Mathematical Model Of Motion Research Articles

On the problem of optimal control of rotation axis reorientation of a spacecraft

Various variants of the formulation of optimal control problem of the reorientation of the axis of dynamic symmetry of the spacecraft (spacecraft), which is the axis of rotation, are considered. It is assumed that the solution to this problem should be found in the class of movements with one directional (flat) rotation, provided that before and after the reorientation of the axis of rotation, the angular velocity of the spacecraft is the same. In this case, the angular motion of the spacecraft is controlled according to the "rotary jet engine" scheme, when the control moment is limited by the ellipsoid of rotation. The corresponding mathematical model of spacecraft motion for the control problem under consideration is given. In addition to the formulation of the problem of the steepest reorientation of the axis of rotation of the spacecraft, the optimal control problem is also formulated, for which optimal control for the full control moment is found. In order to analyze the formulation of the problem under consideration, the results of its reduction to the boundary value problem and to the isoperimetric variational problem are also presented.

Identification of the electric motor mathematical model based on a data sample with feature engineering

The object of this study is a mathematical model of a synchronous electric motor, obtained on the basis of experimental data, which takes into account the temperature mode and uses artificial features to increase the accuracy of its operation. A characteristic feature of this work is that the model takes into account the temperature mode as a component of the technical-operational state of the object. The resulting mathematical model could make it possible to synthesize an optimal automatic control system in terms of the operational state of the object. The problem addressed was to increase the accuracy of the identified mathematical models by applying the approach of feature engineering. The results showed that the identification of mathematical models by the initial data leads to a low level of accuracy of the obtained models, namely 65–70 % for the first output channel, 80–85 % for the second, and 75–80 % for the third, fourth, and fifth output channels. Accordingly, building models with a higher threshold of accuracy requires the use of other, more significant data for identification. This paper reports a method for reformatting the original data into artificial features and provides results of their effectiveness in relation to the original channels. The resulting artificial features and the original features were used for further identification; the resulting mathematical model has on average higher accuracy thresholds, namely 82 %, 93 %, 88 %, 85 % for the corresponding output channels. The results prove the effectiveness of applying the principle of feature engineering since the accuracy of the resulting model is 5–10 % higher compared to the baseline. The scope of practical application of the results includes the synthesis of automatic control systems based on mathematical models of control objects obtained as a result of identification.

Exact solution of a mathematical model for human muscular motion

An ordinary differential equation (ODE) which models human muscular movement is considered. A functional form of the model parameter is specified through the Lie symmetry approach, yielding a different expression from the one derived in the previous study (Kosugi et al., 2019). The Lie point symmetries corresponding to the model parameter are employed for derivation of exact solution.

Applications of Optimal Transportation

The mathematical theory of optimal transportation is constantly expanding its range of application, while applications give impulses for new research directions in the field. This workshop was specifically devoted to applications of optimal transportation in the natural sciences, and to the recent developments of the theory that have been motivated by these. The bouquet of current applications includes mathematical models for large-scale air motion, dynamics of plasmas, material design, pattern formation in fluids, collective behaviour in biology, and many more. Related theoretical developments are in the analysis of the Hellinger-Kantorovich metric for modeling reaction–diffusion processes, and in efficient numerical methods for multi-marginal optimal transport, to name two of many examples encountered in this workshop.

Probabilistic solution of non-linear random ship roll motion by data-driven method

In this paper, a data-driven method is employed to investigate the probability density function (PDF) of nonlinear stochastic ship roll motion. The mathematical model of ship roll motion comprises a linear term with cubic damping and a nonlinear restoring moment represented as an odd-degree polynomial up to the fifth order. The data-driven method integrates maximum entropy, the pseudo-inverse algorithm, and a backpropagation (BP) neural network to obtain the PDF. The process begins with simulating data for the nonlinear stochastic system, followed by dimensional analysis to identify dimensionless parameter clusters. Optimization algorithms are then employed to solve for the coefficients, leading to the development of a BP neural network model trained to predict the PDF across various system characteristics and excitation intensities. The method's effectiveness is validated with Monte Carlo simulations, demonstrating high accuracy and reduced sensitivity to parameter variations.

