scholarly journals Mathematical Modelling of Vehicle Drifting

2020 ◽  
Vol 8 ◽  
pp. 25-29
Author(s):  
Reza N. Jazar ◽  
Firoz Alam ◽  
Sina Milani ◽  
Hormoz Marzbani ◽  
Harun Chowdhury
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Equilibrium Point ◽  
Equations Of Motion ◽  
Force Model ◽  
Algebraic Equations ◽  
Steering Angle ◽  
Yaw Rate ◽  
Weight Lift ◽  
The Mathematical Model

A mathematical model and condition for drifting of vehicles are presented in this paper. Employing the condition for possible steady-state drifting, the mathematical model of a vehicle with lateral weight lift during turning and drifting as well as adopting a combined tyre force model enables to reduce the number of equations of motion to a set of nonlinear coupled algebraic equations. The solution of the equations are the longitudinal and lateral components of the velocity vector of the vehicle at its mass centre and the vehicle’s yaw rate. The numerical values of the variables are associated with an equilibrium at which the vehicle drifts steadily. The equilibrium point should be analysed for stability by examining for any small disturbance should disappear. The procedure applied to a nominal vehicle indicates that an equilibrium point exists for every given value of the steering angle as the input. Also, it is shown that the equilibrium point is unstable. Hence, to keep the vehicle at the associated steady-state drifting, the value of the yaw rate must be kept constant.

MATHEMATICAL ANALYSIS OF THE ENDEMIC EQUILIBRIUM OF MALARIAHYGIENE MODEL

2021 ◽  
Vol 5 (10) ◽  
Author(s):  
Oluwafemi Temidayo J. ◽  
Azuaba E. ◽  
Lasisi N. O.
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
The Mathematical Model ◽  
Globally Stable ◽  
Well Posed ◽  
The Basic Reproduction Number ◽  
Invariant Principle

In this study, we analyzed the endemic equilibrium point of a malaria-hygiene mathematical model. We prove that the mathematical model is biological and meaningfully well-posed. We also compute the basic reproduction number using the next generation method. Stability analysis of the endemic equilibrium point show that the point is locally stable if reproduction number is greater that unity and globally stable by the Lasalle’s invariant principle. Numerical simulation to show the dynamics of the compartment at various hygiene rate was carried out.

scholarly journals New “Full-Bridge Buck Inverter–DC Motor” System: Steady-State and Dynamic Analysis and Experimental Validation

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1216 ◽  
Author(s):  
Eduardo Hernández-Márquez ◽  
Carlos Alejandro Avila-Rea ◽  
José Rafael García-Sánchez ◽  
Ramón Silva-Ortigoza ◽  
Magdalena Marciano-Melchor ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Motor System ◽  
Circuit Simulation ◽  
Dc Motor ◽  
Matlab Simulink ◽  
Duty Cycles ◽  
System Variables ◽  
The Mathematical Model ◽  
Steady State Stability

A mathematical model of a new “full-bridge Buck inverter–DC motor” system is developed and experimentally validated. First, using circuit theory and the mathematical model of a DC motor, the dynamic behavior of the system under study is deduced. Later, the steady-state, stability, controllability, and flatness properties of the deduced model are described. The flatness property, associated with the mathematical model, is then exploited so that all system variables and the input can be differentially parameterized in terms of the flat output, which is determined by the angular velocity. Then, when a desired trajectory is proposed for the flat output, the input signal is calculated offline and is introduced into the system. In consequence, the validation of the mathematical model for constant and time-varying duty cycles is possible. Such a validation of this mathematical model is tackled from two directions: (1) by circuit simulation through the SimPowerSystems toolbox of Matlab-Simulink and (2) via a prototype of the system built by using Matlab-Simulink and a DS1104 board. The good similarities between the circuit simulation and the experimental results allow satisfactorily validating the mathematical model.

