On the stability of the equilibrium of a mechanical system with tracking, potential and small dissipative forces

Krasilnikov, P.; Mayorov, A.

doi:10.31857/S003282350002264-0

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On the stability of the equilibrium of a mechanical system with tracking, potential and small dissipative forces

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On the stability of the equilibrium of a mechanical system with tracking, potential and small dissipative forces

PII

S003282350002264-0-1

DOI

10.31857/S003282350002264-0

Publication type

Article

Status

Published

Authors

P. Krasilnikov

Affiliation: Moscow Aviation Institute (MAI)
Address: Russian Federation

A. Mayorov

Affiliation: Moscow Aviation Institute (MAI)
Address: Russian Federation

Journal name

Prikladnaia matematika i mekhanika

Edition

Volume 82 Issue 5

Pages

582-591

Abstract

Keywords

Acknowledgment

The study was carried out with the financial support of the Russian Foundation for Basic Research (18-01-00820).

Received

15.12.2018

Publication date

18.12.2018

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GOST	Krasilnikov P., Mayorov A. On the stability of the equilibrium of a mechanical system with tracking, potential and small dissipative forces // Prikladnaia matematika i mekhanika – 2018. – V. 82. – Issue 5 C. 582-591 [Electronic resource]. URL: http://ras.jes.su/pmm/s003282350002264-0-1 (circulation date: 20.04.2024). DOI: 10.31857/S003282350002264-0
MLA	Krasilnikov, P., Mayorov, A. "On the stability of the equilibrium of a mechanical system with tracking, potential and small dissipative forces." Prikladnaia matematika i mekhanika 82.5 (2018):582-591. DOI: 10.31857/S003282350002264-0
APA	Krasilnikov P., Mayorov A. (2018). On the stability of the equilibrium of a mechanical system with tracking, potential and small dissipative forces. Prikladnaia matematika i mekhanika 82(5), pp.582-591 DOI: 10.31857/S003282350002264-0

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1. Ehjler L. Metod nakhozhdeniya krivykh linij, obladayuschikh svojstvami libo maksimuma, libo minimuma, ili reshenie izoperimetricheskoj zadachi, vzyatoj v samom shirokom smysle. M.-L.: Gostekhizdat, 1934. 600 c.

2. Nikolai E.L. Ob ustojchivosti pryamolinejnoj formy ravnovesiya szhatogo i skruchennogo sterzhnya // Izv. Leningr. politekhn. in-ta. 1928. Vyp. 31. S. 1–26.

3. Ziegler H. Die Stabilitatskriterien der Elastomechanik // Ing. Arch. 1952. Bd. 20. H. 1. S. 49–56.

4. Sejranyan A.P. Paradoks destabilizatsii v zadachakh ustojchivosti nekonservativnykh sistem // Uspekhi mekh. 1990. T. 13. №. 2. S. 89–124.

5. Bolotin V.V. Nekonservativnye zadachi teorii uprugoj ustojchivosti. M.: Fizmatgiz, 1961. 339 s.

6. Herrmann G. Stability of equilibrium of elastic systems subjected to nonconservative forces // Appl. Mech. Rev. 1967. V. 20. P. 103–108.

7. Merkin D.R. Vvedenie v teoriyu ustojchivosti dvizheniya. M.: Nauka, 1976. 319 s.

8. Bajkov A.E., Krasil'nikov P. S. Ob ehffekte Tsiglera v nekonservativnoj mekhanicheskoj sisteme // PMM. 2010. T. 74. Vyp. 1. C. 74–88.

9. Bajkov A.E. Predel'nyj tsikl pri rezonanse 1:2 v nekonservativnoj sisteme // PMM. 2011. T. 75. Vyp. 3. S. 385–396.

10. Agafonov S.A. K voprosu ustojchivosti nekonservativnykh sistem // Izv. AN. SSSR. MTT. 1986. № 1. S. 47–51.

11. Agafonov S.A. Ob ustojchivosti nekonservativnykh mekhanicheskikh sistem // DAN. T. 322. № 6, 1992, S. 1040–1042.

12. Lakhadanov V.M. O vliyanii struktury sil na ustojchivost' dvizheniya // PMM. 1974. T. 38. Vyp. 2. S. 246–253.

13. Lakhadanov V.M. O stabilizatsii potentsial'nykh sistem // PMM. 1975. T. 39. Vyp. 1. S. 53–58.

14. Krasil'nikov P.S., Amelin R.N. Ob ehffekte destabilizatsii ravnovesiya nekonservativnoj sistemy s tremya stepenyami svobody // Vestnik MAI. T. 20. 2013. № 4. S. 191–197.

15. Majorov A.Yu., Bajkov A.Yu. Ob ustojchivosti polozheniya ravnovesiya diskretnoj modeli za-pravochnogo shlanga pod dejstviem reaktivnoj sily // Nelin. din. 2015. T. 11. № 1. S. 127–146.

16. Aleksandrov A.Yu., Tikhonov A.A. Stabilizatsiya vraschatel'nogo dvizheniya tverdogo tela v uslo-viyakh ubyvayuschej dissipatsii // Vestnik SPbGU. 2017. T. 62. № 4. S. 633–643.

17. Aleksandrov A.Yu., Aleksandrova E.B., Tikhonov A.A.. Monoaxial attitude stabilization of a rigid body under vanishing restoring torque // Nonlin. Dyn. Syst. Theory. 2018. V. 18. No. 1. P. 12–21.

18. Kirillov O.N. Nonconservative Stability Problems of Modern Phisics. Berlin; Boston: de Gruyter, 2013. 446 p.

19. Nikolaev E.I., Pantyukhin K.N. Dinamicheskaya ustojchivost' vertoleta na rezhime raskrutki nesuschego vinta na zemle s uchetom uprugosti lopastej // Vestnik MAI. 2016. T. 23. № 3. S. 112–120.

20. Krasil'nikov P.S., Tkhaj V.N. Obratimye sistemy. Rezonans 1:1 // PMM. 1992. T. 56. Vyp. 4. S. 570–579.

21. Faddeev D.K. Lektsii po algebre. Uchebnoe posobie dlya vuzov. M.: Nauka, Gl. red. fiz.-mat. lit., 1984. 416 s.