EXPLICIT SOLUTIONS TO SOME VECTORIAL DIFFERENTIAL EQUATIONS I. General Results (original) (raw)

EXPLICIT SOLUTIONS TO SOME VECTORIAL DIFFERENTIAL EQUATIONS II. Applications to Theoretical Mechanics

Bul. Inst. Polit. Iasi. 04/2001; Bul. Inst. Polit. Iasi, XLVII (LI)(1-2, s.I., 2001):pp. 315-325..

"This paper presents some applications of the procedures presented in [6] for determining the explicit solution to vectorial differential equations of a certain type. Two classic problems of theoretical mechanics are studied: the motion of an electric charged particle in a non-stationary electromagnetic field with respect to an inertial frame and that of a particle in uniform force fields with respect to a non-inertial frame. To these problems, approximate solutions are usually given."

A Note on Generalized Solution of a Cauchy Problem Given by a Nonhomogeneous Linear Differential System

Acta Marisiensis. Seria Technologica

Generalized solution of a Cauchy problem given by a nonhomogeneous linear differential system is recovered to this approach. It considers the case of the free term having at most countable number of discontinuity points. The method, called successive approach, uses the solution on the previous interval (except the first one) for the condition on the given interval. The sequence of commands for a computer algebra system to this method is given.

φA-algebrizable differential equations

2019

We introduce the φA-differentiability, the corresponding generalized Cauchy-Riemann equations (φA-CREs), the Cauchy-integral theorem, and consider the problem of when a given linear system of two first order partial differential equations results the φA-CREs for some function φ and a two dimensional algebra A. We show that the four dimensional vector fields associated with triangular billiards are φA-differentiable. Keyword: Vector fields, Lorch differentiability, Generalized Cauchy-Riemann equations MSC[2010]: 37C10, 58C20, 53C22. Introduction Consider a linear system of partial differential equations (PDEs) of the form a111ux + a121vx + a131wx + a112uy + a122vy + a132wy = 0 a211ux + a221vx + a231wx + a212uy + a222vy + a232wy = 0 a311ux + a321vx + a331wx + a312uy + a322vy + a332wy = 0 , (1) where aijk are functions of (x, y, z), ux = ∂u ∂x and so on. In this paper we define a type of differentiability for which in particular cases the “Generalized Cauchy-Riemann equations” are line...

The Cauchy -Euler Differential Equation and Its Associated Characteristic Equation

Many natural phenomena, from physics to biology, through the fields of medicine and engineering, can be described by means of differential equations. This article aims to present the solutions of a homogeneous Cauchy-Euler differential equation from the roots of the characteristic equation associated with this differential equation, in order to facilitate the life of the university student. The great algebraic difficulty that a graduate student encounters in solving the homogeneous Cauchy-Euler differential equations is that his solution depends on a polynomial equation of degree n called the characteristic equation. It is hoped that this work can contribute to minimize the lags in teaching and learning of this important Ordinary Differential Equation.

Beer & Jhonston Vector Mechanics fon Enginners

STATICS Vector Mechanics for Enginners, 2012

No soy autor de este manual y su publicación es unicamente con fines académicos. El el presente se encuentra el solucionario a la decima edición de ejercicios del libro STATICS de Beer & Jhonston. Los ejercicios no fueron resueltos por mi. I am not the author of this manual and its publication is for academic purposes only. The present is the solution to the tenth edition of exercises of the STATICS book by Beer & Jhonston. The exercises were not solved by me.

Dynamic Systems and Applications 24 ( 2015 ) 361-374 INTEGRAL CURVES OF A LINEAR VECTOR FIELD IN SEMI-EUCLIDEAN SPACES

2015

In this paper, we study integral curves or flow lines of a linear vector field in (2n+1)dimensional semi-Euclidean space E ν . The skew symmetric matrix has been found depending on the number of timelike vectors are odd or even. Taking into consideration of the structure, we obtained the linear first order system of differential equations. This system gives rise to integral curves of linear vector fields. Meanwhile solution of the system has also been presented and discussed.