Mathieu Equation and its Application

Introduction

The properties of the Free Prooject on Mathieu Equation and its Application are reviewed in order to discuss some of the applications that have appeared in recent years. Those mentioned are: vibrations in an elliptic drum, the inverted pendulum, the radio frequency quadrupole, frequency modulation, stability of a floating body, alternating gradient focusing, the Paul trap for charged particles, and the mirror trap for neutral particles.

With few exceptions, notably Morse and Feshbach, 1 and Mathews and Walker, 2 most authors of textbooks on mathematics for science and engineering choose to omit any discussion of the Mathieu equation. Until recently, this omission could be justified on the basis that the Mathieu equation had only limited scientific application. However, in recent years, many new applications have arisen. We will discuss the equation briefly, and then describe some of the scientific applications.

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