TY - JOUR
T1 - Comparison of Poincare Normal Forms and Floquet Theory for Analysis of Linear Time Periodic Systems
AU - Subramanian, Susheelkumar C.
AU - Redkar, Sangram
N1 - Funding Information:
The authors would like to thank the Interplanetary Initiative of Arizona State University for partially funding this research work. The authors also acknowledge all the peer reviewers in providing valuable input towards improving the quality of this work. The authors dedicate this work to the second authors’ advisor, Dr. Subash C. Sinha, who passed away in June 2019.
Publisher Copyright:
© 2021 American Society of Mechanical Engineers (ASME). All rights reserved.
PY - 2021/1
Y1 - 2021/1
N2 - In this work, the authors draw comparisons between the Floquet theory and Normal Forms technique and apply them towards the investigation of stability bounds for linear time periodic systems. Though the Normal Forms technique has been predominantly used for the analysis of nonlinear equations, in this work, the authors utilize it to transform a linear time periodic system to a time-invariant system, similar to the Lyapunov-Floquet (L-F) transformation. The authors employ an intuitive state augmentation technique, modal transformation, and near identity transformations to facilitate the application of time-independent Normal Forms. This method provides a closed form analytical expression for the state transition matrix (STM). Additionally, stability analysis is performed on the transformed system and the comparative results of dynamical characteristics and temporal variations of a simple linear Mathieu equation are also presented in this work.
AB - In this work, the authors draw comparisons between the Floquet theory and Normal Forms technique and apply them towards the investigation of stability bounds for linear time periodic systems. Though the Normal Forms technique has been predominantly used for the analysis of nonlinear equations, in this work, the authors utilize it to transform a linear time periodic system to a time-invariant system, similar to the Lyapunov-Floquet (L-F) transformation. The authors employ an intuitive state augmentation technique, modal transformation, and near identity transformations to facilitate the application of time-independent Normal Forms. This method provides a closed form analytical expression for the state transition matrix (STM). Additionally, stability analysis is performed on the transformed system and the comparative results of dynamical characteristics and temporal variations of a simple linear Mathieu equation are also presented in this work.
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U2 - 10.1115/1.4048715
DO - 10.1115/1.4048715
M3 - Article
AN - SCOPUS:85099648697
SN - 1555-1415
VL - 16
JO - Journal of Computational and Nonlinear Dynamics
JF - Journal of Computational and Nonlinear Dynamics
IS - 1
M1 - 014502
ER -