| Issue |
E3S Web Conf.
Volume 592, 2024
International Scientific Conference Energy Management of Municipal Facilities and Environmental Technologies (EMMFT-2024)
|
|
|---|---|---|
| Article Number | 04009 | |
| Number of page(s) | 9 | |
| Section | Gas and Oil Industry, Pipelines | |
| DOI | https://doi.org/10.1051/e3sconf/202459204009 | |
| Published online | 20 November 2024 | |
Canonical transformations of linear Hamiltonian systems
Moscow State University of Civil Engineering, 26, Yaroslavskoe shosse, 129337, Moscow, Russia
* Corresponding author: tat_titova@mail.ru
In this paper we consider the linear Hamiltonian systems of differential equations. We explore the normalization of a non-singular Hamiltonian matrix. We solve a system of matrix equations to find the generating function of the canonical transformation. In various cases we obtain the solution of the system of matrix equations. We get the solution of the algebraic matrix Riccati equation under certain conditions. Some properties of the Hamiltonian matrix have been proven. We get the normal form of a non-singular Hamiltonian matrix of order 4. We obtain the new method of normalization of the quadratic Hamiltonian. With this method we can investigate the stability of solutions of Hamiltonian systems.
© The Authors, published by EDP Sciences, 2024
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