Мақаланы E-mail арқылы жіберу On the stability of linear systems with a quadratic integral
- Авторлар: Kozlov V.V.1
-
Мекемелер:
- Steklov Mathematical Institute RAS
- Шығарылым: Том 88, № 1 (2024)
- Беттер: 5-16
- Бөлім: Articles
- URL: https://jdigitaldiagnostics.com/0032-8235/article/view/675071
- DOI: https://doi.org/10.31857/S0032823524010017
- EDN: https://elibrary.ru/YUZUZH
- ID: 675071
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Аннотация
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.
Толық мәтін
Авторлар туралы
V. Kozlov
Steklov Mathematical Institute RAS
Хат алмасуға жауапты Автор.
Email: vvkozlov@presidium.ras.ru
Ресей, Moscow
Әдебиет тізімі
- Kozlov V.V. Linear systems with a quadratic integral // JAMM, 1992, vol. 56, iss. 6, pp. 803–809. doi: 10.1016/0021-8928(92)90114-N
- 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.
- John F. A note on the maximum principle for elliptic differential equations // Bull. Amer. Math. Soc., 1938, vol. 44, pp. 268–271.
- Dines L.L. On linear combinations of quadratic forms // Bull. Amer. Math. Soc., 1943, vol. 49, pp. 388–393.
- Uhlig F. A Reccurring theorem about pairs of quadratic forms and extensions: a survey // Linear Algebra and Its Appl., 1979, vol. 25, pp. 219–237.
- Gantmakher F.R. Matrix Theory. Moscow: Fizmatlit, 2004. 560 p. (in Russian)
- Kirillov O.N. Nonconservative Stability Problems of Modern Physics. Berlin: De Gruyter, 2013.
- Mailybaev A.A., Seyranyan A.P. Multiparameter Stability Problems. Theory and Applications in Mechanics. Moscow: Fizmatlit, 2009. 399 p. (in Russian)
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