The Possition of Eigenvalues in the Gaussian Complex Plane Depending on the Change of the Coefficients of the Homogeneous Linear Differential Equation in the Transport Application Using Matlab

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216275%3A25510%2F22%3A39919547" target="_blank" >RIV/00216275:25510/22:39919547 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.ebooks.ktu.lt/eb/1611/transport-means-2022-part-ii-proceedings-of-the-26th-international-scientific-conference/?fbclid=IwAR29HZfxoaFEizUavsQ7fFjJx3whiOSS2oBVinfXJDmlRlN4h9oX6BQbkj8" target="_blank" >https://www.ebooks.ktu.lt/eb/1611/transport-means-2022-part-ii-proceedings-of-the-26th-international-scientific-conference/?fbclid=IwAR29HZfxoaFEizUavsQ7fFjJx3whiOSS2oBVinfXJDmlRlN4h9oX6BQbkj8</a>

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

The Possition of Eigenvalues in the Gaussian Complex Plane Depending on the Change of the Coefficients of the Homogeneous Linear Differential Equation in the Transport Application Using Matlab

Popis výsledku v původním jazyce

The mathematical solution of vibration of a single-degree-of-freedom dynamical system always leads to the construction and solution of a second-order linear ordinary differential equation with constant coefficients. The coefficients of this equation correspond to the mass of the body, the damping coefficient of the damper, and the stiffness of the spring in a given system. The paper examines how changes of these coefficients influence the position of eigenvalues in the Gaussian complex plane. For the eigenvalues of the second-order homogeneous linear differential equation, it is derived and proved that the product of their distances from the origin of the Gaussian complex plane is constant and equal to the numerical value of the natural circular frequency of the corresponding mass-damper-spring system. It is further shown and proved that these eigenvalues follow the rules of conformal mapping of circular inversion with respect to a reference circle with its center at the origin of the Gaussian complex plane and a radius equal to the square root of the natural circular frequency of the corresponding system. Furthermore, third and higher order homogeneous linear differential equations are also investigated and a similar property is derived and proved, namely that the product of the absolute values of the eigenvalues is linearly dependent on the coefficients of the differential equation. The Matlab system environment is used for modeling.

Název v anglickém jazyce

The Possition of Eigenvalues in the Gaussian Complex Plane Depending on the Change of the Coefficients of the Homogeneous Linear Differential Equation in the Transport Application Using Matlab

Popis výsledku anglicky

The mathematical solution of vibration of a single-degree-of-freedom dynamical system always leads to the construction and solution of a second-order linear ordinary differential equation with constant coefficients. The coefficients of this equation correspond to the mass of the body, the damping coefficient of the damper, and the stiffness of the spring in a given system. The paper examines how changes of these coefficients influence the position of eigenvalues in the Gaussian complex plane. For the eigenvalues of the second-order homogeneous linear differential equation, it is derived and proved that the product of their distances from the origin of the Gaussian complex plane is constant and equal to the numerical value of the natural circular frequency of the corresponding mass-damper-spring system. It is further shown and proved that these eigenvalues follow the rules of conformal mapping of circular inversion with respect to a reference circle with its center at the origin of the Gaussian complex plane and a radius equal to the square root of the natural circular frequency of the corresponding system. Furthermore, third and higher order homogeneous linear differential equations are also investigated and a similar property is derived and proved, namely that the product of the absolute values of the eigenvalues is linearly dependent on the coefficients of the differential equation. The Matlab system environment is used for modeling.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Transport Means 2022 : proceedings of the 26th Internationa Scientific Conference

ISBN

—

ISSN

1822-296X

e-ISSN

2351-7034

Počet stran výsledku

6

Strana od-do

968-973

Název nakladatele

Kaunas University of Technology

Místo vydání

Kaunas

Místo konání akce

ONLINE

Datum konání akce

5. 10. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—