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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

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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

Alternative languages

  • Result language

    angličtina

  • Original language name

    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

  • Original language description

    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.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • OECD FORD branch

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

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2022

  • Confidentiality

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

Data specific for result type

  • Article name in the collection

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

  • ISBN

  • ISSN

    1822-296X

  • e-ISSN

    2351-7034

  • Number of pages

    6

  • Pages from-to

    968-973

  • Publisher name

    Kaunas University of Technology

  • Place of publication

    Kaunas

  • Event location

    ONLINE

  • Event date

    Oct 5, 2022

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article