Nonlinear Oscillations Exact Solutions and their Approximations - Kovacic, Ivana; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2020)
This book presents exact, closed-form solutions for the response of a variety of nonlinear oscillators (free, damped, forced). The solutions presented are expressed in terms of special functions. To help the reader understand these `non-standard' functions, detailed explanations and rich illustrations of their meanings and contents are provided. In addition, it is shown that these exact solutions in certain cases comprise the well-known approximate solutions for some nonlinear oscillations.
Chapter1. Oscillators and Oscillatory Responses in Practical and Theoretical Systems -- Chapter2. Free Conservative Oscillators: from Linear to Nonlinear Systems -- Chapter3. Free Damped Oscillators -- Chapter4. Forced Oscillators -- Chapter5. Nonlinear Isochronous Oscillators -- Chapter6. From Chains of Nonlinear Oscillators to Continuous Nonlinear Systems.
Keywords: Mechanical engineering; Statistical physics; Mechanics; Mechanics, Applied; Mechanical Engineering; Applications of Nonlinear Dynamics and Chaos Theory; Theoretical and Applied Mechanics