scholarly journals Simulation of several flying situations of paragliders

2021 ◽  
Vol 15 (1) ◽  
pp. 79-89
Author(s):  
Thanh Xuan Nguyen ◽  
Phuong Thi-Thu Phan ◽  
Tien Van Pham
Keyword(s):  
Mathematical Modeling ◽  
Differential Equations ◽  
Modeling And Simulation ◽  
Ordinary Differential Equations ◽  
State Space ◽  
Simulation Modeling ◽  
Time Varying ◽  
Gravity Forces

Paragliding is an adventure and fascinating sport of flying paragliders. Paragliders can be launched by running from a slope or by a winch force from towing vehicles, using gravity forces as the motor for the motion of flying. This motion is governed by the gravity forces as well as time-varying aerodynamic ones which depend on the states of the motion of paraglider at each instant of time. There are few published articles considering mechanical problems of paragliders in their various flying situations. This article represents the mathematical modeling and simulation of several common flying situations of a paraglider through establishing and solving the governing differential equations in state-space. Those flying situations include the ones with constant headwind/tailwind with or without constant upwind; the ones with different scenario for the variations of headwind and tailwind combined with the upwind; the ones with varying pilot mass; and the ones whose several parameters are in the form of interval quantities. The simulations were conducted using a powerful Julia toolkit called DifferentialEquations.jl. The obtained results in each situation are discussed, and some recommendations are presented. Keywords: paraglider; simulation; modeling; state-space; ordinary differential equations; Julia; DifferentialEquations.jl

scholarly journals Mathematical Modeling and Simulation of SIR Model for COVID−2019 Epidemic Outbreak: A Case Study of India

2020 ◽  
Author(s):  
Dr. Ramjeet Singh Yadav
Keyword(s):  
Mathematical Modeling ◽  
Infectious Diseases ◽  
Differential Equations ◽  
Modeling And Simulation ◽  
Ordinary Differential Equations ◽  
Initial Level ◽  
Sir Model ◽  
Euler Method ◽  
Epidemic Outbreak

The present study discusses the spread of COVID−2019 epidemic of India and its end by using SIR model. Here we have discussed about the spread of COVID−2019 epidemic in great detail using Euler method. The Euler method is a method for solving the ordinary differential equations. The SIR model has the combination of three ordinary differential equations. In this study, we have used the data of COVID−2019 Outbreak of India on 8 May, 2020. In this data, we have used 135710 susceptible cases, 54340 infectious cases and 1830 reward/removed cases for the initial level of experimental purpose. Data about a wide variety of infectious diseases has been analyzed with the help of SIR model. Therefore, this model has been already well tested for infectious diseases by various scientists and researchers. Using the data to the number of COVID−2019 outbreak cases in India the results obtained from the analysis and simulation of this proposed SIR model showing that the COVID−2019 epidemic cases increase for some time and there after this outbreak decrease. The results obtained from the SIR model also suggest that the Euler method can be used to predict transmission and prevent the COVID−2019 epidemic in India. Finally, from this study, we have found that the outbreak of COVID−2019 epidemic in India will be at its peak on 25 May 2020 and after that it will work slowly and on the verge of ending in the first or second week of August 2020.

scholarly journals Modeling and simulation aspects of AC machines

2016 ◽  
Vol 65 (2) ◽  
pp. 315-326 ◽  
Author(s):  
Michael Popp ◽  
Patrick Laza ◽  
Wolfgang Mathis
Keyword(s):  
Complex System ◽  
Differential Equations ◽  
Modeling And Simulation ◽  
Ordinary Differential Equations ◽  
State Space ◽  
Space Representation ◽  
Ac Machines ◽  
State Space Representation ◽  
Drive Systems ◽  
Algebraic Constraints

Abstract In the field of power and drive systems, electrical AC machines are mostly modeled using a set of explicit ordinary differential equations in a state space representation. It is shown, that by using other equation types for simulation, algebraic constraints arising from aggregating several machines to a more complex system can directly be considered. The effects of different model variants on numerical ODE/DAE solvers are investigated in the focus of this work in order perform efficient simulations of larger systems possessing electrical AC machines.

