On Mathieu equation with damping
- 1 April 1980
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 21 (4) , 722-725
- https://doi.org/10.1063/1.524492
Abstract
A direct variational method is applied to the linear and nonlinear Mathieu equation with damping. It is found that the nature of the periodic solutions and the characteristic curves are modified due to the presence of the damping. A threshold value of β is required to overcome the damping for the existence of the periodic solutions. Stability analyses for the periodic solutions are also carried out.Keywords
This publication has 3 references indexed in Scilit:
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- Variational methods and nonlinear forced oscillationsJournal of Mathematical Physics, 1975
- The stability of the plane free surface of a liquid in vertical periodic motionProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1954