Determination of Propeller-Rudder-Hull Interaction Coefficients in Ship Manoeuvring Prediction

Abstract The assessment of ship manoeuvring properties is a crucial part of the process of ship design and is usually first carried out during the model test phase of the project. According to the International Maritime Organisation (IMO), the manoeuvrability of the ship can be assessed on the basis of the standard trial manoeuvres. In order to do this, free running model tests or captive model tests are used, in conjunction with a mathematical model of ship motion; this is considered to be a reliable prediction method. In recent years, numerical-based methods have also been widely used in ship hydrodynamics and constantly improving computing power and more accurate fluid dynamics models have made the simulation of more complex cases possible. The study presented in this paper focuses on the determination of propeller-rudder-hull interaction coefficients based on the Mathematical Modelling Group (MMG) standard method in ship manoeuvring prediction. The identification of the parameters uses both captive model tests and a simplified numerical method, as well as regression formulas. The results of 35° turning and 10°/10° zig-zag manoeuvres, obtained with the use of each prediction method, are then compared. The test case used in the study is the container type cargo ship equipped with a single propeller and rudder. The model scale, for which the referenced model tests were carried out, is equal to 1:25 and a NACA 0020 rudder profile was used. This research highlights the advantages and disadvantages of each presented prediction method and their potential for future improvement.

Ship Autonomous Berthing Strategy Based on Improved Linear-Quadratic Regulator

There has been significant interest in the research field of ship automatic navigation, particularly in the area of autonomous berthing. To address the key challenges of path planning and control during ship berthing, we propose an enhanced Linear−Quadratic Regulator (LQR) control approach, reinforced by the Covariance Matrix Adaptation Evolution Strategy (CMA−ES), along with an adaptive berthing strategy decision model. This integrated framework encompasses ship motion control, path planning, and berthing strategy selection to facilitate adaptive and autonomous ship berthing. Initially, a dynamic mathematical model of ship motion is established, taking into account wind and current interference effects. Subsequently, an adaptive environment−aware berthing strategy model is introduced to enable automatic selection of berthing strategies based on spatial relationships between environmental factors and the berth. By utilizing the refined LQR method, autonomous motion control for ship berthing is achieved. To validate the effectiveness of our controller, comprehensive simulation analyses are conducted under varying operating conditions to encompass crucial factors such as large drift angle characteristics of ships, shallow water effects, and bank effects across seven diverse working conditions. The simulation results underscore the robustness of our proposed method in responding to environmental interference while demonstrating its capability to select appropriate berthing strategies based on varying operational scenarios.

The challenge of non-Markovian energy balance models in climate.

We first review the way in which Hasselmann's paradigm, introduced in 1976 and recently honored with the Nobel Prize, can, like many key innovations in complexity science, be understood on several different levels. It can be seen as a way to add variability into the pioneering energy balance models (EBMs) of Budyko and Sellers. On a more abstract level, however, it used the original stochastic mathematical model of Brownian motion to provide a conceptual superstructure to link slow climate variability to fast weather fluctuations, in a context broader than EBMs, and led Hasselmann to posit a need for negative feedback in climate modeling. Hasselmann's paradigm has still much to offer us, but naturally, since the 1970s, a number of newer developments have built on his pioneering ideas. One important one has been the development of a rigorous mathematical hierarchy that embeds Hasselmann-type models in the more comprehensive Mori-Zwanzig generalized Langevin equation (GLE) framework. Another has been the interest in stochastic EBMs with a memory that has slower decay and, thus, longer range than the exponential form seen in his EBMs. In this paper, we argue that the Mori-Kubo overdamped GLE, as widely used in statistical mechanics, suggests the form of a relatively simple stochastic EBM with memory for the global temperature anomaly. We also explore how this EBM relates to Lovejoy et al.'s fractional energy balance equation.

