Detail publikace

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

ŠREMR, J.

Anglický název

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

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova anglicky

second-order nonlinear differential equation; stability; instability; Floquet multiplier; Lyapunov exponent; periodic solution

Vydáno

03.02.2025

Nakladatel

SPRINGERNATURE

Místo

LONDON

ISSN

0862-7940

Ročník

70

Číslo

1

Strany od–do

11–45

Počet stran

35

BIBTEX


@article{BUT197361,
  author="Jiří {Šremr},
  title="On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point",
  year="2025",
  volume="70",
  number="1",
  month="February",
  pages="11--45",
  publisher="SPRINGERNATURE",
  address="LONDON",
  issn="0862-7940"
}