@inproceedings{2f6b1421714448529abcfe7507da6d12,
title = "Mathieu Equations Utilizing Symplectic Properties",
abstract = "Several theoretical studies deal with the stability transition curves of the Mathieu equation. A few others present numerical and asymptotic methods to describe the stability of coupled Mathieu equations. However, sometimes the averaging and perturbation techniques deal with cumbersome computations, and the numerical methods spend considerable resources and computation time. This contribution extends the definition of linear Hamiltonian systems to periodic Hamiltonian systems with a particular dissipation. This leads naturally to a generalization of symplectic matrices, to μ-symplectic matrices. This definition enables an efficient way for calculating the stability transition curves of coupled Mathieu equations.",
keywords = "Hamiltonian systems, Parametric excitation, Symplectic matrices",
author = "Barrios, {Miguel Ram{\'i}rez} and Joaqu{\'i}n Collado and Fadi Dohnal",
note = "Publisher Copyright: {\textcopyright} 2020 Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019. All rights reserved.; 1st International Nonlinear Dynamics Conference, NODYCON 2019 ; Conference date: 17-02-2019 Through 20-02-2019",
year = "2020",
doi = "10.1007/978-3-030-34713-0_14",
language = "Ingl{\'e}s",
series = "Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019",
publisher = "Springer Nature",
pages = "137--145",
editor = "Walter Lacarbonara and Balakumar Balachandran and Jun Ma and {Tenreiro Machado}, J.A. and Gabor Stepan",
booktitle = "Nonlinear Dynamics of Structures, Systems and Devices - Proceedings of the 1st International Nonlinear Dynamics Conference, NODYCON 2019",
address = "Estados Unidos",
}