Abstract
The non-linear differential equation\(\ddot x + p(t)x^3 = 0\), wherep(t) is a periodic square wave function of time with period τ, has been integrated by using a table of Jacobian elliptic functions. In the neighborhood of a typical elliptic fixed point, namely that for 11τ, 12-decimal accuracy has been used to determine a region which is stable.
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References
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Bartlett, J. H. and Wagner, C. A.: 1968, Technical Report No. 3, NASA Grant NsG 280-63.
Bozis, G.: 1966,Astron. J. 71, 404.
Hénon, M. and Heiles, C.: 1964,Astron. J. 69, 73.
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Bartlett, J.H., Wagner, C.A. The stability of motion in a periodic cubic force field. Celestial Mechanics 2, 228–236 (1970). https://doi.org/10.1007/BF01229497
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DOI: https://doi.org/10.1007/BF01229497