ДИНАМІЧНА МОДЕЛЬ ІТЕРАЦІЙНОГО ЕЛЕКТРОПРИВОДА ПОДАЧІ З ДВОМА ГВИНТОВИМИ ПЕРЕДАЧАМИ ДЛЯ ПРЕЦИЗІЙНИХ ВЕРСТАТІВ ТА ОБРОБНИХ ЦЕНТРІВ

A variant of a simplified design diagram is proposed and the corresponding kinematic diagram of a two-motor gearless drive mechanism with two screw gears (SG) is given for an iterative two-channel electric drive for the longitudinal feed of the working tool (worktable with a product) of a coordinate multi-purpose metal-cutting machine of especially high precision, model 24K70AF4. Compensators of the negative dynamic interaction of load control channels have been determined. A generalized dynamic model of the cutting process has been constructed, taking into account both the inertia of the cutting process and the influence of the machine “WT-cutter” elastic system dynamics. A dynamic model of a conditional compensator for the cutting process is determined and calculated. A refined mathematical model of motion in steady-state feed modes of the two-channel electric drive has been obtained, taking into account the compensation of the dynamic interaction of the channels on the load and the influence of friction nonlinearities in the drive mechanism and the working tool of the machine. A structural-algorithmic diagram of an iterative two-channel compensated feed electric drive with two SGs and subordinated adjustment of control channels has been designed. The diagram includes a generalized dynamic model of the cutting process and a dynamic model of the corresponding conditional compensator for the cutting process, and also takes into account the main static moments of resistance and nonlinearity of friction in the drive load. References 13, tables 2, figures 5.

Dynamics of a Double Pendulum with Viscous Friction at the Hinges. I. Mathematical Model of Motion and Construction of the Regime Diagram

Dynamics of a Double Pendulum with Viscous Friction at the Hinges. I. Mathematical Model of Motion and Construction of the Regime Diagram

Suppression of Torque Ripple in Switched Reluctance Motors Which is Based on Synchronization Technology

The double salient pole structure of Switched Reluctance Motor (SRM) makes its electromagnetic field exist nonlinear saturation characteristics, resulting in its large torque pulsation in operation, so it is difficult to achieve speed regulation smoothly by traditional control methods. In view of this problem, a sliding mode control strategy which is based on synchronous transmission technology was proposed.Firstly, the basic structure of switched reluctance motor was analyzed, and the mathematical model of mechanical motion of switched reluctance motor was established. Secondly, an improved sliding mode controller which is based on synchronous signal transmission technology was designed by analyzing the reason of large torque ripple of switched reluctance motor, and the stability of the system was proved. Finally, simulation is used to verify the effectiveness of the control strategy.Compared with the traditional PID (Proportional Integral Differential) control algorithm, this control technology not only suppresses the SRM torque ripple effectively , but also makes the sliding mode controller output the precise target electromagnetic torque quickly by increasing the control variables. The results of research indicate that this design can not only restrain the torque ripple effectively, but also adjust the convergence speed and overshoot of the controller by adjusting the design parameters.

Field‐Free Region Scanning‐Based Magnetic Microcarrier Targeting in Multibifurcation Vessels

Navigation of microcarriers in complex environments as a vascular network remains an open challenge due to limited solutions for effective targeting strategy. Simultaneous real‐time visualization and manipulation of microcarriers at any depth in the human body is far to be achieved even though one of each task has been successfully proven. Herein, a novel targeting strategy is proposed that employs field‐free region (FFR) scanning to guide microcarriers through multiple bifurcations within a predefined vessel network. The main challenge of this method lies on how, where, and when to activate FFR to steer a particle to a desired direction, regardless of its spatial feedback. To achieve it, first, a mathematical model of particle motion in a vessel network is developed to predict particle behaviors and positions. Subsequently, an optimization algorithm is formulated to place FFR well‐coordinated around each bifurcation at a designated moment. The established solution for targeting a magnetic microcarrier is preemptively evaluated through finite element simulations and then successfully implemented in in vitro multibranched vessels.

