The Meissner equation is a linear ordinary differential equation that is a special case of Hill's equation with the periodic function given as a square wave.  There are many ways to write the Meissner equation. One is as
and is the Heaviside function shifted to . Another version is
The Meissner equation was first studied as a toy problem for certain resonance problems. It is also useful for understand resonance problems in evolutionary biology.
Because the time-dependence is piecewise linear, many calculations can be performed exactly, unlike for the Mathieu equation. When , the Floquet exponents are roots of the quadratic equation
The determinant of the Floquet matrix is 1, implying that origin is a center if and a saddle node otherwise.
- ^ Richards, J. A. (1983). Analysis of periodically time-varying systems. Springer-Verlag. ISBN 9783540116899. LCCN 82005978.
- ^ E. Meissner (1918). "Ueber Schüttelerscheinungen in Systemen mit periodisch veränderlicher Elastizität". Schweiz. Bauzeit. 72 (11). pp. 95–98.