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Funktsional'nyi Analiz i ego Prilozheniya, 2005, Volume 39, Issue 4, Pages 32–47
DOI: https://doi.org/10.4213/faa83 (Mi faa83) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Restrictions of Quadratic Forms to Lagrangian Planes, Quadratic Matrix Equations, and Gyroscopic Stabilization

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (211 kB) Citations (14)
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DOI: https://doi.org/10.4213/faa83
Abstract: We discuss the symplectic geometry of linear Hamiltonian systems with nondegenerate Hamiltonians. These systems can be reduced to linear second-order differential equations characteristic of linear oscillation theory. This reduction is related to the problem on the signatures of restrictions of quadratic forms to Lagrangian planes. We study vortex symplectic planes invariant with respect to linear Hamiltonian systems. These planes are determined by the solutions of quadratic matrix equations of a special form. New conditions for gyroscopic stabilization are found.
Keywords: Hamiltonian function, symplectic structure, quadratic form, Williamson normal form, vortex plane.
Received: 24.06.2005
English version:
Functional Analysis and Its Applications, 2005, Volume 39, Issue 4, Pages 271–283
DOI: https://doi.org/10.1007/s10688-005-0048-y
Bibliographic databases:
Document Type: Article
UDC: 517.925.51+531.36
Language: Russian
Citation: V. V. Kozlov, “Restrictions of Quadratic Forms to Lagrangian Planes, Quadratic Matrix Equations, and Gyroscopic Stabilization”, Funktsional. Anal. i Prilozhen., 39:4 (2005), 32–47; Funct. Anal. Appl., 39:4 (2005), 271–283
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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