OFFSET
1,2
COMMENTS
The curve crosses the x-axis at (4k-1)/4*Pi.
LINKS
Mark Peters and Michael A. Konyak, The Engineering Analysis and Design of the Aircraft Dynamics Model For the FAA Target Generation Facility
Nicolas J. Schindeler, Phugoid Damping Control
Zachary S. Tseng, Mechanical Vibrations
Wikipedia, Phugoid
FORMULA
Sum_{n=0..inf} (-1)^n * Integral_{x=(4n-1)*Pi/4..(4n+3)*Pi/4} (cos(x) + sin(x))/e^x.
EXAMPLE
1.690976663969001833721646982781196966214169584204517274705652409659480494298183...
MATHEMATICA
Sum[(-1)^n*NIntegrate[ Exp[-x] (Cos[x] + Sin[x]), {x, (4n -1)Pi/4, (4n +3)Pi/4}, AccuracyGoal -> 128, PrecisionGoal -> 128, WorkingPrecision -> 156], {n, 0, 115}]
(* to view the curve *) Plot[Exp[-x] (Cos[x] + Sin[x]), {x, -3/4 Pi, 11/4 Pi}]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Robert G. Wilson v, Apr 27 2017
STATUS
approved