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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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Krylov Bogoliubov Type Analysis of Variants of the Mathieu Equation

Journal of Applied Nonlinear Dynamics 6(1) (2017) 57--77 | DOI:10.5890/JAND.2017.03.005

B. Shayak$^{1}$,$^{3}$; Pranav Vyas$^{2}$

$^{1}$ Department of Physics, Indian Institute of Technology Kanpur, NH-91, Kalyanpur Kanpur - 208016 Uttar Pradesh, INDIA

$^{2}$ Department of Mechanical Engineering, Indian Institute of Technology Kanpur, NH-91, Kalyanpur Kanpur–208016 Uttar Pradesh, INDIA

$^{3}$ Department of Theoretical and Applied Mechanics and Mechanical Engineering, Cornell University, Ithaca, New York –14853 US

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In this work we show that a Krylov-Bogoliubov type analysis is a powerful method for analysing variants of the Mathieu equation. We first demonstrate the technique by rederiving the results obtained by prior authors using different techniques and then apply it to a case where the system has a quasiperiodic drive (inhomogeneity) in addition to a quasiperiodic parametric term. A realistic system where such a forcing is present is an induction motor, so we adopt that as our model system to show the details of the method.


We are grateful to Professor RICHARD RAND for helpful discussion and suggestions which have greatly improved the quality of this manuscript. Shayak is also grateful to Kishore Vaigyanik Protsahan Yojana (KVPY) Government of India for a generous Fellowship.


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