Numerical simulation of hydrodynamics of ocean-observation-used remotely operated vehicle

Remotely operated vehicle is the most widely used underwater robot and can work safely and steadily in complex environments compared to autonomous underwater vehicle and other types. It has obvious advantages in operation time and plays a significant function in marine engineering equipment. Hydrodynamic coefficients are the coefficients of ROV motion equation. In order to simulate the motion and predict the performance of a ROV, the hydrodynamic coefficients must be determined first. The motion mathematical model of remotely operated vehicles is also established, and the hydrodynamic dynamics of the vehicles are simulated using the finite volume method by combining overset mesh technology and governing equations. Finally, a simulation and verification of the standard model SUBOFF model and the calculation process’s dependability are also conducted. The primary hydrodynamic coefficients of the ROV were derived through the simulation data fitting process. The results showed that the ROV’s asymmetry results in an obvious disparity in pressure resistance between the forward and backward sailing, ascending and descending motions, and this disparity becomes significantly greater as the velocity increases. This method confirmed the accuracy of the hydrodynamic simulation computation of the remotely operated vehicle and served as a guide for the maneuverability and design of the vehicle.

Force analysis of the planetary-type mechanisms of the enhanced vibration exciters

The planetary-type vibration exciters are relatively novel and prospective types of actuators for various vibratory technological equipment. Numerous research papers substantiated the possibilities of implementing such exciters for generating circular, elliptical, and rectilinear oscillations of the working members of different technological machines. The present research continues the authors’ previous investigations dedicated to kinematics and dynamics of planetary-type vibration exciters and is focused on the analysis of forces, moments, and torques acting upon the elements of the corresponding actuating mechanisms. The research methodology contains the development of the simplified dynamic diagrams of two different designs of planetary-type mechanisms, derivation of the analytical expressions describing force parameters of the considered mechanical systems, performing the mathematical modeling and computer simulation of the mechanism motion in order to analyze the corresponding forces, moments, and torques. The obtained results present the time dependencies of the mentioned force parameters under different operational conditions and design parameters of the planetary-type mechanism. The major scientific novelty of the paper consists in defining the minimal required torque of the motor needed to be applied for driving the mechanism at different conditions. The research outcomes can be effectively used by engineers while developing new and improving existent vibratory technological machines equipped with the considered planetary-type vibration exciter.

Drug Distribution After Intravitreal Injection: A Mathematical Model.

Intravitreal injection of drugs is commonly used for treatment of chorioretinal ocular pathologies, such as age-related macular degeneration. Injection causes a transient increase in the intraocular volume and, consequently, of the intraocular pressure (IOP). The aim of this work is to investigate how intravitreal flow patterns generated during the post-injection eye deflation influence the transport and distribution of the injected drug. We present mathematical and computational models of fluid motion and mass transport in the vitreous chamber during the transient phase after injection, including the previously unexplored effects of globe deflation as ocular volume decreases. During eye globe deflation, significant fluid velocities are generated within the vitreous chamber, which can possibly contribute to drug transport. Pressure variations within the eye globe are small compared to IOP. Even if significant fluid velocities are generated in the vitreous chamber after drug injection, these are found to have negligible overall effect on drug distribution.

Tensor analysis of tornadoes: a new analytical and numerical model

This research proposes a new mathematical formulation of tornadoes based on the theory of tensor analysis and simulation in a non-inertial dynamics framework, both in two and three dimensions. This model may show the spherical upward movement of air in a tornado without taking into account vertical convection. A tornado requires several elements, including geocentric latitude, the Coriolis effect, increased airspeed in the upper atmosphere, and increased air pressure. Computing the three-dimensional location of the tornado or hurricane, as well as the mathematical models of airflow motion and the Earth's rotation in three-dimensional (3D) space, can determine a tornado's airflow characteristics. To show tornado patterns, we employed computer software that computed motion dynamics and did numerical computations. The results of 2-D modeling and simulation indicated that the greater the initial tornado angular speed, the larger the tornado area. Three-dimensional modeling and simulation also show that tornadoes are more powerful at higher geocentric latitude angles. The novelty of this study is that this model can be used to explain tornado patterns. In our research, we combine tensor analysis, computational modeling, as well as 2D and 3D simulations for simulating tornadoes for the first time. The scientific application of this finding is that researchers at the Meteorology, Climatology, and Geophysics Agency will be able to analyze a tornado and geophysical phenomena more readily with simulations and models.

