Motion of a Sphere on a Plane

1994 ◽  
Author(s):  
Yong-Xian Xu ◽  
Dilip Kohli ◽  
Larry Vezina ◽  
Daniel R. Speranza
Keyword(s):  
Mathematical Model ◽  
Initial Conditions ◽  
Contact Point ◽  
Break Point ◽  
Degree Of Freedom ◽  
Geometric Center ◽  
Inertia Properties ◽  
Gyroscopic Motion ◽  
The Mathematical Model ◽  
First Time

Abstract The motion of a sphere on a plane is a five degree-of-freedom motion. It consists of two independent translations of the geometric center of the sphere and three rotations corresponding to gyroscopic motion of the sphere. The trajectory of an imbalanced sphere on the plane depends on: (1) the physical and inertia properties of the sphere, (2) the initial conditions of motion, and (3) the friction between the sphere and the plane. To predict the trajectory of the sphere, a general Eulerian mathematical model is developed which takes into account these conditions. The mathematical model is verified through experimentation. For the first time, general characteristics of the translatory and rotatory motions of the imbalanced sphere with general inertia distribution are presented. The existence of the “break point” in the trajectory is illustrated by examples. The trajectory (track) of the contact point on the surface of the sphere is also analyzed.

scholarly journals An Optimized Mathematical Model for Items Supplies Planning of a Logistic System

2016 ◽  
Vol 10 (10) ◽  
pp. 133
Author(s):  
Mohammad Ali Nasiri Khalili ◽  
Mostafa Kafaei Razavi ◽  
Morteza Kafaee Razavi
Keyword(s):  
Mathematical Model ◽  
Mixed Integer ◽  
Logistics System ◽  
Proposed Model ◽  
Multiple Objective Decision Making ◽  
System Requirements ◽  
Purchasing Logistics ◽  
The Cost ◽  
The Mathematical Model ◽  
First Time

Items supplies planning of a logistic system is one of the major issue in operations research. In this article the aim is to determine how much of each item per month from each supplier logistics system requirements must be provided. To do this, a novel multi objective mixed integer programming mathematical model is offered for the first time. Since in logistics system, delivery on time is very important, the first objective is minimization of time in delivery on time costs (including lack and maintenance costs) and the cost of purchasing logistics system. The second objective function is minimization of the transportation supplier costs. Solving the mathematical model shows how to use the Multiple Objective Decision Making (MODM) can provide the ensuring policy and transportation logistics needed items. This model is solved with CPLEX and computational results show the effectiveness of the proposed model.

scholarly journals AGV Brake System Simulation

2019 ◽  
Vol 10 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Daniel Varecha ◽  
Robert Kohar ◽  
Frantisek Brumercik
Keyword(s):  
Mathematical Model ◽  
Input Data ◽  
Initial Conditions ◽  
Brake System ◽  
Disc Brake ◽  
Hydraulic Control ◽  
Stopping Distance ◽  
Braking Force ◽  
Braking Process ◽  
The Mathematical Model

Abstract The article is focused on braking simulation of automated guided vehicle (AGV). The brake system is used with a disc brake and with hydraulic control. In the first step, the formula necessary for braking force at the start of braking is derived. The stopping distance is 1.5 meters. Subsequently, a mathematical model of braking is created into which the formula of the necessary braking force is applied. The mathematical model represents a motion equation that is solved in the software Matlab by an approximation method. Next a simulation is created using Matlab software and the data of simulation are displayed in the graph. The transport speed of the vehicle is 1 〖m.s〗^(-1) and the weight of the vehicle is 6000 kg including load. The aim of this article is to determine the braking time of the device depending from the input data entered, which represent the initial conditions of the braking process.

scholarly journals Mathematical model for reliability indicators calculation of tethered UAV hybrid navigation system

2021 ◽  
Vol 2091 (1) ◽  
pp. 012033
Author(s):  
V M Vishnevsky ◽  
K A Vytovtov ◽  
E A Barabanova ◽  
V E Buzdin
Keyword(s):  
Mathematical Model ◽  
Navigation System ◽  
Analytical Method ◽  
Mathematical Expression ◽  
Equation System ◽  
Kolmogorov Equation ◽  
Reliability Indicators ◽  
Technical Vision ◽  
The Mathematical Model ◽  
First Time

