Title: Applications of symbolically computed Lyapunov-Floquet transformation

Authors: Susheelkumar Cherangara Subramanian; Sandesh Ganapati Bhat; Sangram Redkar

Addresses: The Polytechnic School, Ira Fulton School of Engineering, Arizona State University, Mesa, AZ, USA ' The Polytechnic School, Ira Fulton School of Engineering, Arizona State University, Mesa, AZ, USA ' The Polytechnic School, Ira Fulton School of Engineering, Arizona State University, Mesa, AZ, USA

Abstract: This work demonstrates various applications of symbolically computed Lyapunov-Floquet (L-F) transformation towards the analysis of the linear and nonlinear time-periodic systems. In this work, we compute the closed-form expression for L-F transformation with the aid of an intuitive state augmentation and time independent normal forms technique. The main objective of this work is to validate the use of symbolically computed L-F transformation towards the analysis of externally excited, stochastically excited and nonlinear dynamical system with time-periodic coefficients. The computation of the closed-form expression for L-F transformation and its inverse are demonstrated on a simple case of Mathieu equation and compared with the existing techniques. For the externally excited and nonlinear systems, multiple approaches are discussed for the case of an undamped Mathieu equation. Additionally, the analysis of time periodic system with uncertain time varying parameters is demonstrated using the Infante's approach on a damped Mathieu equation.

Keywords: Lyapunov-Floquet; L-F transformation; externally excited systems; nonlinear systems; stochastic parametric excitation.

DOI: 10.1504/IJNDC.2022.124209

International Journal of Nonlinear Dynamics and Control, 2022 Vol.2 No.2, pp.97 - 115

Received: 17 Oct 2021
Accepted: 20 Feb 2022
Published online: 18 Jul 2022 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article