A394907 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.

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

Offset

1,1

Comments

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).

Links

Table of n, a(n) for n=1..18.

Eugene I. Butikov, Analytical expressions for stability regions in the Ince-Strutt diagram of Mathieu equation, Am. J. Phys. 86, 257-267 (2018)

Hugo Pfoertner, Stability (Ince-Strutt-) diagram of the Mathieu equation.

Richard H. Rand, Lecture Notes on Nonlinear Vibrations, (2012). Chapter 6, Mathieu's Equation, 6.4, Harmonic Balance, provides expansions of the transition curves.

Eric Weisstein's World of Mathematics, Mathieu Characteristic Exponent.

Example

2.52168098937661553...

Crossrefs

A394908 gives the corresponding characteristic amplitude.

Cf. A394701.

Sequence in context: A180957 A124780 A369872 * A108437 A226029 A152765

Adjacent sequences: A394904 A394905 A394906 * A394908 A394909 A394910

Keyword

nonn,cons,more

Author

Hugo Pfoertner, Apr 13 2026

Status

approved