Abstract The mathematical model for reliability indicators calculation of the hybrid navigation system containing microwave and technical vision subsystems is proposed in this paper for the first time. The proposed method is based on the translation matrix concept of solutions to the Kolmogorov equation system and it allows us to obtain the mathematical expression of availability factor, downtime ratio, and other reliability indicators. Also the presented approach allows finding the reliability indicators for the cases of jump change of transition intensities caused by external influences. Besides the analytical method can be used for investigation of hybrid navigation system transient mode functioning. The results of the numerical calculations clearly demonstrated correctness of the proposed approach.

scholarly journals Mathematical modeling of processes of heat and mass transfer during drying of wood biomass

2018 ◽  
Vol 194 ◽  
pp. 01012
Author(s):  
Natalya Ivanova ◽  
Elena Bulba
Keyword(s):  
Mathematical Model ◽  
Evaporation Rate ◽  
Woody Biomass ◽  
Moisture Removal ◽  
Wood Biomass ◽  
Evaporation Front ◽  
Drying Time ◽  
Mass Evaporation ◽  
The Mathematical Model ◽  
First Time

For the first time, a mathematical model for the drying of woody biomass during conductive heating with localization of the evaporation front has been formulated. The processes of moisture removal during the filtration of steam through the porous structure of the material at an ambient temperature of Te = 373 K were considered. Humidity was varied (in the range from 6% to 40%) and dimensions of wood blanks (Rd = 0.0035 - 0.035 m). Based on the results of numerical simulation, the conditions and characteristics (evaporation rate Wisp, drying time τ dry) of the process of moisture removal from wood biomass are determined. The mathematical model allows to calculate the drying time, as well as the mass evaporation rate for different sizes of wood sample, humidity and temperature conditions.

scholarly journals Simulation Analysis of One Degree of Freedom Motion of Electromagnetic Spherical Joint based on Maxwell

2021 ◽  
Vol 2085 (1) ◽  
pp. 012014
Author(s):  
Haoran Wang ◽  
Fucong Liu ◽  
Sai Lou
Keyword(s):  
Mathematical Model ◽  
Simulation Analysis ◽  
Lagrange Equation ◽  
Degree Of Freedom ◽  
Spherical Joint ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Structure And Motion ◽  
The Mathematical Model ◽  
The Relationship

Abstract In order to improve the stiffness of the spherical joint of the robot, reduce the difficulty of manufacturing and the complexity of the control system, this paper proposed a method of spherical joint and digital drive of the robot based on the electromagnetic principle. Firstly, introduces the structure and motion principle of the spherical joint of the robot, establishes the mathematical model of the spherical joint and establishes the dynamic model according to the second Lagrange equation. after that, the relationship between the number of ampire-turns of the electromagnet on the spherical joint, the attitude Angle of the rotor and the force of the rotor was obtained by simulating the single degree of freedom of the joint based on Ansys maxwell and Matlab, which provided a basis for the realization of the digital drive of the spherical joint.

scholarly journals Weak resonances of periodical nonlinear oscillations

2017 ◽  
Vol 58 ◽  
Author(s):  
Olga Lavcel-Budko ◽  
Aleksandras Krylovas
Keyword(s):  
Mathematical Model ◽  
Asymptotic Solution ◽  
Space Variable ◽  
Nonlinear Oscillations ◽  
Initial Conditions ◽  
Perturbation Technique ◽  
The Mathematical Model

The mathematical model of nonlinear oscillations of weightless string is analyzed. Coefficients of the mathematical model and initial conditions are periodical functions of the space variable. A multiscale perturbation technique and integrating along characteristics are used to construct asymptotic solution without secular members.

