian ratchet models, such as rocking ratchets and closed-loop control ratchets. In previous studies, the directional transportation of Brownian ratchet is affected by conservative forces. These conservative forces include constant force, elastic force or harmonic force. However, whether the ratchet system can produce directional motion under the action of non-conservative forces is still rarely studied. Owing to the complex environment in the organism, for the studies of two-dimensional systems, the transport behavior of molecular motor has not been fully explained. Therefore, it is more practical to study the transport of Brownian particles in a two-dimensional ratchet potential.</sec><sec>The directional transport of two-dimensional Brownian particles subjected to conservative forces and non-conservative forces are studied in this work. It is found that the non-conservative external force has the effect of promoting the directional transport of coupling ratchets. With the change of the free length of the spring and spring coefficient, the average velocity of the coupled particles can be reversed. This means that the coupling effect can induce the inversion of two-dimensional Brownian ratchets. At the same time, the reverse transportation of coupled particles is enhanced under the interaction effect of conservative forces (spring elasticity) and non-conservative external forces. By choosing different kinds of external forces (conserved and non-conserved), in the experiment, it is possible to provide new method of separating two-dimensional coupled Brownian particles.</sec>

Modeling the navigation of a weaver ant in a simple, unfamiliar environment

The ant species Oecophylla smaragdina, commonly known as the weaver ant, is native to tropical Asia and Africa. All ants are known for highly-organized, co-operative behavior and weaver ants are particularly adept at working together, in numbers, to accomplish large-scale tasks. Considered an example of a coherent many-body system, weaver ants have been studied by researchers in various fields. As a first step towards understanding weaver ant coordinated motion, we want to find the algorithm that a single ant employs for its own navigation. Having previously tracked the motion of individual ants within a small, bounded arena, we here present a simple theoretical model that can describe this motion. We show that their navigation can be adequately modeled as Brownian motion: the ant velocity changes by random impulses drawn independently from a robust probability distribution. Using established Brownian motion theory, we show that the ant’s tendency to remain near boundaries can be explained as a result of pure chance: having been stopped at the boundary, random motion is unlikely to bring the ant back to the arena interior. All qualitative aspects of ant motion are captured by a model with few parameters and without any assumptions about the ant’s intent. that an ant has preferences for position or velocity.

Dynamic light scattering in flowing dispersion

Dynamic light scattering is a standard technique of sub-micrometer particle sizing based on the theory of the Brownian motion, whereas it is not applicable when the particles undergo not only the random motion but also the directional movement, especially in uncertain direction. In this paper, we derive the intensity autocorrelation function of the scattered light for the particle systems containing random motion as well as directional movement. In contrast to the traditional one, the new function contains two additional sinc functions, corresponding to the contribution of the directional movement of the particles. These sinc functions accelerate the attenuation of the intensity autocorrelation function of the scattered light, and the attenuation rate is related to the direction of the directional movement. Interestingly, we found that the effect of the direction on the autocorrelation function can be eliminated when the incident light beam width is equal to the scattering volume width at the scattering angle of 90°. The experimental results are in good agreement with our derivation. Since our results can be applied to particle systems undergoing directional movement not only in a known direction, but also in an unknown direction, we believe it can extend the application of the technique of dynamic light scattering to investigate the complex fluid systems.

M. King Hubbert and "The Theory of Ground-Water Motion".

M. King Hubbert and "The Theory of Ground-Water Motion".

Theoretical and Experimental Designs of the Planetary Boundary Layer Dynamics through a Multifractal Theory of Motion

The accurate determination of atmospheric temperature with telemetric platforms is an active issue, one that can also be tackled with the aid of multifractal theory to extract fundamental behaviors of the lower atmosphere, which can then be used to facilitate such determinations. Thus, in the framework of the scale relativity theory, PBL dynamics are analyzed through the aid of a multifractal hydrodynamic scenario. Considering the PBL as a complex system that is assimilated to mathematical objects of a multifractal type, its various dynamics work as a multifractal tunnel effect. Such a treatment allows one to define both a multifractal atmospheric transparency coefficient and a multifractal atmospheric reflectance coefficient. These products are then employed to create theoretical temperature profiles, which lead to correspondences with real results obtained by radiometer data (RPG-HATPRO radiometer), with favorable results. Such methods could be further used and refined in future applications to efficiently produce atmospheric temperature theoretical profiles.

