A394907 - OEIS

%I #12 Apr 15 2026 13:35:40

%S 2,5,2,1,6,8,0,9,8,9,3,7,6,6,1,5,5,3

%N Decimal expansion of the maximum of the characteristic parameter on the right limit curve of principal parametric resonance in the Ince-Strutt diagram of the Mathieu equation.

%C In engineering texts and parts of the mathematical literature, the stability diagram is often given with a different axis scale. The x-axis without the factor of 4, i.e., an excitation with twice the fundamental frequency then corresponds to an axis value of 0.25, and the y-axis without the factor of 2, i.e., the amplitude of the vertically moving suspension point is given in units of the reduced pendulum length. With this more common scale, the limit of the unstable region considered here has the approximate coordinates (0.63042, 1.4387).

%H Eugene I. Butikov, <a href="https://doi.org/10.1119/1.5021895">Analytical expressions for stability regions in the Ince-Strutt diagram of Mathieu equation</a>, Am. J. Phys. 86, 257-267 (2018)

%H Hugo Pfoertner, <a href="/A394907/a394907.pdf">Stability (Ince-Strutt-) diagram of the Mathieu equation</a>.

%H Richard H. Rand, <a href="https://hdl.handle.net/1813/28989">Lecture Notes on Nonlinear Vibrations</a>, (2012). Chapter 6, Mathieu's Equation, 6.4, Harmonic Balance, provides expansions of the transition curves.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MathieuCharacteristicExponent.html">Mathieu Characteristic Exponent</a>.

%e 2.52168098937661553...

%Y A394908 gives the corresponding characteristic amplitude.

%Y Cf. A394701.

%K nonn,cons,more

%O 1,1

%A _Hugo Pfoertner_, Apr 13 2026