Part of the Communications and Control Engineering Series book series (CCE)
The Mathieu Equation
The Mathieu equation in its standard form
is the most widely known and, in the past, most extensively treated Hill equation. In many ways this is curious since the equation eludes solution in a usable closed form; yet many investigators have sought to describe experiments in terms of a Mathieu equation, most probably only because it contains a simple sinusoid as its periodic coefficient. By association with Fourier series it may have been assumed that once solutions to the Mathieu equation had been determined, solutions to Hill equations in general would follow. Indeed, in many ways the opposite is true in the context of the methods presented in Chap. 5.
$$\ddot x + (a - 2q\cos 2t)x = 0$$
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References for Chapter 6
- 1.Mc. Lachlan, N. W.: Theory and application of Mathieu functions. Clarendon: Oxford U.P. 1947. Reprinted by Dover, New York 1964Google Scholar
- 3.Dawson, P. H.; Whetten, N. R.: Ion storage in three dimensional, rotationally symmetric, quadrupole fields. I. Theoretical treatment. J. Vac. Sci. Technol. 5 (1968) 1–6Google Scholar
© Springer-Verlag Berlin, Heidelberg 1983