Students' perspective on offline and online learning in the Pencak Silat course

This study aims to examine the perspectives of students from the 2019 Health Physical Education and Recreation (PJKR) Program Study of the Faculty of Sport Science in State University of Malang regarding lectures using offline and online systems in the motion theory course and the martial arts practice course. The study used a quantitative descriptive survey design. The population of this study amounted to 227 students of the year 2019 PJKR Study Program. The sample of this study was 94 students and the analysis technique used was quantitative descriptive statistics. The results showed that student responses in offline lectures for theory courses were mostly positive as much as 94%, 79% positively agree with offline lectures for practical subjects, 70% respondents agree with online lectures for theory courses, and 89% students positively responded on online lectures for practical courses. Based on the research results obtained, it can be concluded that the response of the class of 2019 students to offline and online system lectures in theory and practice courses can be said to have been good and effective because they are in accordance with good learning principles.

UAV based adaptive trajectory tracking control with input saturation and unknown time‐varying disturbances

AbstractThis paper proposes an adaptive control method for an underactuated complex nonlinear system, that is, unmanned aerial vehicle (UAV), to realize high‐precision trajectory tracking under input saturation constraint and other disturbances via artificial neural network and anti‐saturation auxiliary system. First, the rigid body motion theory is applied to establish a simplified nonlinear dynamic model of the UAV. Then a Lyapunov function is designed with the error surface to form the preliminary control law based on dynamic surface control. Afterwards, a radical basis function neural network is developed and used to estimate and compensate the disturbance, while the input saturation is also addressed via the designed anti‐saturation auxiliary system. Thus the stability and signal consistency of the closed‐loop UAV control system can be proved via the Lyapunov stability theory with appropriately tuned parameters. Simulation experiments are performed to verify that the proposed control algorithm can be used for UAV high‐precision trajectory tracking under time‐varying disturbances.

Image encryption algorithm based on a new chaotic system with Rubik's cube transform and Brownian motion model

In this paper a new two-dimensional chaotic map based on Logistic map and Chebyshev map is proposed. The performance analysis and evaluation show the proposed map has a very wide range of chaos and good ergodicity. Further, a new image encryption algorithm is designed using the chaotic map with Rubik's Cube transform and Brownian motion model. The encryption process is ‘confusion - Rubik's cube transformation - diffusion’. In the confusion stage, a method combining Brownian motion theory and chaotic sequence is proposed. Then combining the advantages of chaotic system and Rubik's cube, a Rubik's Cube transformation algorithm is proposed. The scrambled pixel matrix and the chaotic matrix are spliced into a hexahedron structure, and the Rubik's Cube is dynamically scrambled through a pseudo-random sequence. Finally, the XOR operation is performed on the basis of the two-dimensional Hénon chaotic map. The experimental results show that the algorithm has the advantages of large key space, strong robustness and high security, and can resist common cryptanalysis attacks.

