On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F25%3APU156033" target="_blank" >RIV/00216305:26210/25:PU156033 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.21136/AM.2025.0206-24" target="_blank" >https://link.springer.com/article/10.21136/AM.2025.0206-24</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/AM.2025.0206-24" target="_blank" >10.21136/AM.2025.0206-24</a>
Alternative languages
Result language
angličtina
Original language name
On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point
Original language description
We discuss Lyapunov stability/instability of both lower and upper equilibria of free damped pendulum with periodically oscillating suspension point. We recall the results of Bogolyubov and Kapitza, provide new effective criteria of stability/instability of the equilibria of pendulum equation, and give the exact and complete proofs. The criteria obtained are formulated in terms of positivity/negativity of Green's functions of the periodic boundary value problems for linearized equations. Furthermore, we show that if both lower and upper equilibria are stable, then the pendulum considered may possess a periodic motion that corresponds to the "quasistatic solution" of Bogolyubov as well as to the "quasistatic balance" of Kapitza.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10100 - Mathematics
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
APPLICATIONS OF MATHEMATICS
ISSN
0862-7940
e-ISSN
1572-9109
Volume of the periodical
70
Issue of the periodical within the volume
1
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
35
Pages from-to
11-45
UT code for WoS article
001414813700001
EID of the result in the Scopus database
2-s2.0-105001084413