Inverse Approach Using Bio-Inspired Algorithm Within Bayesian Framework for the Estimation of Heat Transfer Coefficients During Solidification of Casting

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
P. S. Vishweshwara ◽  
N. Gnanasekaran ◽  
M. Arun
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Initial Conditions ◽  
Bayesian Framework ◽  
Simultaneous Estimation ◽  
Unknown Parameters ◽  
Single Experiment ◽  
Inverse Approach ◽  
Solidification Problem ◽  
The Mathematical Model

Abstract In any parameter estimation problem, it is desirable to obtain more information in one single experiment. However, it is difficult to achieve multiple objectives in one single experiment. The work presented in this paper is the simultaneous estimation of heat transfer coefficient parameters, latent heat, and modeling error during the solidification of Al–4.5 wt %Cu alloy with the aid of Bayesian framework as an objective function that harmoniously matches the mathematical model and measurements. A 1D transient solidification problem is considered to be the mathematical model/forward model and numerically solved to obtain temperature distribution for the known boundary and initial conditions. Genetic algorithm (GA) and particle swarm optimization (PSO) are used as an inverse approach and the estimation of unknown parameters is accomplished for both pure and noisy temperature data. The use of Bayesian framework for the estimation of unknown parameters not only provides the information about the uncertainties associated with the estimates but also there is an inherent regularization term in which the inverse problem boils down to well-posed problem thereby plethora of information is extracted with less number of measurements. Finally, the results of this work open up new prospects for the solidification problem so as to obtain a feasible solution with the present approach.

Mathematical model of oil-containing water purification process in the volume of granulated media

2018 ◽  
Vol 233 (3) ◽  
pp. 879-885
Author(s):  
Valeriy Ivanovich Istomin ◽  
Elena Stanislavovna Solodova ◽  
Viktoria Valer’evna Khlebnikova
Keyword(s):  
Mathematical Model ◽  
Physical Model ◽  
Water Purification ◽  
Theoretical Research ◽  
Purification Process ◽  
Operational Parameters ◽  
Filtering Element ◽  
The Mathematical Model ◽  
First Time ◽  
Further Development

A mathematical model of oil-containing water purification process in the volume of granulated media is developed. On the basis of this model, the purifying ability of filtering unit with granulated coalescing media, which regenerates filtering media in the mode of pseudo liquefaction of granule without disassembling and replacement of filtering element, is studied. In the process of theoretical research, the physical model of oil-containing water purification process in the volume of granulated coalescing media is elaborated. The consistent patterns of the analysed process have gained further development. Due to these patterns, the factors which determine the effectiveneness of purification are established. After realization of the experiment plan for the first time, the mathematical model of a ship’s oil-containing water purification process in the volume of granulated media on the basis of the regression equation has been received. This model allows to calculate the rational constructive and operational parameters of the plant with granulated filter elements.

Probabilistic model of structural phase transition in perovskites

2021 ◽  
pp. 2150211
Author(s):  
S. H. Jabarov ◽  
R. T. Aliyev ◽  
N. A. Ismayilova
Keyword(s):  
Mathematical Model ◽  
Phase Transitions ◽  
Crystal Structures ◽  
Structural Phase ◽  
Random Variable ◽  
Structural Phase Transitions ◽  
The Moment ◽  
The Mathematical Model ◽  
First Time

In this work, the crystal structures and phase transitions of compounds with perovskite structure were investigated. The classification of structural phase transitions in perovskites was carried out, the most common crystal structures and structural phase transitions were shown. A mathematical model was constructed, a theorem was given and proved for the probability of a possible transition. The formulas [Formula: see text] and [Formula: see text] are given for the mathematical expectation and variance of random variable [Formula: see text], which is the moment when the stochastic process [Formula: see text] deviation from the boundary [0, [Formula: see text]] interval for the first time. According to the mathematical model, one of the trajectories of random processes corresponding to the phase transitions that occur in perovskites is constructed.

scholarly journals Correlation between Animal and Mathematical Models for Prostate Cancer Progression

2009 ◽  
Vol 10 (4) ◽  
pp. 241-252 ◽  
Author(s):  
Z. Jackiewicz ◽  
C. L. Jorcyk ◽  
M. Kolev ◽  
B. Zubik-Kowal
Keyword(s):  
Mathematical Model ◽  
Cancer Progression ◽  
Growth Rates ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Tumour Progression ◽  
Prostate Cancer Progression ◽  
The Mathematical Model

This work demonstrates that prostate tumour progressionin vivocan be analysed by using solutions of a mathematical model supplemented by initial conditions chosen according to growth rates of cell linesin vitro. The mathematical model is investigated and solved numerically. Its numerical solutions are compared with experimental data from animal models. The numerical results confirm the experimental results with the growth ratesin vivo.

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