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Stability of Motion. / Tovstik, Petr Evgenievich; Yushkov, Mikhail Petrovich.

Foundations in Engineering Mechanics. Springer Nature, 2021. p. 3-30 (Foundations in Engineering Mechanics).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Tovstik, PE & Yushkov, MP 2021, Stability of Motion. in Foundations in Engineering Mechanics. Foundations in Engineering Mechanics, Springer Nature, pp. 3-30. https://doi.org/10.1007/978-3-030-64118-4_1

APA

Tovstik, P. E., & Yushkov, M. P. (2021). Stability of Motion. In Foundations in Engineering Mechanics (pp. 3-30). (Foundations in Engineering Mechanics). Springer Nature. https://doi.org/10.1007/978-3-030-64118-4_1

Vancouver

Tovstik PE, Yushkov MP. Stability of Motion. In Foundations in Engineering Mechanics. Springer Nature. 2021. p. 3-30. (Foundations in Engineering Mechanics). https://doi.org/10.1007/978-3-030-64118-4_1

Author

Tovstik, Petr Evgenievich ; Yushkov, Mikhail Petrovich. / Stability of Motion. Foundations in Engineering Mechanics. Springer Nature, 2021. pp. 3-30 (Foundations in Engineering Mechanics).

BibTeX

@inbook{344566c09e7b4ea2b51bab2ce245a5ec,
title = "Stability of Motion",
abstract = "In this chapter, we define the Lyapunov stability and give Lyapunov{\textquoteright}s theorems. We formulate Lagrange, Lyapunov and Chetaev{\textquoteright}s theorems on the stability. Thompson and Tait{\textquoteright}s theorems is discussed. Routh–Hurwitz{\textquoteright}s and Mikhailov{\textquoteright}s criteria are given. The stability of periodicmotions of nonautonomous systems is studied from the linear approximation. The stability of the zero solution of the Mathieu equation is considered, to which one may reduce oscillations of a pendulum with vibrating suspension point.",
author = "Tovstik, {Petr Evgenievich} and Yushkov, {Mikhail Petrovich}",
note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.",
year = "2021",
doi = "10.1007/978-3-030-64118-4_1",
language = "English",
series = "Foundations in Engineering Mechanics",
publisher = "Springer Nature",
pages = "3--30",
booktitle = "Foundations in Engineering Mechanics",
address = "Germany",

}

RIS

TY - CHAP

T1 - Stability of Motion

AU - Tovstik, Petr Evgenievich

AU - Yushkov, Mikhail Petrovich

N1 - Publisher Copyright: © 2021, Springer Nature Switzerland AG.

PY - 2021

Y1 - 2021

N2 - In this chapter, we define the Lyapunov stability and give Lyapunov’s theorems. We formulate Lagrange, Lyapunov and Chetaev’s theorems on the stability. Thompson and Tait’s theorems is discussed. Routh–Hurwitz’s and Mikhailov’s criteria are given. The stability of periodicmotions of nonautonomous systems is studied from the linear approximation. The stability of the zero solution of the Mathieu equation is considered, to which one may reduce oscillations of a pendulum with vibrating suspension point.

AB - In this chapter, we define the Lyapunov stability and give Lyapunov’s theorems. We formulate Lagrange, Lyapunov and Chetaev’s theorems on the stability. Thompson and Tait’s theorems is discussed. Routh–Hurwitz’s and Mikhailov’s criteria are given. The stability of periodicmotions of nonautonomous systems is studied from the linear approximation. The stability of the zero solution of the Mathieu equation is considered, to which one may reduce oscillations of a pendulum with vibrating suspension point.

UR - http://www.scopus.com/inward/record.url?scp=85120878546&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-64118-4_1

DO - 10.1007/978-3-030-64118-4_1

M3 - Chapter

AN - SCOPUS:85120878546

T3 - Foundations in Engineering Mechanics

SP - 3

EP - 30

BT - Foundations in Engineering Mechanics

PB - Springer Nature

ER -

ID: 92421649