Collaborative communication-based ocean observation research with heterogeneous unmanned surface vessels

Unmanned surface vehicles (USVs) are crucial in ensuring maritime safety and observation, attracting widespread attention and research. However, a single USV exhibits limited performance and cannot effectively observe complex marine environments. In contrast, clusters of USVs can collaborate to execute complex maritime tasks, thereby enhancing the overall operational efficiency. USVs typically form heterogeneous clusters by combining vehicles with varying maneuverabilities and communication network capabilities. This has sparked an increased interest in cooperative communication research within heterogeneous USV clusters. The heterogeneous USVs discussed in this paper share the same dynamic model; however, they differ in dynamic parameters and communication capabilities. First, this study establishes a three-degree-of-freedom motion mathematical model for an underdriven USV considering environmental interference. It estimates the dynamic parameters of four USVs and evaluates their communication abilities, laying the foundation for researching the cooperative control of heterogeneous USV clusters and their application in Ocean Observation. Next, the communication capability of the USVs is assessed by studying the communication mode and signal transmission loss within the USV clusters. This study investigates the problem of cooperative communication in USV cluster formation, starting with the communication delay of USV clusters under a directed switching topology. Finally, a coherent formation controller is designed under a switching communication topology to address the dynamic transformation of communication topologies within heterogeneous USV clusters. This verifies that heterogeneous USV clusters can seamlessly form and maintain formation shapes during communication topology transformations through formation simulation experiments involving four heterogeneous USVs was 22% higher than that of dispersed control topology structures. This study provides a solid foundation for future investigations into the cooperative control of heterogeneous USV clusters and their applications in marine observations.

Development of a mathematical model and algorithm for the sequence of fault detection of the ship's hull

The labor intensity of the hull fault detection process, which generally consists of work performed directly on the vessel and the preparation of the final report, can be reduced through the use of modern methods of computer data analysis. The sequence of measurements of defects on the vessel (residual thicknesses, deformations, cement and other sealings, cracks, holes) can be justified by solving a modified traveling salesman problem, reflecting the optimization of the path between points in space, with the goal function in the form of the spent finite time, which is the sum of the time for performing the measurements themselves, moving between the points of such measurements, various technical works, for example, installing a ladder for access to the area located above human growth and its movement to the right sector of work. The article develops a mathematical model of human motion in the space around the vessel, an algorithm of movement. The adaptation of the genetic algorithm for the problem under consideration is given, including the features of solution coding, crossing and mutation of solutions, and choosing the best option. The results of the test debugging simulation for the bow of the river pusher hull showed the operability of the developed algorithm and the possibility of its application for research and practical tasks.

Nonparametric modeling of a high-speed USV at three speed regions based on Gaussian process regression with a hybrid kernel function

Due to the complexity and variability of the ocean environment, it is difficult for high-speed unmanned surface vehicles (USVs) to construct a unified mathematical model for nonlinear motion under different Froude numbers. In this paper, a nonparametric modeling method for high-speed USVs at three speed regions is presented based on Gaussian process regression with a hybrid kernel function (HKF-GPR). First, the hybrid kernel functions are designed based on the forecasting performance of Gaussian process regression with different single kernel functions (SKF-GPR) using sea trial speed data from the “Jiuhang 750” USV. Second, to better capture the dynamic performance of the USVs, the sea trial speed data are clustered into three speed regions by an improved k-means++ algorithm; these regions are the displacement, semiplanning, and planning regions. Finally, USV modeling and forecasting are performed in the three speed regions using HKF-GPR. The trained model shows good modeling accuracy and forecasting, verifying the effectiveness of the proposed method.

Prediction-correction pedestrian flow by means of minimum flow problem

We study a new variant of mathematical prediction-correction model for crowd motion. The prediction phase is handled by a transport equation where the vector field is computed via an eikonal equation [Formula: see text], with a positive continuous function [Formula: see text] connected to the speed of the spontaneous travel. The correction phase is handled by a new version of the minimum flow problem. This model is flexible and can take into account different types of interactions between the agents, from gradient flow in Wassersetin space to granular type dynamics like in sandpile. Furthermore, different boundary conditions can be used, such as non-homogeneous Dirichlet (e.g. outings with different exit-cost penalty) and Neumann boundary conditions (e.g. entrances with different rates). Combining finite volume method for the transport equation and Chambolle–Pock’s primal dual algorithm for the eikonal equation and minimum flow problem, we present numerical simulations to demonstrate the behavior in different scenarios.