Ordinary differential equations and calculus of variations

2020 ◽  
Author(s):  
Efim Kogan
Keyword(s):  
Mathematical Modeling ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Calculus Of Variations ◽  
Applied Mechanics ◽  
Technological Systems ◽  
Technological Means ◽  
Independent Work

The textbook contains theoretical information in a volume of the lecture course are discussed in detail and examples of typical tasks and test tasks and tasks for independent work. Designed for students enrolled in directions of preparation 15.03.03 "Applied mechanics" 01.03.02 "mathematics" (specialization "Mathematical modeling"), major 23.05.01 "Land transport and technological means" (specialization "Dynamics and strength of transport and technological systems"). Can be used by teachers for conducting practical classes.

scholarly journals Using Ordinary Differential Equations to Explore Cancer-Immune Dynamics and Tumor Dormancy

2016 ◽  
Author(s):  
Kathleen P. Wilkie ◽  
Philip Hahnfeldt ◽  
Lynn Hlatky
Keyword(s):  
Mathematical Modeling ◽  
Immune Response ◽  
Differential Equations ◽  
Tumor Growth ◽  
Ordinary Differential Equations ◽  
Systemic Disease ◽  
Growth Dynamics ◽  
Tumor Dormancy ◽  
Cytotoxic Action ◽  
General Method

AbstractCancer is not solely a disease of the genome, but is a systemic disease that affects the host on many functional levels, including, and perhaps most notably, the function of the immune response, resulting in both tumor-promoting inflammation and tumor-inhibiting cytotoxic action. The dichotomous actions of the immune response induce significant variations in tumor growth dynamics that mathematical modeling can help to understand. Here we present a general method using ordinary differential equations (ODEs) to model and analyze cancer-immune interactions, and in particular, immune-induced tumor dormancy.

Steady-state analysis of DC converter using Galerkin’s method

2019 ◽  
Vol 38 (6) ◽  
pp. 2057-2069
Author(s):  
Igor Korotyeyev
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Galerkin Method ◽  
State Space ◽  
Time Interval ◽  
Time Varying ◽  
Content Type ◽  
State Process ◽  
The Galerkin Method ◽  
Steady State Process

Purpose The purpose of this paper is to present the Galerkin method for analysis of steady-state processes in periodically time-varying circuits. Design/methodology/approach A converter circuit working on a time-varying load is often controlled by different signals. In the case of incommensurable frequencies, one can find a steady-state process only via calculation of a transient process. As the obtained results will not be periodical, one must repeat this procedure to calculate the steady-state process on a different time interval. The proposed methodology is based on the expansion of ordinary differential equations with one time variable into a domain of two independent variables of time. In this case, the steady-state process will be periodical. This process is calculated by the use of the Galerkin method with bases and weight functions in the form of the double Fourier series. Findings Expansion of differential equations and use of the Galerkin method enable discovery of the steady-state processes in converter circuits. Steady-state processes in the circuits of buck and boost converters are calculated and results are compared with numerical and generalized state-space averaging methods. Originality/value The Galerkin method is used to find a steady-state process in a converter circuit with a time-varying load. Processes in such a load depend on two incommensurable signals. The state-space averaging method is generalized for extended differential equations. A balance of active power for extended equations is shown.

Dynamic Response of a Coupled Spinning Timoshenko Shaft System

1999 ◽  
Vol 121 (1) ◽  
pp. 110-113 ◽  
Author(s):  
E. Wong ◽  
J. W. Zu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Time Varying ◽  
Chebyshev Series ◽  
Bending Vibration ◽  
Linear Ordinary Differential Equations ◽  
Simply Supported ◽  
Shaft System

The dynamic behavior of a simply-supported spinning Timoshenko shaft with coupled bending and torsion is analyzed. This is accomplished by transforming the set of nonlinear partial differential equations of motion into a set of linear ordinary differential equations. This set of ordinary differential equations is a time-varying system and the solution is obtained analytically in terms of Chebyshev series. A beating phenomoenon is observed from the numerical simulations, which is not observed for shaft systems where only bending vibration is considered.

Avoidance Control

1972 ◽  
Vol 94 (2) ◽  
pp. 152-154 ◽  
Author(s):  
R. Aggarwal ◽  
G. Leitmann
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
State Space ◽  
Admissible Control ◽  
Existence Theorems ◽  
Control Processes ◽  
Avoidance Control

An avoidance control is an admissible control which permits avoidance of a givenset of state space Rn. Existence theorems for avoidance controls are given for control processes governed by ordinary differential equations.

Mathematical modeling of adaptive immune response after transplantation

2020 ◽  
Vol 13 (08) ◽  
pp. 2050167
Author(s):  
Anka Markovska
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Immune Response ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Cellular Immunity ◽  
Adaptive Immune Response ◽  
Nonlinear Ordinary Differential Equations ◽  
Adaptive Immune

A mathematical model of adaptive immune response after transplantation is formulated by five nonlinear ordinary differential equations. Theorems of existence, uniqueness and nonnegativity of solution are proven. Numerical simulations of immune response after transplantation without suppression of acquired cellular immunity and after suppression were performed.

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