Numerical Kinematical Analysis of the Articulated Quadrilateral Mechanism

2019 ◽  
Vol 17 (17) ◽  
pp. 52-62
Author(s):  
Mircea Bogdan Tătaru ◽  
Vladimir Dragoş Tătaru
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Reference System ◽  
Electronic Computer ◽  
System Of Differential Equations ◽  
First Order ◽  
Kinematical Analysis ◽  
Fixed Reference ◽  
Numerical Integration Methods ◽  
Kinematical Parameters

AbstractThe paper presents a numerical method of kinematical analysis of the articulated quadrilateral mechanism. Starting from Euler’s relation concerning the distribution of speeds written in projections on the fixed reference system axes, a system of differential equations describing the movement of the mechanism was obtained. This system of differential equations was then solved using numerical integration methods and the variation with respect to time of the position kinematical parameters, of the velocities (the first order kinematical parameters), and of the accelerations (the second order kinematical parameters), was obtained. Matrix writing of the differential equations was used in order to make the differential equations set out in the paper easier to solve using the electronic computer.

Numerical Kinematical Analysis of the Shaping Mechanism

2019 ◽  
Vol 17 (17) ◽  
pp. 37-49
Author(s):  
Vladimir Dragoş Tătaru ◽  
Mircea Bogdan Tătaru
Keyword(s):  
Differential Equations ◽  
Machine Tool ◽  
Numerical Integration ◽  
Reference System ◽  
First Order ◽  
Kinematical Analysis ◽  
Machine Tool Structure ◽  
Numerical Integration Methods ◽  
Linear Differential ◽  
Kinematical Parameters

AbstractThe paper deals with the complete kinematical analysis of the mechanism that enters the machine tool structure designed to generate, in particular, plane surfaces. A machine tool of this kind is called shaping machine. For this purpose, Euler’s relations concerning the velocities distribution, written in projections on the fix reference system axes will be used. Starting from these relations we will get to a system of the first order linear differential equations whose unknowns are the kinematical parameters of the mechanism elements. The variation in time of these parameters will be obtained by solving the differential equations system the differential equations system using numerical integration methods.

A Difference Method for Plane Problems in Magnetoelastodynamics

1972 ◽  
Vol 39 (3) ◽  
pp. 689-695 ◽  
Author(s):  
W. W. Recker
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Method ◽  
Difference Method ◽  
Necessary Condition ◽  
Two Dimensional ◽  
Symmetric Hyperbolic System ◽  
Von Neumann ◽  
First Order ◽  
Independent Variables

The two-dimensional equations of magnetoelastodynamics are considered as a symmetric hyperbolic system of linear first-order partial-differential equations in three independent variables. The characteristic properties of the system are determined and a numerical method for obtaining the solution to mixed initial and boundary-value problems in plane magnetoelastodynamics is presented. Results on the von Neumann necessary condition are presented. Application of the method to a problem which has a known solution provides further numerical evidence of the convergence and stability of the method.

Modeling of the Process of Drying and Coalescing Nanodispersion Spreading

2021 ◽  
Vol 887 ◽  
pp. 557-563
Author(s):  
D.M. Mordasov ◽  
M.D. Mordasov
Keyword(s):  
Contact Angle ◽  
Differential Equations ◽  
Mathematical Description ◽  
Transition Function ◽  
System Of Differential Equations ◽  
Theoretical Justification ◽  
Spreading Process ◽  
Optimal Amount ◽  
First Order ◽  
Energy Processes

The spreading process of drying and coalescing nanodispersion was simulated using the method of analogies. A mathematical description of the energy processes in the proposed physical model was obtained in the form of a system of differential equations of the first order. A transition function that describes the dynamics of the change in the contact angle when the nanodispersion drop spreads was obtained as a result of solving the system of differential equations. The physical meaning of the transition function coefficients was established. Based on the analysis of the ratio of the transition function coefficients, a theoretical justification for the results of experiments on choosing the optimal amount of desiccant introduced into styrene-acrylic nanodispersion was given.

A first order system of differential equations for covariant σ models

1979 ◽  
Vol 20 (12) ◽  
pp. 2619-2620
Author(s):  
C. Reina ◽  
M. Martellini ◽  
P. Sodano
Keyword(s):  
Differential Equations ◽  
Order System ◽  
System Of Differential Equations ◽  
First Order

scholarly journals Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Hua Dong ◽  
Xianghua Zhao
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Chebyshev Polynomial ◽  
Polynomial Approximation ◽  
Risk Model ◽  
Arbitrary Distribution ◽  
System Of Differential Equations ◽  
Numerical Result ◽  
Chebyshev Polynomial Approximation ◽  
Markov Modulated

This paper considers a perturbed Markov-modulated risk model with two-sided jumps, where both the upward and downward jumps follow arbitrary distribution. We first derive a system of differential equations for the Gerber-Shiu function. Furthermore, a numerical result is given based on Chebyshev polynomial approximation. Finally, an example is provided to illustrate the method.

scholarly journals A Numerical Method for Fuzzy Differential Equations and Hybrid Fuzzy Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
K. Ivaz ◽  
A. Khastan ◽  
Juan J. Nieto
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Sufficient Conditions ◽  
Numerical Algorithms ◽  
Stability And Convergence ◽  
First Order

Numerical algorithms for solving first-order fuzzy differential equations and hybrid fuzzy differential equations have been investigated. Sufficient conditions for stability and convergence of the proposed algorithms are given, and their applicability is illustrated with some examples.

scholarly journals On conditions of solvability of three-dimensional integralsystem in quadratures

2017 ◽  
Vol 21 (10) ◽  
pp. 40-46
Author(s):  
E.A. Sozontova
Keyword(s):  
Differential Equations ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Original System ◽  
Goursat Problem ◽  
System Of Differential Equations ◽  
Third Order ◽  
First Order ◽  
Three Dimensional Space

In this paper we consider the system of equations with partial integrals in three-dimensional space. The purpose is to find sufficient conditions of solvability of this system in quadratures. The proposed method is based on the reduction of the original system, first, to the Goursat problem for a system of differential equations of the first order, and after that to the three Goursat problems for differential equations of the third order. As a result, the sufficient conditions of solvability of the considering system in explicit form were obtained. The total number of cases discussing solvability is 16.

scholarly journals A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations

BIOMATH ◽  
2016 ◽  
Vol 5 (2) ◽  
pp. 1608111
Author(s):  
Ishwariya Raj ◽  
Princy Mercy Johnson ◽  
John J.H Miller ◽  
Valarmathi Sigamani
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Numerical Method ◽  
Shishkin Mesh ◽  
Singularly Perturbed ◽  
Initial Value ◽  
First Order ◽  
Non Linear ◽  
Perturbation Parameters ◽  
Non Linear System

In this paper an initial value problem for a non-linear system of two singularly perturbed first order differential equations is considered on the interval (0,1].The components of the solution of this system exhibit initial layers at 0. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be almost first order convergent in the maximum norm uniformly in the perturbation parameters.

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