ДОСЛІДЖЕННЯ МОРЕХІДНОСТІ РИБАЛЬСЬКИХ СУДЕН ЗА ДОПОМОГОЮ CFD МЕТОДІВ

Seakeeping performance is quite important for certain ship types. Fishing vessels often operate in areas with frequent storms, and sometimes it is necessary to continue fishing despite the worsening sea state. The development of hull forms providing good seakeeping performance of fishing vessels is the problem of current interest in ship design. The conventional approach to seakeeping studies is testing models in ship model basins. However, it is time-consuming and expensive, especially when many hull form variants are studied. For this reason, computer calculations based on the theory of ship motions and strip theory were developed and introduced. Today the more advanced methods of computational fluid dynamics (CFD) can be applied to the problem. The study of ship motions with the help of Reynolds-averaged Navier-Stokes (RANS) CFD method is considered in this paper. A suggested numerical model implies the generation of waves through initial and boundary conditions, which express fully developed waves with preset parameters. An object of research is the seagoing trawler with an overall length of 44.6 m. Three versions of hull form are used in simulations. All versions have similar transom afterbodies, but different forebodies: one similar to Axe Bow, a bulbous bow and one similar to X-bow. Ship movement with headings 180° and 150° at speed of 3.5 knots was studied to reveal differences in added resistance and ship motions. While added resistance and characteristics of heaving and pitching have shown no clear advantages among the considered shapes of forebodies, the version similar to X-bow has demonstrated a significant decrease in rolling at heading 150°. The results of the study have shown that the suggested numerical setup in combination with the CFD methods described can be used for quite realistic simulations of ship behaviour in rough seas. Keywords: seakeeping simulations, seakeeping of fishing vessels, CFD for ship design, improved seakeeping performance, simulation of ship motions.

Projectile Motion in Midair Using Simple Analytical Approximations

The study of the motion of a projectile, thrown at an angle to the horizon, is a wonderful classical problem. This issue has been the subject of great interest to investigators for centuries. Currently, the study of parabolic motion, in the absence of any drag force, is a common example in introductory physics courses. The theory of parabolic motion allows you to analytically determine the trajectory and all important characteristics of the movement of the projectile. Introduction of air resistance forces into the study of the motion, however, complicates the problem and makes it difficult to obtain analytical solutions. This especially applies to the movement of the projectile, subjected to quadratic air drag force. Numerical studies of projectile motion with quadratic dependence on projectile speed have been performed in many works. From an educational point of view, many students are not confident with numerical methods and gain little insight from using them. So the description of the projectile motion by means of simple approximate analytical formulas under air resistance has great methodological and educational importance. The main goal of this work is to give analytical approximations for the projectile trajectory and movement characteristics as simple as possible from a technical point of view, in order to be grasped even by first-year undergraduates.

Badminton Skills Diagnostic Model (BSDM) Instrument Design: Based on Cybernetic Theory

This research aims to observe the contribution of the cybernetic-based badminton skills diagnostic model (BSDM) instrument design formulation as an effective instrument for achieving good motion analysis. Technical and tactical actions are very decisive in competitive badminton players' terms. The use of cybernetic theory becomes the diagnosing basis and improving skills. Cybernetics regulates a goal-directed self-regulation system based on the stimulus process, and the response that occurs. This study uses the Research & Development method. This process is carried out in four distinct steps: first, review of the scientific literature; second, qualitative and quantitative assessments were carried out by 8 experts in the fields of motion theory, tests and measurements and badminton; third, content validity was estimated using the Aiken V Coefficient; Finally, the intra-observer reliability and inter-observer reliability were tested by two badminton-specific observers using the Kappa Cohen coefficient and the intraclass correlation coefficient. For practicality and effectiveness, testing was carried out on 95 badminton players. Footwork, Execution, Shuttlecock running, and Stroke are used as units of measure by observation instruments in badminton. The data analysis process uses SPSS 25 statistical software. Based on the results, an observation instrument designed to be valid, reliable, and effective to analyze the technical and tactical actions of badminton playing skills. It is possible to analyze players who are lower class and elite class. The result of the flagship project is to present the instrument design solution of cybernetic-based badminton skills diagnostic model (BSDM).

On the theory of the issue of cleaning the filtration surface from accumulated contaminants during the processing of unrefined vegetable oils by vibration and ultrasonic oscillatory movements

The article presents the results of a theoretical analysis of the issue of cleaning the filtration surface from the sediment of contaminants that prevent the passage of the cleaned oil through the adsorption layer in the installation for cleaning oil from oxidation products. Based on the classical theory of oscillatory motion, the conditions necessary for the floating and mixing of sediment particles by reducing their sidementation stability are considered.