Variational method and Mathieu equation
- 1 May 1978
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 19 (5) , 1147-1151
- https://doi.org/10.1063/1.523775
Abstract
A variational method is developed to study the linear and nonlinear Mathieu equations. For the linear Mathieu equation, various modes of the Mathieu functions, the characteristic curves, and the stability regions are found, which agree with the established results. The variational method is then applied to the nonlinear Mathieu equation. Approximate periodic solutions of various modes are found in a similar manner, and their stability also investigated.Keywords
This publication has 1 reference indexed in Scilit:
- Variational methods and nonlinear forced oscillationsJournal of Mathematical Physics, 1975