Sensitivity Analysis of Dissipative Reversible and Hamiltonian Systems: A Survey: A survey

Oleg Kirillov; Ferdinand Verhulst

doi:10.1115/IMECE2009-10449

Sensitivity Analysis of Dissipative Reversible and Hamiltonian Systems: A Survey: A survey

Oleg Kirillov, Ferdinand Verhulst

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

1 Citation (Scopus)

Abstract

The paradox of destabilization of a conservative or nonconservative system by small dissipation, or Ziegler's paradox (1952), has stimulated an evergrowing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary. What is less known is that the first complete explanation of Ziegler 's paradox by means of the Whitney umbrella singularity dates back to 1956. We revisit this undeservedly forgotten pioneering result by Oene Bottema that outstripped later findings for about half a century. We discuss subsequent developments of the perturbation analysis of dissipation-induced instabilities and applications over this period, involving structural stability of matrices, Krein collision, Hamilton-Hopf bifurcation and related bifurcations.

Original language	English
Title of host publication	Proceedings of the ASME International Mechanical Engineering Congress and Exposition 2009, IMECE 2009
Publisher	American Society of Mechanical Engineers (ASME)
Pages	655-670
Number of pages	16
Volume	10
Edition	PART B
ISBN (Print)	9780791843833
DOIs	https://doi.org/10.1115/IMECE2009-10449 https://doi.org/10.1115/IMECE2009-10449
Publication status	Published - 11 Dec 2009
Event	ASME 2009 International Mechanical Engineering Congress and Exposition, IMECE2009 - Lake Buena Vista, FL, United States Duration: 13 Nov 2009 → 19 Nov 2009

Conference

Conference	ASME 2009 International Mechanical Engineering Congress and Exposition, IMECE2009
Country/Territory	United States
City	Lake Buena Vista, FL
Period	13/11/09 → 19/11/09

Access to Document

Cite this

Kirillov, O., & Verhulst, F. (2009). Sensitivity Analysis of Dissipative Reversible and Hamiltonian Systems: A Survey: A survey. In Proceedings of the ASME International Mechanical Engineering Congress and Exposition 2009, IMECE 2009 (PART B ed., Vol. 10, pp. 655-670). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/IMECE2009-10449, https://doi.org/10.1115/IMECE2009-10449

@inproceedings{14d611bcee894b1a931a69251fc5205c,

title = "Sensitivity Analysis of Dissipative Reversible and Hamiltonian Systems: A Survey: A survey",

abstract = "The paradox of destabilization of a conservative or nonconservative system by small dissipation, or Ziegler's paradox (1952), has stimulated an evergrowing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary. What is less known is that the first complete explanation of Ziegler 's paradox by means of the Whitney umbrella singularity dates back to 1956. We revisit this undeservedly forgotten pioneering result by Oene Bottema that outstripped later findings for about half a century. We discuss subsequent developments of the perturbation analysis of dissipation-induced instabilities and applications over this period, involving structural stability of matrices, Krein collision, Hamilton-Hopf bifurcation and related bifurcations.",

author = "Oleg Kirillov and Ferdinand Verhulst",

year = "2009",

month = dec,

day = "11",

doi = "10.1115/IMECE2009-10449",

language = "English",

isbn = "9780791843833",

volume = "10",

pages = "655--670",

booktitle = "Proceedings of the ASME International Mechanical Engineering Congress and Exposition 2009, IMECE 2009",

publisher = "American Society of Mechanical Engineers (ASME)",

address = "United States",

edition = "PART B",

note = "ASME 2009 International Mechanical Engineering Congress and Exposition, IMECE2009 ; Conference date: 13-11-2009 Through 19-11-2009",

}

Kirillov, O & Verhulst, F 2009, Sensitivity Analysis of Dissipative Reversible and Hamiltonian Systems: A Survey: A survey. in Proceedings of the ASME International Mechanical Engineering Congress and Exposition 2009, IMECE 2009. PART B edn, vol. 10, American Society of Mechanical Engineers (ASME), pp. 655-670, ASME 2009 International Mechanical Engineering Congress and Exposition, IMECE2009, Lake Buena Vista, FL, United States, 13/11/09. https://doi.org/10.1115/IMECE2009-10449, https://doi.org/10.1115/IMECE2009-10449

Sensitivity Analysis of Dissipative Reversible and Hamiltonian Systems: A Survey: A survey. / Kirillov, Oleg; Verhulst, Ferdinand.
Proceedings of the ASME International Mechanical Engineering Congress and Exposition 2009, IMECE 2009. Vol. 10 PART B. ed. American Society of Mechanical Engineers (ASME), 2009. p. 655-670.

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

TY - GEN

T1 - Sensitivity Analysis of Dissipative Reversible and Hamiltonian Systems: A Survey

T2 - ASME 2009 International Mechanical Engineering Congress and Exposition, IMECE2009

AU - Kirillov, Oleg

AU - Verhulst, Ferdinand

PY - 2009/12/11

Y1 - 2009/12/11

N2 - The paradox of destabilization of a conservative or nonconservative system by small dissipation, or Ziegler's paradox (1952), has stimulated an evergrowing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary. What is less known is that the first complete explanation of Ziegler 's paradox by means of the Whitney umbrella singularity dates back to 1956. We revisit this undeservedly forgotten pioneering result by Oene Bottema that outstripped later findings for about half a century. We discuss subsequent developments of the perturbation analysis of dissipation-induced instabilities and applications over this period, involving structural stability of matrices, Krein collision, Hamilton-Hopf bifurcation and related bifurcations.

AB - The paradox of destabilization of a conservative or nonconservative system by small dissipation, or Ziegler's paradox (1952), has stimulated an evergrowing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary. What is less known is that the first complete explanation of Ziegler 's paradox by means of the Whitney umbrella singularity dates back to 1956. We revisit this undeservedly forgotten pioneering result by Oene Bottema that outstripped later findings for about half a century. We discuss subsequent developments of the perturbation analysis of dissipation-induced instabilities and applications over this period, involving structural stability of matrices, Krein collision, Hamilton-Hopf bifurcation and related bifurcations.

UR - https://www.scopus.com/pages/publications/77954340906

U2 - 10.1115/IMECE2009-10449

DO - 10.1115/IMECE2009-10449

M3 - Conference contribution

AN - SCOPUS:77954340906

SN - 9780791843833

VL - 10

SP - 655

EP - 670

BT - Proceedings of the ASME International Mechanical Engineering Congress and Exposition 2009, IMECE 2009

PB - American Society of Mechanical Engineers (ASME)

Y2 - 13 November 2009 through 19 November 2009

ER -

Sensitivity Analysis of Dissipative Reversible and Hamiltonian Systems: A Survey: A survey

Abstract

Conference

Access to Document

Other files and links

Fingerprint

Cite this