Theoretical and Experimental Study of the Dynamics of the Tripod-Ball Sliding Joint With Clearance

2001 ◽  
Author(s):  
Jia Xiaohong ◽  
Ji Linhong ◽  
Jin Dewen ◽  
Zhang Jichuan
Keyword(s):  
Mathematical Model ◽  
Equations Of Motion ◽  
Experimental Studies ◽  
Active System ◽  
New Concepts ◽  
Sliding Joint ◽  
New Type ◽  
Set Up ◽  
The Mathematical Model ◽  
Kane Method

Abstract Clearance is inevitable in the kinematic joints of mechanisms. In this paper the dynamic behavior of a crank-slider mechanism with clearance in its tripod-ball sliding joint is investigated theoretically and experimentally. The mathematical model of this new-type joint is established, and the new concepts of basal system and active system are put forward. Based on the mode-change criterion established in this paper, the consistent equations of motion in full-scale are derived by using Kane method. The experimental rig was set up to measure the effects of the clearance on the dynamic response. Corresponding experimental studies verify the theoretical results satisfactorily. In addition, due to the nonlinear elements in the improved mathematical model of the joint with clearance, the chaotic responses are found in numerical simulation.

Features of mathematical modeling of wood-polymer composite sandy

10.12737/8462 ◽  
2015 ◽  
Vol 4 (4) ◽  
pp. 130-139
Author(s):  
Стародубцева ◽  
Tamara Starodubtseva ◽  
Аскомитный ◽  
Aleksey Askomitnyy
Keyword(s):  
Mathematical Modeling ◽  
Mechanical Properties ◽  
Mathematical Model ◽  
Initial Data ◽  
Algebraic Equations ◽  
Wood Polymer ◽  
Composite Interface ◽  
Input Form ◽  
The Mathematical Model ◽  
Wood Polymer Composite

This article describes a technique for modeling of wood polymer-sandy composite. Interface input form of initial data for modeling; differential equations underlying the mathematical model are presented. To solve the system of differential and algebraic equations computer program "Program to simulate the struc-ture and mechanical properties of wood polymer-sandy composite" is developed. The program, developed in the environment of Borland Delphi 7.0, programming language Object Pascal, is intended for modeling the mechanical behavior of wood polymer-sandy composite of given composition.

scholarly journals Approximation of potential-driven flow dynamics in large-scale self-similar tree networks

2011 ◽  
Vol 467 (2134) ◽  
pp. 2810-2824 ◽  
Author(s):  
Jason Mayes ◽  
Mihir Sen
Keyword(s):  
Mathematical Model ◽  
Analytical Solutions ◽  
Large Scale ◽  
Differential Algebraic Equations ◽  
Flow Dynamics ◽  
Algebraic Equations ◽  
Tree Networks ◽  
Self Similar ◽  
Large Scale Flow ◽  
The Mathematical Model

Dynamic analysis of large-scale flow networks is made difficult by the large system of differential-algebraic equations resulting from its modelling. To simplify analysis, the mathematical model must be sufficiently reduced in complexity. For self-similar tree networks, this reduction can be made using the network’s structure in way that can allow simple, analytical solutions. For very large, but finite, networks, analytical solutions are more difficult to obtain. In the infinite limit, however, analysis is sometimes greatly simplified. It is shown that approximating large finite networks as infinite not only simplifies the analysis, but also provides an excellent approximate solution.

Pointwise Optimal Control of Dynamical Systems Described by Constrained Coordinates

1999 ◽  
Vol 121 (4) ◽  
pp. 594-598 ◽  
Author(s):  
V. Radisavljevic ◽  
H. Baruh
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Feedback Control ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Control Law ◽  
Algebraic Equations ◽  
The Stability ◽  
The Mathematical Model

A feedback control law is developed for dynamical systems described by constrained generalized coordinates. For certain complex dynamical systems, it is more desirable to develop the mathematical model using more general coordinates then degrees of freedom which leads to differential-algebraic equations of motion. Research in the last few decades has led to several advances in the treatment and in obtaining the solution of differential-algebraic equations. We take advantage of these advances and introduce the differential-algebraic equations and dependent generalized coordinate formulation to control. A tracking feedback control law is designed based on a pointwise-optimal formulation. The stability of pointwise optimal control law is examined.

scholarly journals Colpitts Chaotic Oscillator Coupling with a Generalized Memristor

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Ling Lu ◽  
Changdi Li ◽  
Zicheng Zhao ◽  
Bocheng Bao ◽  
Quan Xu
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Fourth Order ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Nonlinear Phenomena ◽  
Unique Equilibrium ◽  
First Order ◽  
The Mathematical Model ◽  
Order Parallel

By introducing a generalized memristor into a fourth-order Colpitts chaotic oscillator, a new memristive Colpitts chaotic oscillator is proposed in this paper. The generalized memristor is equivalent to a diode bridge cascaded with a first-order parallel RC filter. Chaotic attractors of the oscillator are numerically revealed from the mathematical model and experimentally captured from the physical circuit. The dynamics of the memristive Colpitts chaotic oscillator is investigated both theoretically and numerically, from which it can be found that the oscillator has a unique equilibrium point and displays complex nonlinear phenomena.

