电邮这篇文章 On the stability of linear systems with a quadratic integral
- 作者: Kozlov V.V.1
-
隶属关系:
- Steklov Mathematical Institute RAS
- 期: 卷 88, 编号 1 (2024)
- 页面: 5-16
- 栏目: Articles
- URL: https://manmiljournal.ru/0032-8235/article/view/675071
- DOI: https://doi.org/10.31857/S0032823524010017
- EDN: https://elibrary.ru/YUZUZH
- ID: 675071
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详细
The problem of stability of non-degenerate linear systems admitting a first integral in the form of a non-degenerate quadratic form is considered. New algebraic criteria for stability, as well as complete instability of such systems, have been established in the form of equality to zero of traces of products of matrices, which include an additional symmetric matrix. These conditions are closely related to the symplectic geometry of the phase space, which is determined by the matrix of the original linear system and the symmetric matrix defining the first integral. General results are applied to finding conditions for complete instability of linear gyroscopic systems.
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作者简介
V. Kozlov
Steklov Mathematical Institute RAS
编辑信件的主要联系方式.
Email: vvkozlov@presidium.ras.ru
俄罗斯联邦, Moscow
参考
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- Kozlov V.V. Linear hamiltonian systems: quadratic integrals, singular subspaces and stability // R.&C. Dyn., 2018, Vol. 23, no 1, pp. 26–46.
- Kozlov V.V., Karapetyan A.A. On the stability degree // Differ. Eqns., 2005, vol. 41, no. 2, pp. 195–201.
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- Mailybaev A.A., Seyranyan A.P. Multiparameter Stability Problems. Theory and Applications in Mechanics. Moscow: Fizmatlit, 2009. 399 p. (in Russian)
