On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

APPLICATIONS OF MATHEMATICS

ISSN

0862-7940

e-ISSN

1572-9109

Svazek periodika

70

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

35

Strana od-do

11-45

Kód UT WoS článku

001414813700001

EID výsledku v databázi Scopus

2-s2.0-105001084413