The Effect of Leakage on Railroad Brake Pipe Steady State Behavior

1988 ◽  
Vol 110 (3) ◽  
pp. 329-335 ◽  
Author(s):  
K. Abdol-Hamid ◽  
D. E. Limbert ◽  
G. A. Chapman
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Transmission Lines ◽  
Computation Time ◽  
State Behavior ◽  
Implicit Finite Difference Scheme ◽  
Inlet Flow Rate ◽  
Model Equations ◽  
The Mathematical Model ◽  
Steady State Behavior

A mathematical model for pneumatic transmission lines containing leakage is developed. This model is used to show the effect of leakage size and distribution on the steady state behavior of the brake pipe on a train brake system. The model equations are solved using the implicit finite difference scheme without neglecting any terms. The model is presented in a nonlinear continuous network form, consisting of N sections. Each of the network sections represents one car and may contain one leakage. A computer program was developed to solve the model equations. This program is capable of simulating a train with cars of various lengths and takes a minimum amount of computation time as compared with previous methods. Through analysis and experimentation, the authors have demonstrated that pressure gradient and inlet flow rate are very sensitive to leakage locations as compared with leakage size. The results, generated by the mathematical model, are compared with the experimental data of two different brake pipe set-ups having different dimensions.

scholarly journals Mathematical Model of Spatial Motion of the Controlled Parachute-Tether System of the Wind Kite Type

2021 ◽  
Vol 24 (4) ◽  
pp. 17-24
Author(s):  
V.M. Churkin ◽  
T.Yu. Churkina ◽  
A.M. Girin
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Solid Body ◽  
Equations Of Motion ◽  
Vertical Plane ◽  
Spatial Motion ◽  
Mathematical Task ◽  
Spatial Movement ◽  
Elastic Thread ◽  
The Mathematical Model

Mathematical modeling is created for the mathematical task of spatial motion of the controlled parachute-tether system of the “wind kite” type. The mathematical model parachute-tether system consists of a model of the main parachute and a model of the braking parachute. The parachutes are connected by the tether. The model of the main parachute is supposed to be the solid body. This solid body has two planes of symmetry. The braking parachute is the solid body with axial symmetry. The tether model is an absolutely flexible elastic thread. The tether is connected by ideal hinges with the main parachute and braking parachute. The control of the main parachute is carried out by changing the length of the control slings. Changing the length causes deformation of the dome. This is the reason for the change in its aerodynamics. Maneuvering of the main parachute occurs in the vertical plane, when the length of the control slings changes simultaneously. Maneuvering of the main parachute in space is carried out when the length of the control slings changes, when the slings are given a travel difference. The system of dynamic and kinematic equations is designed for calculating the controlled spatial movement of the main parachute, braking parachute and tether. The option exists when the mass of the tether and the forces applied to the tether cannot be neglected. The motion of the tether is represented by the equations of motion of an absolutely flexible elastic thread in projections on the axis of a natural trihedron. The mathematical model is represented by a system of ordinary differential equations and partial differential equations. The problem is solved using various numerical methods. The solution is possible with the help of an integrated numerical and analytical approach as well.

scholarly journals Mass transfer during electrodeposition of metals at a periodically changing rate

1999 ◽  
Vol 64 (5-6) ◽  
pp. 317-340 ◽  
Author(s):  
Miodrag Maksimovic ◽  
Konstantin Popov
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Steady State ◽  
Layer 4 ◽  
Millisecond Range ◽  
The Mathematical Model ◽  
Pulsating Current ◽  
Pulsating Overpotential ◽  
Changing Rate ◽  
Electrodeposition Of Metals

1. Introduction 2. Mass transfer in the steady state periodic condition 2.1. Reversing current 2.2. Pulsating current 2.3. Alternating current superimposed on direct current 3. The influence of the charge and discharge of the electrical double layer 4. The validity of the mathematical model 4.1. Reversing current in the millisecond range 4.2. Reversing current in the second range 4.3. Pulsating current 4.4. Pulsating overpotential 5. Conclusion

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