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A256719
Decimal expansion of the location of the near bifurcation cusp in the Zeeman catastrophe machine.
2
1, 4, 0, 4, 0, 7, 1, 4, 8, 3, 4, 8, 3, 0, 0, 8, 7, 2, 6, 8, 1, 2, 1, 8, 4, 2, 8, 4, 5, 7, 6, 4, 6, 8, 7, 0, 6, 8, 0, 8, 0, 1, 1, 3, 5, 7, 2, 8, 6, 8, 9, 7, 0, 1, 4, 3, 1, 0, 2, 6, 2, 8, 7, 7, 4, 8, 6, 3, 7, 0, 0, 4, 8, 6, 4, 2, 3, 0, 6, 5, 5, 2, 5, 0, 7, 7, 6, 6, 7, 3, 2, 0, 0, 9, 6, 1, 8, 8, 1, 3, 5, 3, 6, 5, 0
OFFSET
1,2
COMMENTS
Positive root of 6*x^2-7*x-2, equal to (7+sqrt(97))/12 (Poston 1978).
Applies to the 'classical' Zeeman machine with a disk of diameter 1 and the distance between the pivot and the fixed point equal to 2. With respect to the pivot, the near and far bifurcation cusps are located on opposite side the fixed point. This constant is the near cusp's distance from the pivot.
REFERENCES
T. Poston and I. Stewart, Catastrophe Theory and its Applications, Pitman Publishing Ltd, 1978, Chapter 5, page 76.
LINKS
The Nonlinear Dynamics Group at Drexel University, Zeeman's Catastrophe Machine
E. C. Zeeman, Catastrophe Theory, Scientific American, April 1976, pages 65-70, 75-83.
FORMULA
Satisfies 3*a*(2*a-1)=2*(2*a+1).
EXAMPLE
1.40407148348300872681218428457646870680801135728689701431...
MATHEMATICA
RealDigits[(7 + Sqrt[97])/12, 10, 111][[1]] (* Robert G. Wilson v, Apr 20 2015 *)
PROG
(PARI) a=(7+sqrt(97))/12 \\ Use \p 2020, and keep 2000 digits
CROSSREFS
Cf. A256720 (far bifurcation cusp).
Sequence in context: A345450 A098002 A241658 * A362209 A343722 A035622
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Apr 09 2015
STATUS
approved