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Chiellini integrability and quadratically damped oscillators
Institution:1. Department of Physics, Ferdowsi University of Mashhad, 91775-1436 Mashhad, Iran;2. Department of Physics, University of Sistan and Baluchestan, Zahedan, Iran;3. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore;4. Institute for Metals Superplasticity Problems RAS, Khalturin Street 39, 450001 Ufa, Russia;5. Research Laboratory for Mechanics of New Nanomaterials, Peter the Great St. Petersburg Polytechnical University, St. Petersburg 195251, Russia
Abstract:In this paper a new approach to study an equation of the Liénard type with a strong quadratic damping is proposed based on Jacobi's last multiplier and Chiellini's integrability condition. We obtain a closed form solution of the transcedental characteristic equation of the Liénard type equation using the Lambert W-function.
Keywords:Quadratic damping  Liénard equation  Chiellini integrability condition
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