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
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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
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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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
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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
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